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## Reasoning ability Questions Quiz Set 9 for IBPS/SBI/SSC

Reasoning ability Questions Quiz Set 9 for IBPS/SBI/SSC

Directions (1-5): Study the following arrangement of the English alphabet and answer the questions given below: M 1 E $R B 3 A K 7 £ # 9$ U D I N 4 6 % F H 2 @ 8 W

1. How many such consonants are there in the above sequence each of which is immediately followed by a number and immediately preceded by a vowel?

1) Nil 2) One 3) Two 4) Three 5) Four

2. Four of the following five are alike in a certain way and so form a group, based on the above arrangement. Which is the one that does not belong to that group?

1) % H N 2) I 4 $3) 9 D £ 4)3 5$ 5) $B M 3. How many such vowels are there in the above arrangement, each of which is immediately preceded by a symbol and immediately followed by a consonant? 1) Nil 2) One 3) Two 4) Three 5) None of these 4. If the order of the first fifteen elements in the above arrangement is reversed, then which of the following will be the eighth to the left of the twelfth letter/number/symbol from the right end? 1) A 2) £ 3) 3 4) K 5) None of these 5. What should come in place of questions mark in the following series based on the above arrangement? E B M A £ B 9 D £? H 8 % 1) N % D 2) N F D 3) 4 F D 4) I 6 D 5) None of these Directions (6-10): Answer these questions referring to the symbol-letter number sequence given below: 2 P J @ 8$ L B 1 V # Q 6 α G W 9 K C D 3 © £ 5 F R 7 A Y 4

6. How many symbols and numbers are there in the sequence which are either immediately preceded or immediately followed by the letter which is from the first half of the English alphabet?

1) 6 2) 7 3) 8 4) 9 5) None of these

7. Four of the following five are similar in relation to their positions in the above sequence and hence form a group. Which one does not belong to that group?

1) Q K 5 2) L 6 D 3) P L δ 4) 1 G © 5) K £ 4

8. Each symbol exchanges its position with its immediate right symbol/ letter/ number. Now, how many letters are there in the sequence which are immediately followed by a number and immediately preceded by a symbol?

1) Nil 2) One 3) Two 4) Three 5) None of these

9. P @ L is to Y75 in the same way as $1 # is to 1) R £ © 2) F £ 3 3) 5 £ © 4) 5 • D 5) None of these 10. Which of the following indicates the total number of symbols, letters and number respectively, which get eliminated from the sequence when every second element of the sequence from your left is dropped from the sequence? 1) 5, 8, 2 2) 6, 9, 1 3) 5, 8, 1 4) 5, 9, 1 5) None of these Directions (11 - 15): In the following questions, the symbols @, ©, %, * and$ are used with the following meanings as illustrated below:

‘P @ Q’ means ‘P is either greater than or equal to Q’;

‘P © Q’ means ‘P is either smaller than or equal to Q’;

‘P % Q’ means ‘P is greater than Q’;

‘P * Q’ means ‘P is smaller than Q’;

‘P $Q’ means ‘P is neither greater than nor smaller than Q’. Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them are definitely true? Give answer 1) if only conclusion I is true; 2) if only conclusion II is true; 3) if either conclusion I or II is true; 4) if neither I nor II is true; and 5) if both conclusions I and II are true 11. Statements: M@R, R%T, T$K

Conclusions: I. K*M II. T*M

Conclusions: I. F$J II. J%F 13. Statements: D$M, M%W, W@R

 Question No Answers 1 3 2 3 3 2 4 1 5 1 6 3 7 3 8 3 9 5 10 4 11 5 12 3 13 1 14 4 15 4


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# SSE in Assembly - wrong output

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hi, I put together a small app to try using SSE in assembly, but I am getting the wrong output.
these are the .cpp file and the .asm file

#define WIN32_LEAN_AND_MEAN#include <iostream>using namespace std;extern "C" int *myFunc(float *a, float *b, float *result);int main(int argc, char *argv[]){	float inA[] = {1.0f, 2.0f, 3.0f, 4.0f};	float inB[] = {1.0f, 2.0f, 3.0f, 4.0f};	float ret[4];	myFunc(inA, inB, ret);	cout << ret[0] << endl;	cout << ret[1] << endl;	cout << ret[2] << endl;	cout << ret[3] << endl;	system("pause");		return 0;}

.586P.XMM.MODEL FLAT, C.STACK.DATA.CODEmyFunc PROC a:DWORD, b:DWORD, result:DWORDmovups xmm0, [a]movups xmm1, addps xmm0, xmm1movups [result], xmm0retmyFunc ENDPEND

I was expecting to get the result
Quote:
 2468

Quote:
 -1.07374e+008-1.07374e+008-1.07374e+008-1.07374e+008

can anyone help me out?

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Hey there,

One thing I did notice is you did not align your data. SSE can only accept 16 bit aligned data.

So I think you need to do a __declspec(align(16)) (if the underscores did not get posted then there are two underscores before declspec).

Ive not seen the movups command before. I would first load the data into a normal asm register (eax for example) and the do movdqa xmm0, [eax].

Hope this helps

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You should probably try using the compiler intriniscs.
That would let you write all the code inline with your C++ code, without needing the extra assember file at all.

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Hmmmm, i think that a, being a label, is actually the address of the pointer to the floating point data (&a, not a, in c notation). So i think you are currently loading &a and 96 more garbage bytes into xmm0 and you actualy need to dereference twice. Something like this:
mov rcx, [a]movups xmm0, [rcx]

a and b should already be in the CPU's registers according to C's calling convention. Compiler SSE intrinsics are much more convenient and are the same at least across GCC, Microsoft and Intel compilers, but some people say that they produce suboptimal code in some cases. I hope I helped...

[Edited by - D_Tr on July 20, 2010 4:42:47 PM]

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Kazuo5000, you are right. Someone on another forum also told me that it was because you can't directly dereference a label.

this is allowed:
mov edi, amovups xmm0, [edi]

but this is not:
mov xmm0, [a]

I would like to know why I have to do an extra copy for nothing though =/

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CPPNick, I think its because you cant directly access the SSE registers like you can with normal CPU registers, but I am not entirely sure on this. You could always try loading in the address of [a] instead using the lea command.

Personally, I don't have a great deal of knowledge in SSE but have a little bit of experience in it.

Again I hope this helps

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Right, posts cleaned up.

2) but don't jump down someone elses throat when they do that however.

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Is it just me or are these proc declarations a bit confusing? They provide a level of abstraction, which should not be there when you are a beginner. The "pure" way to write a function in assembly is to write the function code under a label and jump to it using the call instruction, accessing the data according to the calling convention you are planning to use (in the OP's case the C calling convention). Doing things the "pure" way will help you understand assembly language better. A great assembly tutorial using nasm (in the form of a short book) can be found here

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Just use the intrinsics.

#include <xmmintrin.h>int main(){	__declspec(align(16)) float inA[] = {1.0f, 2.0f, 3.0f, 4.0f};	__declspec(align(16)) float inB[] = {1.0f, 2.0f, 3.0f, 4.0f};	__m128 i1 = _mm_load_ps(inA);	//if you don't align it, you have to use _mm_loadu_ps	__m128 i2 = _mm_load_ps(inB);	i1 = _mm_add_ps(i1, i2);		return 0;}

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thank phantom.

D_Tr: I would rather use MASM..just preference I guess. The way it looks makes more sense to me. I'm past the point of having a hard time understanding assembly, I just need to learn the details and nuances now. I will definitely take a look at the book you recommended...at first glance I am relieved that its only 195 pages....not nearly as intimidating as "The Art of Assembly" which is over 1400...scary

clashie: I have tried that, and it did seem to help. I have a question though. In an isolated case like your example, you have to move a total of 48 bytes of data to get the the data in and back out. Does it really work out to be faster?
I am doing what I am doing for two reasons; One is just to learn some more assembly, and the second is to try and avoid as much overhead as possible and streamline the procedure. I made the inner embedded loop of a function in assembly using the same method as my original post, and it turned out to be slower. Once I examined the disassembly, I found that VC++ was adding another 15 lines of junk before each call to my assembly procedure to protect the contents of the registers I was overwriting. I figured that if I made the whole procedure assembly instead of only the inner embedded loop, I could avoid that.

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Probability

Algebra Level 5

Let $$P(x) = x^2 - 3x - 9$$. A real number $$x$$ is chosen at random from the interval $$5 \le x \le 15$$. The probability that $$\lfloor\sqrt{P(x)}\rfloor = \sqrt{P(\lfloor x \rfloor)}$$ is equal to $$\frac{\sqrt{a} + \sqrt{b} + \sqrt{c} - d}{e}$$, where $$a, b, c, d$$, and $$e$$ are positive integers. Find $$a + b + c + d + e$$.

×


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# Background

In contrast to a dimensionality-reduction approach to feature-extraction, sparse coding is an unsupervised method which attempts to construct a novel representation of the data by mapping it linearly into a higher-dimensional space. This transformation is performed with the objective of obtaining a new feature space in which, for each vector, we can find a smaller subset of features that largely reconstruct it. Essentially, this allows us to perform case-specific feature-extraction, as for a given input, we seek a smaller subset of features to which we will assign the majority of the weight for its representation, with the remainder being negligibly small. This provides us with a procedure which attempts to flexibly represent unseen instances of the input space.

The introduction of a larger set of spanning vectors is a consequence of the desire to produce accurate reconstructions across a broad range of possible input from the original space. However, the algebra of linear transformations tells us that input vectors will no longer have a unique representation in the higher-dimensional feature space. This short-coming is alleviated by the fact that we would like to assign the majority of influence to only a subset of the new features. We implement this goal using the notion of sparsity; namely, we will penalize large weight values.

Unfortunately, there are some implementation issues which prevent the use of sparse coding in certain contexts. The fact that we must find a representation for each new case the system is provided with often renders the procedure infeasible for online processing tasks, as new data must be handled in real-time. Several approximation algorithms have been proposed to address issues in processing speed. However, these methods suffer from deficiencies in their ability to take into account some relevant conditional-independence structures in the data. To resolve these limitations, the authors introduce a feed-forward architecture which utilizes these approximation schemes, giving a new procedure which is demonstrated to be ~10 times more efficient than the previous state-of-the-art approximation, in empirical testing.The main contribution of this paper is a highly efficient learning-based method that computes good approximations of optimal sparse codes in a fixed amount of time.

# Review of Sparse Coding

For an input $X \epsilon \mathbb{R}^n$, we seek a new representation $Z \epsilon \mathbb{R}^m$ which satisfies the previously-stated objective. In order to find an optimal code $\, Z$ of $\, X$, we also require a dictionary $W_d \epsilon \mathbb{R}^{m x n}$, the matrix of normalized vectors that the coordinates of $\, Z$ are defined in relation to. Given a training set, we will estimate the optimal sparse codes for each training case, in pursuit of the dictionary matrix to be used in coding novel input.

These solutions will be found based on a loss function taking into account the squared reconstruction error and the complexity of the code:

$E_{W_d}(X, Z) = \frac{1}{2}\|X - W_dZ\|_2^2 + \alpha \|Z\|_1$,

where $\, \alpha$ is the specified sparsity penalty. Using this, the optimal code for input $X$ is naturally defined as $\, Z^* = argmin_Z E(X, Z)$.

From here, the dictionary is learned in an unsupervised manner, typically through the application of stochastic gradient descent to the minimization of the average loss $E_{W_d}(X, Z^*)$ across a subset of the training cases. The dictionary to be applied to new cases is learned prior to the execution of the approximation proposed here.

# Pre-existing Approximations: Iterative Shrinkage Algorithms

Here baseline iterative shrinkage algorithms for finding sparse codes are introduced and explained. The ISTA and FISTA methods update the whole code vector in parallel, while the more efficient Coordinate Descent method (CoD) updates the components one at a time and carefully selects which component to update at each step. Both methods refine the initial guess through a form of mutual inhibition between code component, and component-wise shrinkage.

## Iterative Shrinkage & Thresholding (ISTA)

The Iterative Shrinkage & Thresholding Algorithm (ISTA) and its sped-up variant Fast ISTA approximate the optimal code vector of an input by updating all the code components in parallel. The idea is that, at each iteration, we should shift our current code in the direction of greatest reconstruction error, and then apply a component-wise shrinkage function to enforce sparsity. Initializing $\, Z^{(0)} = 0$, we have the recursive update rule:

$Z^{(k + 1)} = h_{\theta}(Z^{(k)} - \frac{1}{L}W_d^T(W_dZ^{(k)} - X)) = h_{\theta}(W_eX + SZ^{(k)})$ (**),
where $W_e = \frac{1}{L}W_d^T$ is the filter matrix, and $S = I - \frac{1}{L}W_d^TW_d$ is the mutual-inhibition matrix.

Here, $\, L$ is an upper-bound on the size of the eigenvalues of $W_d^TW_d$, and $\, h_{\theta}( )$ is the shrinkage function with components $\, h_{\theta}(V)_i = sign(V_i)$ $\, max(|V_i| - \theta_i,$ $\, 0)$, where $\theta \epsilon \mathbb{R}^m$ consists of the sparsity thresholds for the components of the code. Thresholds are typically set to $\theta_i =\frac{\alpha}{L}$.

### Fast ISTA

Depending on a few possible choices to be made in implementing this scheme, the per-iteration time complexity in using ISTA to construct a code for a new input will be $\, O(m^2)$, $\, O(nm)$, or $\, O(km)$, with $\, k$ being the average sparsity across samples and iterations.

Fast ISTA is a modification of this approximation which ensures faster convergence through the addition of a momentum term. Here, our update rule becomes:

$Z^{(k + 1)} = h_{\theta}(Z^{(k)}) + \lambda (h_{\theta}^{(k-1)} - h_{\theta}^{(k - 2)})$

In other words, the updated code is the shrinkage function applied to the current code, plus a multiple of the difference of the outputs of the shrinkage function for the preceding two iterations. This second term the rate at which the approximated code is changing.

## Coordinate Descent

Instead of automatically updating all the entries of the code in parallel, we might consider strategically selecting a single component to be updated each iteration. Coordinate Descent (CoD) adopts this mentality, and resultantly yields a superior approximation to the parallel ISTA methods in the same order of time. In fact, Coordinate Descent was widely believed to be the most efficient algorithm available for approximating sparse codes.

The CoD algorithm is presented below:

$\textbf{function} \, \textbf{CoD}\left(X, Z, W_d, S, \alpha\right)$

$\textbf{Require:} \,S = I - W_d^T W_d$
$\textbf{Initialize:} \,Z = 0; B = W_d^TX$
$\textbf{repeat}$
$\bar{Z} = h_{\alpha}\left(B\right)$
$\,k = \mbox{ index of largest component of} \left|Z - \bar{Z}\right|$
$\forall j \in \left[1, m\right]: B_j = B_j + S_{jk}\left(\bar{Z}_k - Z_k\right)$
$Z_k = \bar{Z}_k$
$\textbf{until}\,\text{change in}\,Z\,\text{is below a threshold}$
$Z = h_{\alpha}\left(B\right)$

$\textbf{end} \, \textbf{function}$

In each iteration of the procedure, we search for the entry of the current code which, if updated so as to minimize the corresponding loss while holding the other components constant, results in the largest change in comparison to the current code. This search step takes $\, O(m)$ operations, and, so in also accounting for each component-wise optimization performed (which follows a similar process to that of the parallel case), each iteration requires $\, O(m^2)$ steps. Alternatively, we could repeat the update process $\, O(n)$ times instead, to achieve a per-iteration complexity of $\, O(nm)$, which is again comparable to ISTA. This algorithm has a similar feedback concept to ISTA, but can it can expressed as a linear feedback operation with a very sparse matrix (since only one component is updated at a time). Either way, it turns out that, deploying both for an approximately equal amount of time, Coordinate Descent will out-perform the ISTA methods in its approximation to an optimal code.

# Encoders for Sparse Code Approximation

In seeking an approach to further improve upon the efficiency of Coordinate Descent, the authors present the use of feed-forward networks for real-time sparse code inference. Essentially, for the training phase, we will perform learning for a neural network which takes our original input $\, X \epsilon \mathbb{R}^n$ and generates a prediction of its optimal code with respect to the previously-estimated dictionary. The training set will consist of the original $\, X$ as our input, and their sparse codes estimated via Coordinate Descent as the target values. In learning the network weights, we use stochastic gradient descent to minimize the average squared-error between the network's predictions and these estimated sparse codes. The size of the network will be chosen with consideration of its feasibility in applying it to online processing.

## A Simplistic Architecture and its Limitations

The most straight-forward approach to this task would be to use a single-layer feed-forward network. However, since we have the additional requirement that the network output is to be sparse, special consideration of the activation function must be made. The authors consider three such candidates: double tanh, a learned non-linearity, and the shrinkage function $\, h_{\theta}( )$ used for ISTA. The three approaches perform comparably in the authors' empirical testing, and so they opt to use $\, h_{\theta}( )$ to maintain a strong basis for comparison with the previous methods.

Despite the appeal of its simplicity, this network configuration is unable to learn "explaining-away" phenomena, a conditional-independence structure relevant to this task. Essentially, this means that if the learned weight matrix happens to contain two highly similar rows, the network will uniformly represent two components of the code as nearly-equal. However, this inability to select only one of the components and suppress the other redundant one is clearly indicative of a limitation of the network's ability to produce sparse encodings. Consequently, a more sophisticated architecture is proposed.

## Learned ISTA & Learned Coordinate Descent

To address explaining-away phenomena, interaction terms between components are introduced. To implement these terms controlling redundancy amongst the components, the authors design a sequence of feed-forward networks structured so as to be analogous to executing some number of steps of ISTA or a pre-determined number of steps of Coordinate Descent. The use of ISTA versus Coordinate Descent corresponds to two distinct encoders, both of which can be viewed as a "time-unfolded" recurrent network.

Before understanding the rationale behind this approach, we must recognize a few relevant values which are inherently fixed in the process of executing ISTA or Coordinate Descent. The recursive equations iterated over in these procedures can both be re-expressed in terms parameters including a threshold vector $\, \theta$, a filter matrix $\, W_e$, and a mutual-inhibition matrix $\, S$, where these terms are defined differently for the two procedures. Now, instead of using these fully-determined parameter forms and iterating the procedure until it converges, this encoder-driven approach purposes to learn $\, \theta$, $\, W_e$, $\, S$, and then execute only a fixed number of steps of one of these procedures, in order to reduce the total computational cost. Using the available data to adaptively set these parameters allows the corresponding network to handle the issues pertaining to explaining-away.

In Learned ISTA (LISTA), the encoder structure takes the form defined by the recursive update for ISTA (**), iterated for a fixed number of times T. We learn the parameters $\, W_e$, $\, \theta$, and $\, S$ by using stochastic gradient descent to minimize the previously-described squared-error loss for sparse code prediction. From its definition, we can see that $\, S$ is shared across the $T$ time steps, and so we use back-propagation through time to compute the error gradient for gradient descent.

Similarly, in Learned Coordinate Descent (LCoD), the network architecture is defined by the recursive update for Coordinate Descent (omitted for brevity) iterated for a fixed number of time steps. The parameters $\, W_e$, $\, \theta$, and S are learned analogous to the procedure for LISTA, except for the technicality that sub-gradients are propagated, resulting from the fact that we search for the component inducing the largest update in the code Z.

The algorithm for LCoD can be summarized as

A main advantage of the system proposed in this paper is speed, so it is necessary to take note of the asymptotic complexity of the above algorithm: only $\, O(m)$ operations are required for each step of the bprop procedure, and each iteration only requires $\, O(m)$ space; as almost all of the stored variables are scalar, with the exception of $\, B(T)$. (Recall that m refers to the number of dimensions in the new feature space with the sparse representations.)

# Empirical Performance

Two sets of experiments were undertaken:

• The procedures were compared in their performance on exact sparse code inference, using the Berkeley image database.
• The MNIST digits dataset was used in assessing whether improved error-rates in code-prediction yields superior performance in recognition tasks.

Overall, the results indicate that this proposal to construct encoders from a set of iterations of ISTA or Coordinate Descent yields a significantly-reduced runtime when compared to the pre-existing procedures, at a pre-specified error-rate.

## Berkeley Image Database

From this database, 10x10-pixel image patches were randomly drawn to compare (Fast) ISTA with LISTA, and Coordinate Descent with LCoD, in sparse code prediction. Performance was tested on dictionaries of sizes m = 100 and m = 400, using a sparsity penalty of $\alpha = 0.5$, and the squared-error loss for the distance between the estimate and the optimal code, as computed by Coordinate Descent.

Figure 1 suggests that, LISTA notably out-performs FISTA here. Furthermore, 18 iterations of FISTA are required to achieve the error-rate produced by 1 iteration of LISTA when m = 100, and 35 iterations when m = 400. This leads the authors to conclude that LISTA is ~20 times faster than FISTA.

Figure 1: Comparison of LISTA and FISTA. Squared-error in code prediction plotted against number of iterations. In the legend, "1x" denotes m = 100, and "4x" for m = 400

Figure 2 indicates that, for a moderately-large number of iterations, LCoD has superior accuracy to Coordinate Descent. When the number of iterations is larger, Coordinate Descent out-performs LCoD, but this can be reversed by initializing matrices with their CoD values prior to training.

Figure 2: Comparison of LCoD and Coordinate Descent. Squared-error in code prediction plotted against number of iterations. In the legend, "1x" denotes m = 100, and "4x" for m = 400. Open Circles indicate that matrices have been initialized with their CoD values prior to training

## MNIST Digits

Here, the authors examined whether these coding approximations could be effectively applied in classification tasks. Evaluation was conducted using both the entire 28x28-pixel images to create 784-dimensional codes, as well as extracted 16x16-pixel patches for codes with 256 components. In addition to the finding that increasing the number of iterations reduced classification error across all procedures, it was observed that Learned Coordinate Descent approached the optimal error rate after only 10 iterations.

A complete feature vector consisted of 25 concatenated such vectors, extracted from all 16 × 16 patches shifted by 3 pixels on the input. The features were extracted for all digits using CoD with exact inference, CoD with a fixed number of iterations, and LCoD. Additionally a version of CoD (denoted CoD’) used inference with a fixed number of iterations during training of the filters, and used the same number of iterations during test (same complexity as LCoD). A logistic regression classifier was trained on the features thereby obtained.

Classification errors on the test set are shown in the following figures . While the error rate decreases with the number of iterations for all methods, the error rate of LCoD with 10 iterations is very close to the optimal (differences in error rates of less than 0.1% are insignificant on MNIST)

MNIST results with 784-D sparse codes

MNIST results with 25 256-D sparse codes extracted from 16 × 16 patches every 3 pixels

# Conclusions

The idea of time unfolding an inference algorithm in order to construct a fixed-depth network in application to sparse coding is introduced in this paper. In sparse coding, inference algorithms are iterative and converge to a fixed point. In this paper it is proposed to unroll an inference algorithm for a fixed number of iterations in order to define an approximator network.The main result of this paper is the demonstration that the number of iterations required to reach a given code prediction error can be heavily reduced - by a factor of about 20 - when learning the filters and mutual inhibition matrices FISTA and CoD, when truncated. In other words, not much data-specific mutual inhibition is required to handle the phenomenon of "explaining away" superfluous parts of the code vector.

# References

References Beck, A. and Teboulle, M. A fast iterative shrinkagethresholding algorithm with application to waveletbased image deblurring. ICASSP’09, pp. 693–696, 2009. Chen, S.S., Donoho, D.L., and Saunders, M.A. Atomic decomposition by basis pursuit. SIAM review, 43(1): 129–159, 2001.

Daubechies, I, Defrise, M., and De Mol, C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. on Pure and Applied Mathematics, 57:1413–1457, 2004.

Donoho, D.L. and Elad, M. Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimization. PNAS, 100(5):2197–2202, 2003.

Elad, M. and Aharon, M. Image denoising via learned dictionaries and sparse representation. In CVPR’06, 2006. Hale, E.T., Yin, W., and Zhang, Y. Fixed-point continuation for l1-minimization: Methodology and convergence. SIAM J. on Optimization, 19:1107, 2008. Hoyer, P. O. Non-negative matrix factorization with sparseness constraints. JMLR, 5:1457–1469, 2004. Jarrett, K., Kavukcuoglu, K., Ranzato, M., and LeCun, Y. What is the best multi-stage architecture for object recognition? In ICCV’09. IEEE, 2009.

Kavukcuoglu, Koray, Ranzato, Marc’Aurelio, and LeCun, Yann. Fast inference in sparse coding algorithms with applications to object recognition. Technical Report CBLL-TR-2008-12-01, Computational and Biological Learning Lab, Courant Institute, NYU, 2008.

Lee, H., Battle, A., Raina, R., and Ng, A.Y. Efficient sparse coding algorithms. In NIPS’06, 2006.

Lee, H., Chaitanya, E., and Ng, A. Y. Sparse deep belief net model for visual area v2. In Advances in Neural Information Processing Systems, 2007.

Lee, H., Grosse, R., Ranganath, R., and Ng, A.Y. Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations. In International Conference on Machine Learning. ACM New York, 2009. Li, Y. and Osher, S. Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm. Inverse Problems and Imaging, 3 (3):487–503, 2009.

Mairal, J., Elad, M., and Sapiro, G. Sparse representation for color image restoration. IEEE T. Image Processing, 17(1):53–69, January 2008.

Mairal, J., Bach, F., Ponce, J., and Sapiro, G. Online dictionary learning for sparse coding. In ICML’09, 2009. Olshausen, B.A. and Field, D. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381(6583):607–609, 1996.

Ranzato, M., Huang, F.-J., Boureau, Y.-L., and LeCun, Y. Unsupervised learning of invariant feature hierarchies with applications to object recognition. In CVPR’07. IEEE, 2007a.

Ranzato, M.-A., Boureau, Y.-L., Chopra, S., and LeCun, Y. A unified energy-based framework for unsupervised learning. In AI-Stats’07, 2007b.

Rozell, C.J., Johnson, D.H, Baraniuk, R.G., and Olshausen, B.A. Sparse coding via thresholding and local competition in neural circuits. Neural Computation, 20: 2526–2563, 2008.

Vonesch, C. and Unser, M. A fast iterative thresholding algorithm for wavelet-regularized deconvolution. In IEEE ISBI, 2007.

Wu, T.T. and Lange, K. Coordinate descent algorithms for lasso penalized regression. Ann. Appl. Stat, 2(1): 224–244, 2008.

Yang, Jianchao, Yu, Kai, Gong, Yihong, and Huang, Thomas. Linear spatial pyramid matching using sparse coding for image classification. In CVPR’09, 2009. Yu, Kai, Zhang, Tong, and Gong, Yihong. Nonlinear learning using local coordinate coding. In NIPS’09, 2009.


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# Rocket Calculations

A 20 000kg rocket exhausts gases at a constant 600kg per second at 300ms^-1

a) Calculate the momentum of the exhaust gases

b) Deduce the thrust applied to the rocket engines

Any help would be much appreciated

## Answers and Replies

Just use:

p=mv

and a=dv/dt

(and F=ma, of course).


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Thread: Movin' on. View Single Post

## Movin' on.

Long story short: I messed up. She gets me (and trust me, very few do) and she always stuck around. It's an idea that's crossed my mind a few times but I always figured I'd be better off* on my own and shrugged the idea off. She's leaving in less than a week for Europe (undergrad study). Won't be back until next year. So trying anything at all right now is *not* worth it.

Not that having done something about this would've (more like, could've!) changed things much but at least we'd have had fun (!) for a while. Serves me right.

*Not very certain of that. In general, I don't trust anyone. Over the years I got used being on my own. But nothing's constant. And all that is a little disturbing. The minute there's any kind attachment/affection thrown into the equation, things get all messy. And nobody likes messy.

What is the purpose of this thread? Ah who knows, I reckon I just wanted to let it out. Any stories, people? :)
 PhysOrg.com science news on PhysOrg.com >> Leading 3-D printer firms to merge in $403M deal (Update)>> LA to give every student an iPad;$30M order>> CIA faulted for choosing Amazon over IBM on cloud contract


text:
Work at SourceForge, help us to make it a better place! We have an immediate need for a Support Technician in our San Francisco or Denver office.

## Diff of /doc/doc.tex[ab8377] .. [3f3db1] Maximize Restore

### Switch to side-by-side view

--- a/doc/doc.tex
+++ b/doc/doc.tex
@@ -118,10 +118,12 @@
\url{http://octave.sourceforge.net/fem-fenics/overview.html}
\end{center}
and if you would like to contribute to the project or give a look to the source code
-you can clone it from the following repository using mercurial
+you can clone it from the following repository using Mercurial
\begin{center}
\url{http://sourceforge.net/p/octave/fem-fenics/} .
\end{center}
+The pkg is provided with an example function \texttt{femfenics\_examples}
+which allows the user to select and run one of the examples provided with the pkg.

\chapter{Introduction to Fem-fenics}\label{intr}

@@ -1038,8 +1040,8 @@
because it is assembled copying element-by-element the values contained in the input vector.

\subsection{Sparse Matrices}
-The \texttt{assemble} function discretize the continuos problem and
-return a sparse matrix. To deal with problems of big size, they are stored
+The \texttt{assemble} function discretizes the continuos problem and
+returns a matrix. To deal with problems of big size, the matrices are stored
using a compressed technique \cite{Formaggia_matr} both in DOLFIN and in Octave.
Unfortunately, DOLFIN uses row major orientation while Octave uses
column major orientation. They have thus to be converted efficiently from
@@ -1183,7 +1185,7 @@
In this chapter more examples are provided.
At the beginning of each section, the problem is briefly presented and then
the Octave script for the resolution of the problem using Fem-fenics is presented alongside the code
-written in C++ and/or the Python.
+written in C++ or in Python.
For each problem, we refer the reader to the complete desciption on the FEniCS website.
\iffalse
In the following examples we can see directly in action the classes and the functions presented in the
@@ -1206,7 +1208,7 @@
\fi
\section{Mixed Formulation for the Poisson Equation}
In this example the Poisson equation is solved with a
-''mixed approach'': it is usedthe stable FE space obtained using Brezzi-Douglas-Marini
+''mixed approach'': it is used the stable FE space obtained using Brezzi-Douglas-Marini
polynomial of order 1 and Dicontinuos element of order 0.
\begin{align*}
-\mathrm{div}\ ( \mathbf{\sigma} (x, y) ) ) &= f (x, y) & \quad \mbox{ in } \Omega \\
@@ -1664,7 +1666,7 @@
\end{changemargin}

\section{HyperElasticity}
-This time we compare the code with the c++ version of DOLFIN.
+This time we compare the code with the C++ version of DOLFIN.
The problem for an elastic material can be expressed as a minimization problem
\begin{align*}
\min_{u \in V} \Pi\\
@@ -1675,7 +1677,7 @@
is a traction force.

A complete description of the problem is avilable on the Fenics website \cite{hyperelasticity}.
-The final solution will look like in figure \ref{Hyp}.
+The final solution will look like figure \ref{Hyp}.
\begin{figure}
\begin{center}
\includegraphics[height=6 cm,keepaspectratio=true]{./HyperElasticity.png}


text:
• CC is the total cost of the campaign ($) • #CV is the total number of completed views To calculate the cost per completed view, divide the total cost of the campaign by the total number of completed views. ## How to Calculate Cost Per Completed View? The following steps outline how to calculate the Cost Per Completed View. 1. First, determine the total cost of the campaign ($).
2. Next, determine the total number of completed views.
3. Next, gather the formula from above = CPCV = CC / #CV.
4. Finally, calculate the Cost Per Completed View.
5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

total cost of the campaign (\$) = 10,000

total number of completed views = 350

CPCV = CC / #CV = ?


text:
A Valley Without Wind 2
Razorflamekun 7. čvc. 2013 v 6.57 odp.
How you get by here?
Visit this screenshot: http://cloud-2.steampowered.com/ugc/630785219621727373/944A3E62B1F55920A423A2C04AF4464CF535F41B/

Please let me know how you get by here, because there is a perk token there that I want to get :(

Thanks!
Zobrazeno 14 z 4 komentářů
tigersfan  [vývojář] 8. čvc. 2013 v 3.03 dop.
That looks like a bug, I'm sorry, I'm not sure you can get there. :(
Razorflamekun 8. čvc. 2013 v 12.01 odp.
Nope, this doesn't look like a bug. In fact, I think this is something that requires the second feat of the game, Minimize/Shrink in order to get by.
Naposledy upravil Razorflamekun; 9. čvc. 2013 v 1.43 odp.
Jokaabel 3. zář. 2013 v 2.04 odp.
BA|Razorflamelight původně napsal:
Nope, this doesn't look like a bug. In fact, I think this is something that requires the second feat of the game, Minimize/Shrink in order to get by.

Hi Razorflamelight

The shrink feat is probably your ticket for this issue.

hope this helps
Naposledy upravil Jokaabel; 3. zář. 2013 v 2.05 odp.
Razorflamekun 3. zář. 2013 v 3.19 odp.
Thanks. That's what I thought.
Zobrazeno 14 z 4 komentářů
Na stránku: 15 30 50
Datum odeslání: 7. čvc. 2013 v 6.57 odp.
Počet příspěvků: 4

Další diskuze


text:
# Red box around characters when using escapeinside option with minted

I'm trying to typeset Elixir code using minted. I run into problems when I want to color a custom keyword. More in particular, I run into errors when I use the escapeinside option.

As soon as I pass the escapeinside option to the minted listing every right-hand curly brace is outlined by a red box, even when I'm not actually escaping text in the source code. Below is a MWE and a screenshot of the output.

I have tried passing in multiple delimiters: |, \#, \%, <an actual backtick> and so on. But all of them cause the red outlining on curly braces. I also tried ruby as language, and that seems to work fine. Although not every keyword is highlighted properly in that case.

Is there perhaps another approach to this? I'm going to assume that when I submit this paper I will have no control over the pygments version or the compiler they use, so any modification on that end is not an option.

## Input

\documentclass{article}
\usepackage{minted}
\begin{document}

\begin{figure}[htb]
\begin{minted}{elixir}
def foo() do
{:bar, :baz}
end
\end{minted}
\end{figure}

\definecolor{wgreen}{HTML}{158915}
\begin{figure}[htb]
\begin{minted}[escapeinside=||]{elixir}
|\textcolor{wgreen}{\textbf{customkeyword}}| foo() do
{:bar, :baz}
end
\end{minted}
\end{figure}

\end{document}

## Output

• Related: Minted red box around greek characters. The red box represents a highlighting error and is produced by \fcolorbox. Hence the workaround is to redefine \fcolorbox inside minted environment. – muzimuzhi Z Sep 19 '20 at 22:35


text:
# Eliminating linear combinations from lists

Suppose I have a list of simple expressions, something like:

list = {{a-b-2c-d+e+2f},{-a-2b-c+d+2e+f},{-2a-b+c+2d+e-f},{x-y-z},{-x+y-z},{-x-y+z}};

These expressions are going to become elements in a linear combination. But notice that the third element in this list is itself already a linear combination of the first two. Therefore, my "basis" really should be this list without one of the first three elements (it doesn't matter which one goes away, but for consistency I would like to remove the third of them). Is there an automated way in Mathematica to search a list of expressions like this, identify when elements are linear combinations of others, and then remove the extraneous elements?

• "But notice that the third element in this list is itself already a linear combination of the first two." Nope. Check it (especially $e$). Nov 12 '18 at 5:49
• Yeah, typo. Fixed now. Thank you for pointing it out! Nov 13 '18 at 19:53

Take your list and fix it so that the 3rd element dependent on the first two:

list[[3]] = (list[[2]] + list[[1]])/3 // Expand;
list
(*
{{2a + b - c - 2d - e + f}, {a + 2b + c - d - 2 e - f}, {-a + b + 2c + d - e - 2f},
{x - y - z}, {-x + y - z}, {-x - y + z}}
*)

Convert system of linear functions to a matrix:

vars = Variables@list;
linsys = CoefficientArrays[Flatten@list, vars][[2]];

Extract linearly independent elements of list:

Extract[list,
FirstPosition[#, 1, Nothing] & /@ RowReduce[Transpose@linsys]]
(*
{{a - b - 2 c - d + e + 2 f}, {-a - 2 b - c + d + 2 e + f},
{x - y - z}, {-x + y - z}, {-x - y + z}}
*)

Or row reduce to get an equivalent basis:

RowReduce[linsys].vars // DeleteCases[0]
(*  {a - c - d + f, b + c - e - f, x, y, z}  *)

• The example I started with does have the third entry dependent on the first two (element 2 minus element 1 is element 3). But regardless, your approach worked perfectly! Thank you! Nov 12 '18 at 19:13
• @KevinAusman You're welcome. (Maybe there's a typo in the question because elt. 2 minus elt. 1 should have a + e in the expression, but there are no e.) Nov 12 '18 at 19:40
• Huh. You are obviously correct about the typo. Thank you! Fixing it now. Nov 13 '18 at 19:47
• And I accidentally, in trying to fix the problem, tried to edit your response! So sorry... I don't know how to withdraw my suggested edit. Clearly I didn't get enough sleep last nigh. Nov 13 '18 at 19:51
• @KevinAusman No problem. New users' edits of other posts go through a queue for approval. Those who review it might reject it, if they spot the error. If it does go through, it can be rolled back. Hopefully they will see your comment and reject it. Nov 13 '18 at 19:55

What I would do is replace symbols by numeric vectors with a function like

ClearAll[toNumbers];
toNumbers[list_, vars_] :=

toNumbers[{a, b, a + b}, {a, b}]
(*{{1, 0}, {0, 1}, {1, 1}}*)

then perform some linear algebra and convert the result back into symbols with something like

ClearAll[fromNumbers];
fromNumbers[list_, vars_] := Replace[
list,
x_ :> x.vars,
{1}
];

fromNumbers[{{1, 0}, {0, 1}, {1, 1}}, {a, b}]
(*{a, b, a + b}*)

The linear algebra logic can be something like Fold which checks a vector and appends it to a list if it is linear independent form the vectors in the list:

Fold[
f,
{},
{{1, 1, 0}, {0, 1, 0}, {1, 1, 1}}
]

where

ClearAll[f];
f[vecs_, vec_] := With[
{
vecs2 = Append[vecs, vec]
},
vecs2 /; MatrixRank[vecs2] == Length[vecs2]
];
f[vecs_, vec_] := vecs;

Gathering all together (except f):

ClearAll[leaveLinearIndependent];
leaveLinearIndependent[list_, vars_] := Replace[
Fold[
f,
{},
],
x_ :> x.vars,
{1}
];

leaveLinearIndependent[{a, a + b, b, c}, {a, b, c}]
(*{a, a + b, c}*)

list = {{a-b-2c-d+e+2f},{-a-2b-c+d+2e+f},
{-2a-b+c+2d+e-f},{x-y-z},{-x+y-z},{-x-y+z}};

First extract coefficient arrays.

coeffArrays = Normal[CoefficientArrays[list]][[2,All,1]]

(* ut[29]= {{1, -1, -2, -1, 1, 2, 0, 0, 0},
{-1, -2, -1, 1, 2, 1, 0, 0, 0},
{-2, -1, 1, 2, 1, -1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, -1, -1},
{0, 0, 0, 0, 0, 0, -1, 1, -1}, {0, 0, 0, 0, 0, 0, -1, -1, 1}} *)

Find null vectors of the transpose.

nulls = NullSpace[Transpose@dd]

(* Out[30]= {{1, -1, 1, 0, 0, 0}} *)

We want to remove vectors in positions of last nonzero value in each null vector (of which there is but one, in this case). We can automate the task of finding the list to remove as below.

Flatten[Length[nulls[[1]]] + 1 -


text:
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## Q. 1.18

Determine the central transverse load W which will produce central deflection $\delta$ in the initially straight bar AB of area A and length 2L hinged at both ends as shown in Fig. 1.28.

## Verified Solution

Solution Equilibrium condition: The forces in section AC and CB will be equal due to symmetry. Therefore, from free body diagram,

$W = 2F \sin \alpha= 2F \times \frac{\delta }{L^\prime}$ (i)

Compatibility condition: Elongation of section AC is given by,

$\Delta L = L^\prime — L=\frac{FL}{AE}$ (ii)

From Eqs (i) and (ii),

$W =\frac{2\left(L^\prime-L\right) A E}{L} \times \frac{\delta}{L^\prime}=\frac{2 \delta A E}{L}\left(1-\frac{L}{L^\prime}\right)$

$=\frac{2 \delta A E}{L}\left(1-\frac{1}{\sqrt{L^2+\delta^2}}\right)$


text:
# Data frame of results

#### leonedelman

##### New Member
Hi all

Suppose I have 10 different models as such:

Code:
fit1.glm <- glm(admit ~ gre , data = dat, family = "binomial")
fit2.glm <- glm(admit ~ gpa, data = dat, family = "binomial")
fit3.glm <- glm(admit ~ rank, data = dat, family = "binomial")
...
Suppose then, I want to form a data frame as such:

variable Odds ratio lower CI upper CI
gre
gpa
rank
...
How could this be done? Ciao!!

#### Dason

##### Ambassador to the humans
It would probably be cleaner if you you originally did something like
Code:
fit <- list()
fit[[1]] <- glm(admit ~ gre , data = dat, family = "binomial")
fit[[2]] <- glm(admit ~ gpa, data = dat, family = "binomial")
fit[[3]] <- glm(admit ~ rank, data = dat, family = "binomial")
...
And even that could be cleaned up. But if you store directly into a list you can use functions like lapply to easily apply the same function to each element which saves a lot of typing later on.


text:
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

3 typo + some remarks

For a locally compact (Hausdorff) abelian group $G$ we have following theorem (see e.g. Folland):

"For every (strongly continuous) unitary representation $(\pi,\mathcal{H_{\pi}})$ of $G$, there exists a unique regular $\mathcal{H}_{\pi}$-projection-valued measure $P$ on $\hat{G}$ such that $\pi$ decomposes as:

$\pi (g)=\int_{\hat{G}}\left\langle g,\chi\right\rangle dP\left(\chi\right)$ for every $g \in G$."

To which extent is this theorem true for nilpotent Lie groups (say, connected and simply connected)? That is, do we have a canonical decomposition of a unitary representation of such a group in terms of its irreducible unireps and a projection-valued some sort of measure on the unitary dual?

The proof of the above theorem has two major ingredients: the identification of the spectrum of $L^1 (G)$ with $\hat{G}$ when $G$ is abelian and the spectral theory of commutative Banach algebras. It is not clear to me whether any of these ingredients has a suitable analogue in the nilpotent case. Furthermore, in thie this case $\hat{G}$ is not a group or even a Hausdorff space, so I'm plus one would have to integrate an operator-valued function which assumes operators acting on different Hilbert spaces as its values. Thus I am not so sure if the standard theory of projection-valued measures can be so easily applied in this case.

2 minor clarification

For a locally compact (Hausdorff) abelian group $G$ we have following theorem (see e.g. Folland):

"For every (strongly continuous) unitary representation $(\pi,\mathcal{H_{\pi}})$ of $G$, there exists a unique regular $\mathcal{H}_{\pi}$-projection-valued measure $P$ on $\hat{G}$ such that $\pi$ decomposes as:

$\pi (g)=\int_{\hat{G}}\left\langle g,\chi\right\rangle dP\left(\chi\right)$ for every $g \in G$."

To which extent is this theorem true for nilpotent Lie groups (say, connected and simply connected)? That is, do we have a canonical decomposition of a unitary representation of such a group in terms of its irreducible unireps and a projection-valued measure on the unitary dualspace?

The proof of the above theorem has two major ingredients: the identification of the spectrum of $L^1 (G)$ with $\hat{G}$ when $G$ is abelian and the spectral theory of commutative Banach algebras. It is not clear to me whether any of these ingredients has a suitable analogue in the nilpotent case. Furthermore, in thie case $\hat{G}$ is not a group or even a Hausdorff space, so I'm not sure if the theory of projection-valued measures can be so easily applied in this case.

1

# Decomposing an arbitrary unitary representation of a connected nilpotent Lie group in terms of its irreps

For a locally compact (Hausdorff) abelian group $G$ we have following theorem (see e.g. Folland):

"For every (strongly continuous) unitary representation $(\pi,\mathcal{H_{\pi}})$ of $G$, there exists a unique regular $\mathcal{H}_{\pi}$-projection-valued measure $P$ on $\hat{G}$ such that $\pi$ decomposes as:

$\pi (g)=\int_{\hat{G}}\left\langle g,\chi\right\rangle dP\left(\chi\right)$ for every $g \in G$."

To which extent is this theorem true for nilpotent Lie groups (say, connected and simply connected)? That is, do we have a canonical decomposition of a unitary representation of such a group in terms of its irreducible unireps and a projection-valued measure on the dual space?

The proof of the above theorem has two major ingredients: the identification of the spectrum of $L^1 (G)$ with $\hat{G}$ when $G$ is abelian and the spectral theory of commutative Banach algebras. It is not clear to me whether any of these ingredients has a suitable analogue in the nilpotent case. Furthermore, in thie case $\hat{G}$ is not a group or even a Hausdorff space, so I'm not sure if the theory of projection-valued measures can be so easily applied in this case.


text:
# Inequality with Three Linear Constraints

### Proof 1

Denote $a+b=s,\;$ $ab=p.\;$ Then $0\lt s\le 5\;$ and $c\le 11-s.\;$ Hence,

$\displaystyle\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{s}{p}+\frac{1}{11-s}.$

Thus, suffice it to show that $\displaystyle\frac{s}{p}+\frac{1}{11-s}\ge 1.$

That inequality is equivalent to $11s-s^2-p(10-s)\ge 0.\;$ We'll maximize $p.$

For any fixed $s\in[0,5],\;$ define, for $a\in (0,\min\{2,s\}],\;$ quadratic function $f_s(a)=a(s-a).\;$ We consider two cases:

$\mathbf{s\le 4}$

By the AM-GM inequality, $a(s-a)\le\displaystyle\frac{s^2}{4},\;$ implying $p\le\displaystyle\frac{s^2}{4}.\;$ It follows that

\displaystyle\begin{align} 11s-s^2-p(10-s) &\ge 11s-s^2-\frac{s^2}{4}(10-s)\\ &=\frac{s[s-(7-\sqrt{5})][s-(7+\sqrt{5})]}{4}\\ &\gt 0. \end{align}

$\mathbf{4\lt s\le 5}$

Function $f_s\;$ is strictly increasing on $(0,2]\;$ so that

$\max p=\max f_s=f_s(2)=2(s-2).$

It follows that

\displaystyle\begin{align} 11s-s^2-p(10-s) &\ge 11s-s^2+2(s-2)(s-10)\\ &=(s-5)(s-8)\\ &\ge 0. \end{align}

### Proof 2

Set $x=3a,\;$ $y=2b,\;$ and $z=c.\;$ Then the constraints become

(1)

$x\le 6,$

(2)

$2x+3y\le 30,$

(3)

$2x+3y+6z\le 66.$

By the AM-GM inequality, (2) implies

$30\ge 2x+3y =x+x+y+y+y\ge 5\sqrt[5]{x^2y^3},$

so that $6\ge\sqrt[5]{x^2y^3},\;$ i.e.,

(4)

$x^2y^3\le 6^5.$

From (3), $66\ge 11\sqrt[11]{x^2y^3z^6},\;$ so that

(5)

$x^2y^3z^6\le 6^11.$

Now, multiplying (1) (twice), (4), and (5) gives $(xyz)^6\le 6^{18},\;$ or

(6)

$xyz\le 6^3.$

Further, multiplying (1) and (4) gives $(xy)^3\le 6^6,\;$ or

(7)

$xy\le 6^2.$

Now, multiply (1), (6), and (7) to get

(8)

$x^3y^2z\le 6^6.$

Finally, using AM-GM inequality once more, with a reference to (8),

\displaystyle\begin{align} \frac{1}{a}+\frac{1}{b}+\frac{1}{c} &= \frac{3}{x}+\frac{2}{y}+\frac{1}{z}\\ &\ge 6\sqrt[6]{\frac{1}{x^3y^2z}}\\ &\ge 6\sqrt[6]{\frac{1}{6^6}}\\ &=1. \end{align}

Equality is achieved for $x=y=z,\;$ or $3a=2b=c,\;$ i.e., $(a,b,c)=(2t,3t,6t),\;$ $t\in [0,1].$

### Proof 3

It can be verified directly or with the Taylor expansions that

\displaystyle\begin{align} \frac{1}{a} &= \frac{1}{2}+\frac{2-a}{4}+\frac{(2-a)^2}{4a},\\ \frac{1}{b} &= \frac{1}{3}+\frac{3-b}{9}+\frac{(3-b)^2}{9b},\\ \frac{1}{c} &= \frac{1}{6}+\frac{6-c}{36}+\frac{(6-c)^2}{36c}.\\ \end{align}

Now,

\displaystyle\begin{align} \frac{1}{a}+\frac{1}{b}+\frac{1}{c} &= \left(\frac{1}{2}+\frac{2-a}{4}+\frac{(2-a)^2}{4a}\right)\\ &\qquad+\left(\frac{1}{3}+\frac{3-b}{9}+\frac{(3-b)^2}{9b}\right)+= \frac{1}{6}+\frac{6-c}{36}+\frac{(6-c)^2}{36c}\\ &=1+\frac{5(2-a)+3(5-(a+b))+(11-(a+b+c))}{36}\\ &\qquad+\frac{(2-a)^2}{4a}+\frac{(3-b)^2}{9b}+\frac{(6-c)^2}{36c}\\ &\ge 1, \end{align}

as the last four terms are not-negative.

### Acknowledgment

The problem (by Nguyen Viet Hung) was communicated to me by Leo Giugiuc, along with his solution (Proof 1). Imad Zak has replied with a different solution (Proof 2). Proof 3 is an example of a more general technique found in Martin Celli's article Convexity, and Hung’s inequality with linear constraints from the Romanian Mathematical Magazine, Jan 27, 2017.


text:
# Draw Angles Online

Keep playing until the problems seem easy and you can solve them quickly. Draw three views of the following components, either in first or third angle projection. This online calculator finds the reference angle and the quadrant of a trigonometric a angle in standard position. help kids learn to learn types of lines the fun way. Last 6 Months All Time Last Month Last Week. io doesn't understand where to draw a shadow, which line(s) the line width applies to, etc. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. Differentiated and visual lesson to support students with use of rulers and protractors. Classic - GeoGebra. 4) Links verified on 8/28/2013. Enter the at symbol (@) and the length, followed by the left angle bracket (<) and the angle, for example @6. In the top left, click Insert Drawing New. Reference Angle and Quadrant Calculator. Learn some basic geometry with this worksheet all about the angle. is a right angle and would make a standard 'T' joint. All three axes are scaled uniformly. Circular hole becomes ellipse Distorted width Accurately presents object’s details, i. Description. Making statements based on opinion; back them up with references or personal experience. Therefore, the order of selecting these objects is relevant for the Angle tool. When angle B is used, a is the side adjacent (SA) and b is the side opposite (SO). Code to add this calci to your website. All start and end angles in between are measured by going clockwise from the start towards the end (so from 3 o'clock to 4 o'clock all the way back to the 3 o'clock position again). A one point perspective street scene typically combines repetitive manmade elements with stacked, cut and angular forms. How to Use a Protractor to Measure and Draw Angles. Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles. An angle can be drawn anywhere in the image by defining three points (handles) such as shown for the red angle below. Math and Games for Kids, Teachers and Parents. Angles and Degrees. 1 Types of angles In elementary geometry, angles are always considered to be positive and not larger than 360. You find the Protractor tool in a few different parts of SketchUp's interface: Construction toolbar; Large Tool Set. Suitable for 10 - 12 year olds. Draw horizontal, parallel lines across the page. DraftSight Tutorial for Beginners. Check your knowledge about measuring angles by taking this online angles test. A join angle of 90 deg. Angle brackets may occur in linguistics. Choose whether the angles to measure should start/end with a horizontal line. Similar to direct x-y coordinate entry, the distance-angle can be absolute, relative to the last point placed, or relative to a user-defined base-point. Press the Spacebar or Enter. Draw P&ID diagrams online in the browser with Google Docs. Popular skills in Anime. About Drawing Basics: If I can do it, so can you. So, when you read the angle of the miter, if the tool you are using says that the angle is 17-1/2 degrees (for example) you're all set. Although the length of the day is an important factor in explaining why summers are hot and winter cold, the angle of sunlight is probably more important. The angle symbol is a mathematical symbol that is placed ahead of characters, usually uppercase italic letters representing spatial points, to describe a geometric angle formed by the intersection of two lines, line segments, or rays. #N#Something I want to emphasize in this portrait drawing tutorial is to look for lines that flow into one another. We have detected that you are are on a small device such as a mobile phone. For printing, the scale can be specified. The difference between the two orientations is a rotation, and that causes the angles to change: flat topped angles are 0°, 60°, 120°, 180°, 240°, 300° and pointy topped angles are 30°, 90°, 150°, 210°, 270°, 330°. This online activity only works on computers and. It can also provide the calculation steps and how the right triangle looks. Draw a custom stickman and watch him come to life in this interactive stickman adventure. One ray is already lined up with 0°. Measuring angles using a protractor. Drawing and measuring angles with a protractor. This Maths planning tool, which is based on the UK National Curriculum APP levels, is fully searchable and categorised into different assessment focuses, including number, fractions, decimals, percentages, problem solving, shape, measures, time, angles and data handling. Using a protractor, we draw another line MV at an angle of 42 degrees to it. Accuracy, neatness and legibility are of great importance in engineering drawing. Trouble Playing This Game? Advertisement | Go Ad-Free!. February 22, 2020· Drawings. Drawing is a skill you can master at any age. Keep playing until the problems seem easy and you can solve them quickly. The Draw Events are some of the many events that can be triggered in an instance and may contain code or actions. Change the compass to the third distance, and draw another arc. Have students create vocabulary index cards with drawings and definitions for each of the bolded words on the worksheet; vertex, degrees, right angle, obtuse angel, and acute angle. scalar quantities with magnitude - time, temperature, mass etc. Math is about practice! This arcade style triangles math game will. But why don't you work with your family on the rest of the problems. Suitable for 10 - 12 year olds. svg extension. In radian measure, the reference angle $$\text{ must be } \frac{\pi}{2}$$. The steps of construction of isometric scale are given below ; refer Fig. Angle C and angle 3 cannot be entered. The reference angle is defined as the acute angle between the terminal side of the given angle and the x axis. Grade 3 geometry worksheets. 3 Measurement and Draw Angles. There are 360° in a full turn. Draw horizontal, parallel lines across the page. On your computer, open a document. The curved green line shows the given angle. a line 6 units of length and tilt it 60º from the. A website with an option to use coordinates to plot points and other tools to draw polygons. KS2 - KS4 Teaching Resources Index. But, if you are reading this - you definitely have a desktop, laptop or mobile device with a web browser. 1 One- Point Perspective 7. Try rotating the device so that it is in a landscape position. These three independent variables were within‐subject factors. Example - Adding Forces. In order for students to be successful in drawing angles accurately and precisely, they need practice and to be able to compare their angle to one this is drawn correctly. DXF files) to the new VectorDraw format standards (VDML, VDCL) and vice versa. Do one of the following to specify the length:. Can also be used to make a person appear isolated or small. Angles and Side Calculation Online. Create an equilateral triangle. 3 Three-Point Perspective WEEK 8 DIMENSIONS FOR TECHNICAL DRAWING 8. 6 — Measure angles in whole-number degrees using a protractor. This mismatch between what you draw and what the molecule actually looks like can lead to problems if you aren't careful. Aluminum angle stock is available in full size and custom cut lengths. Math and Games for Kids, Teachers and Parents. Technology Euclidean Grid, Gray technology grid background, half round gray illustration free png size: 2014x2589px filesize: 290. Discover The Secrets Of Drawing Realistic Pencil Portraits. Inside Radius: 0. Drawing and measuring angles with a protractor. Pixels Centimeters Millimeters Inches Points Picas Ems Exs. Go to Solution. [Geometry Goal 1] • Use quarter-turns to describe right angles. On your computer, open a document. Overstock is committed to ensuring the safety of both our customers and employees. (It is also used in monochromatic heraldic representations to indicate what the tincture of a "full-colour" emblazon would be. This free triangle calculator computes the edges, angles, area, height, perimeter, median, as well as other values of a triangle. Given 4 lengths and an angle, we can use this information to draw a quadrilateral. Essential Skills. Number of problems 4 problems 8 problems. As Featured in Ultralearning by Scott H. Advertisement. Then adjust the line vertically. when done click on the line you want again and draw the second line the same way, put in the angle and move it into position. #N#It seems that in Art there are two ways of drawing a person - 1. Volume & Radius. ” Envision this: Winger leaning off her patio while hanging on with her left hand to a harness. The closer you get to the target angle the more points you will score. This lesson show haw a negative angle can be drawn on a unit circle. hold angled lines at specific angles to help keep corners straight for mouse drawing. Angles are often measured in degrees. For the pyramid, you'll finish the drawing by connecting the three lines at the bottom. We collected 72 of the best free online drawing games. We explain Drawing a Negative Angle with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. Measure angles in whole-number degrees using a protractor. Essential Skills. Then we can use Bretschneider's formula to calculate the area, $$K$$. Do one of the following to specify the angle: Enter the left angle bracket (<) and the angle, for example <45, and move the cursor to indicate the direction. Generally, semi-circular in shape, protractors are also available in full-circle, 360-degree versions. Entering the data for this example: The join angle defines angle at which the branch pipe joins the main pipe. (d) Again, draw OD bar as bisector of ∠ AOC. Right triangle calculator to compute side length, angle, height, area, and perimeter of a right triangle given any 2 values. Create an obtuse triangle. Problem is when I erase the lines it looks like a channel not leaving a clean face. Simple online geometry shapes graphing calculator that allows you to draw/graph a triangle given the required values. One ray is already lined up with 0°. There are 360° in a full turn. The starting angle, in radians (0 is at the 3 o'clock position of the arc's circle) Play it » eAngle: The ending angle, in radians: Play it » counterclockwise: Optional. Create an isosceles triangle. Constructing a triangle when given the three angles will require you to pay close attention to the lengths. To link to this page, copy the following code to your site:. Overstock is committed to ensuring the safety of both our customers and employees. Create an equilateral triangle. 10-22-2009 05:19 PM. This way a polyline would orient exactly the same way as the angle mentioned. You can input only integer numbers or fractions in this online calculator. Create an obtuse triangle. User clicks to generate random angle, measures or draws with movable protractor and then clicks to check answer! Measuring Angles. Explore angles in standard position, coterminal angles using an HTML 5 applet. You will place the center of the protractor on the known point where you are plotting your bearing. Studyladder is an online english literacy & mathematics learning tool. LINK IN BIO👇🏻 linkin. Drawing the cube and similar objects (such as books, boxes etc. Angle a Calculator. It is a perfect blend of both cute and classy and thus will work great as a tattoo. Please wait while the map loads. This is the currently selected item. Aluminum angle stock is available in full size and custom cut lengths. “I’m providing all these views so I can show them what exactly they need to be doing,” she said. ORTHOGONAL / ORTHOGRAPHIC DRAWING Term used in Victoria Term used in New Zealand ISOMETRIC DRAWING They can be used for: Exercises in class if appropriate, maybe as a quick 10 minute exercise at the beginning of a lesson Test questions Homework Consolidation of learning / Advanced students /. a line 6 units of length and tilt it 60º from the. Use up and down to turn drawing on and off, or just use the setx, sety, or goto functions to move without drawing. online drawing tools 1. There are six different types of angles: Acute Angle - between 0° and 90° degrees. This website is an online drawing tool where you can create nice draws and animate images too. You will have to read all the giv. Even in this modern age of CAD there is still a large demand for traditional drawing equipment from Architects and planners to civil and mechanical engineers. For printing, the scale can be specified. Drawing and identifying a polygon in the coordinate plane Online Quiz - Following quiz provides Multiple Choice Questions (MCQs) related to Drawing and identifying a polygon in the coordinate plane. Activity Sheet 1: Angles, Arcs, and Segments in Circles Name Date Complete the following activities, using a dynamic geometry software package. Turn Feature: If you are unable to measure the Rise & Run measurements of an angle, Apex allows you to enter the actual angle directly into the line dimension string. Angle a Calculator. Free hand angles is a nice paper folding activity using circular pieces of paper, Bearings and Bearings and Scale Drawing gives a good introduction to drawing diagrams to scale whilst Journeys requires students to begin by sketching the diagram before drawing accurately. They're the ability to: recognize edges, lines, and angles; to reckon proportion and perspective; deciphering shadow, highlights, and gradations of tone; and lastly, the ability to unconsciously drawstring them all together - which comes to you with practice. Straigh angles, acute angles, obtuse angles Do you want to know what they are and how to measure them? Emma and Andrew Learn Shapes and Math with Fun Kids Toys | Educational Videos for. Cone angle :. Common Core Connection for 4th Grade Recognize that angles are formed when two rays share a common endpoint. Hatching (hachure in French) is an artistic technique used to create tonal or shading effects by drawing (or painting or scribing) closely spaced parallel lines. The angle symbol is a mathematical symbol that is placed ahead of characters, usually uppercase italic letters representing spatial points, to describe a geometric angle formed by the intersection of two lines, line segments, or rays. Clark zooms into school, crashes through the classroom, and is rowdy at recess. Estimation - visualize angle sizes. We collected 72 of the best free online drawing games. - All shapes can be duplicated. Back to practice. No cutting for will call. When you are ready, you can learn the basics of drawing by taking a free online drawing class. As you can see, this drawing is very simple and quick to implement. In order for students to be successful in drawing angles accurately and precisely, they need practice and to be able to compare their angle to one this is drawn correctly. These games include browser games for both your computer and mobile devices, as well as driving games apps for your Android and iOS phones and tablets. com at 80% off the normal price through. Students will use a 360° protractor to draw the angles. We recommend you use a larger device to draw your structure. 1 Types of angles In elementary geometry, angles are always considered to be positive and not larger than 360. Angles in circles. 1 This is how I draw angle iron and square tubing using the Computer Aided Design program called Alibre PE. Perspective jaws: This is my favorite way of getting angles right. 25 inches (0. In third angle projection, the default front view from the part or assembly is displayed at the lower left, and the other two views are the top and right views. The bottom ellipse is a bit more "open" to us, or in other words it has to be wider on the vertical side. After that move your mouse and draw the line in the word document. On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Draw the components for any forces or acceleration that does not lie along the X or Y axis, and identify the angle that is given (or being looked for). Drawing and identifying a polygon in the coordinate plane Online Quiz - Following quiz provides Multiple Choice Questions (MCQs) related to Drawing and identifying a polygon in the coordinate plane. In this game, students will practice classifying triangles as as acute, right, or obtuse by dragging and dropping different figures in the correct basket in less than two minutes. Perfect for putting up garage door opener if you have a way to cut it up. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Back to practice. With the AccuMASTER 2-in-1 Digital Level and Angle With the AccuMASTER 2-in-1 Digital Level and Angle Gauge you can find true level and precisely check angles on any job that requires precise angle measuring: woodworking, engine building and more. A Full Circle is 360 ° Half a circle is 180° (called a Straight Angle). io offers pre-built shapes, as well as raster and SVG images that you can pull in and use. Great when you can’t find a proper reference at just the right angle. help kids learn to learn types of lines the fun way. This online activity only works on computers and. It is one-dimensional and can vary in width, direction, and length. 1 Types Of Dimensioning Techniques. Lesson 4 - Y6 Summer Block 1 ANS7 Angles in a triangle - missing angles 2020. For example, consider the simple molecule with the molecular formula CH 2 Cl 2. This portion of the procedure uses this Pipe Joint Template Online Software. The utility exports the above files to PDF, SVG and. 2D shapes: names Video 1 Practice Questions Textbook Exercise. com is a website created for kids who can enjoy Internet safely. In this second grade geometry worksheet, your child will practice finding the line or lines of symmetry on a variety of different shapes. Sign in - Google Accounts. Draw straight lines from each end of "A", to the corresponding end of "B", but carry the lines through until they meet. This will help you to achieve mastery in a very short period of time. Next page: How to draw a sphere and more shapes. Sample: angle A = 30 degrees and and angle B = 60 degrees. Most protractors are either circular or semicircular, and are typically made of transparent plastic for better precision. “I’m providing all these views so I can show them what exactly they need to be doing,” she said. Direct distance-angle entry Use the keyboard to enter precise distance-angle or polar coordinates, for example, 23,<90 or 23,<135, where the '<' indicates an angle in degrees. What I want to Find. Drawing and measuring angles with a protractor. For reflex interior angles the value of the exterior angle is shown. Angles and. If you “grab” the map, you can tilt it or spin it and look at it from different viewing angles. com is amongst the best websites for kids' activities. Draw Angles - Plotting Program. The Protractor tool enables you to measure angles and set a precise angled guide line. Follow their account to see all their photos and videos. Steps of construction: (a) Draw a ray OA. [Geometry Goal 1] • Identify the vertex and sides of an angle. In the top left, click Insert Drawing New. Putting It All Together. The triangles in solution 1 and solution 2 are said to be congruent. Decide the Angle- You are being attacked by Aliens and you need to set your laser at the correct angle in degrees to hit it. Type the line distance and then press the [L] or [R] keys for tuning to the Left or to the. Draw the angle you create in Step 2. Two concepts that are related but not the same are supplementary. All three axes are scaled uniformly. An end angle of 2 * Math. Drawing is a skill you can master at any age. Create the worksheets you need with Infinite Geometry. Measuring angles review. Open the compass. Protractors are fun and easy to use. Play Drawing Games at Free Online Games. Gann, a method of predicting price movements through the relation of geometric angles in charts depicting time and price. This online practice module will help students learn to use a protractor to measure precise angle measures. We have two new topic booklets covering Ratio and Proportion. You can use the ITP to demonstrate and explore properties of shapes, such as the internal angles of different pentagons and the properties of opposite sides of. 6 years ago. Common Core Standards: Grade 4 Geometry. In these worksheets, students use a protractor to draw and measure angles and determine if the angles are acute, obtuse, straight or 90 degrees. Here are some step-by-step instructions, provided by ScienceStruck, on how to use a protractor. Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. help kids learn to learn types of lines the fun way. Taper and angle calculation : Fill-in below, three of the parameters from your borehole, then the remain parameter will be automaticaly calculated. Basic Vector Operations Both a magnitude and a direction must be specified for a vector quantity, in contrast to a scalar quantity which can be quantified with just a number. Measuring and Drawing Angles with GeoGebra. This game provides practice opportunities for students to identify measures of angles, types of angles, and to determine the relationships of angles as complementary, supplementary, or congruent. In this step-by-step guide, Lee will teach you how to recreate every aspect of your model's face: the eyes, nose. Clark the Shark celebrates boisterous enthusiasm – and knowing when it’s time for indoor voices. Circles are represented by ellipses. Then we can use Bretschneider's formula to calculate the area, $$K$$. Learning to draw is hard. Use these Measuring Angles Worksheets for your students to practise drawing and measuring angles. Click Home tab > Draw panel > Line. Multiplying square roots. This free triangle calculator computes the edges, angles, area, height, perimeter, median, as well as other values of a triangle. ) Notice how even more dragon heads and tails. [Geometry Goal 1] • Identify the vertex and sides of an angle. Measure angles in whole-number degrees using a protractor. You draw with your finger or the mouse. ISO compared with U. An isometric drawing is a type of 3D drawing that is set out using 30-degree angles. 98% of products ordered ship from stock and deliver same or next day. ” Envision this: Winger leaning off her patio while hanging on with her left hand to a harness. An angle less than 90° is acute. Subscribe to RSS Feed. Recognize angles as geometric shapes formed wherever 2 rays share a common endpoint. Qty= 02 No's/Set. Let ∠AOB be any reflex angle. Math · Basic geometry · Angles · Measuring and. For graphing, the angle's initial side is the positive x-axis; its terminal side is the green line, because angles are drawn going anti-clockwise. The rugged, all-purpose VZXF angle seat valve is ideal for any application requiring open-loop control of media flows—whether gaseous, liquid, or highly viscous. here you can type in the specific angle you want your line at. Drawing Angles Objective To guide children as they draw angles as records of rotations. With P and Q as centres draw two arcs of radius little more than half of it and let they intersect each other in C. You can 3D-optimize your drawing in the sketch window before copying to 3D. Drawing a persons body - this is called Figure Drawing. asked Feb 2, 2018 in Class IX Maths by aman28 ( -872 points). A half turn is degrees. Draw three views of the following components, either in first or third angle projection. Drawing Of One Point Perspective. In this game, students will practice classifying triangles as as acute, right, or obtuse by dragging and dropping different figures in the correct basket in less than two minutes. The given angle may be in degrees or radians. No cutting for will call. dc100ghz wrote: > ACAD 2009. Check line angles with your pencil. Draw a custom stickman and watch him come to life in this interactive stickman adventure. Constructing angles review. It has a degrees setting so that you can set it at a precise angle, if necessary. A protractor is an instrument used to measure or draw angles. Open a new sketch. This allows you to concentrate on the lines that you add to the drawing. Step 4: Drawing Lines and Angles Accurately Year 5 Summer Block 2 Resources. (It is the edge opposite to the right angle and is c in this case. Measuring Angles. If you want to draw a perfect circle, you can hold Ctrl to constrain the shape as you draw it. Donate or volunteer today!. Insert shapes, lines or text with the editing tools. To apply protractor knowledge to drawing angles accurately, using measurements given. Note: (1) All dimensions are in mm. Volume & Height. We know that the angles in an equilateral triangle are all 60º in size. Lesson 4 - Y6 Summer Block 1 WO7 Angles in a triangle - missing angles 2020. Online angle meter. Get the Challenges. Hello! If you were registered before you can sign in using Facebook or with your username and password. Protractors are fun and easy to use. Click Home tab Draw panel Line. For more details on how the thickness for edge lines grow, refer to the width notes of the pygame. Lines and angles starter. The experience he brings from the classroom will greatly accelerate your learning process. Drawing Sheets. Types of Angles. Gann, a method of predicting price movements through the relation of geometric angles in charts depicting time and price. The Angle tool lets you visualize angles such as the ones below. A one point perspective street scene typically combines repetitive manmade elements with stacked, cut and angular forms. dc100ghz wrote: > ACAD 2009. (d) An angle is a straight angle if it equals 180. This lesson show haw a negative angle can be drawn on a unit circle. Open in full-screen mode. I use programs such as Adobe Photoshop CC, Clip Studio Paint, Procreate, and Sketchbook Pro 8. In these worksheets, students use a protractor to draw and measure angles and determine if the angles are acute, obtuse, straight or 90 degrees. Go to Solution. They are used with a T-square to drawing vertical and angled lines. You can drag the other party's vehicle from the upper right into the sketch. Step 2: Place the point of the compass at P and draw an arc that passes through Q. Construct segment AB. Step 2: Place the centre of the protractor at the vertex B and adjust the base line to be aligned to BC. I begin this lesson by showing students how to draw an angle using a protractor. This is the currently selected item. The Angle measurement mode is engaged. Automatic spacing. Create an equilateral triangle. A quarter turn is degrees. An isosceles triangle has 2 congruent sides. Worksheet | Angles, Points, Lines* covers all of the basic rules with angles, including naming types of angles, angles on a line, angles around a point and vertically opposite angles. Draw and label an example of each Classify each pair of lines as parallel, intersecting, or perpendicular Classify each angle as acute, obtuse, straight, or right Classify polygons Classify triangles Classify triangles according to lengths Circles Plane Figures Mixed Review. You draw with your finger or the mouse. – Set the range of values allowed into each element. Many different colleges a. Drawing and measuring angles with a protractor. It's a type of axonometric drawing in which the same scale is used for every axis, resulting in a non-distorted image. Find the center point for your protractor. , 0 degrees (north) , 90 degrees, 75 degrees etc. Logo is a wonderful application to use when learning about the properties of shapes and angles. Change the compass to the third distance, and draw another arc. Step 4: Drawing Lines and Angles Accurately Year 5 Summer Block 2 Resources. "Good steel" - by Lilyanasmama. Number of problems 4 problems 8 problems. Shape Menu. 2243 - Auto Roof Returns and Variable Overhangs 2505 - Drawing Walls at Any Angle. Drawing Lines and Angles Accurately Year 5 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Summer Block 2. This portion of the procedure uses this Pipe Joint Template Online Software. io, and many other free games. February 23, 2020· Drawings. (c) Draw OC bar as the bisector of ∠ AOB. It gives you the sublevel for every single Maths objective and is useful to ensure coverage of the UK national curriculum. Create an obtuse triangle. Set base depth, cube depth, 3D angle and many other properties easily with Creately. Angles and. Your goal is to populate the paper with 3D cubes as seen from various angles. by National Hardware. Conjecture: An inscribed angle has a measure of half the measure of the intercepted arc. The class was described as “an opportunity to draw and connect over embodiment. We know that the angles in an equilateral triangle are all 60º in size. To modify an angle: Activate the Pointer tool;. Play Drawing Games at Free Online Games. 3 Three-Point Perspective WEEK 8 DIMENSIONS FOR TECHNICAL DRAWING 8. Explore angles in standard position, coterminal angles using an HTML 5 applet. Constructing angles review. After that move your mouse and draw the line in the word document. Add a Solution. National Hardware 4020BC Slotted Steel Angle, 1-1/2 by 48-Inch, Galvanized. Have a look at this animation (press the play button) to see how to make a neat angle using a protractor and ruler:. To activate freehand drawing, hold the Shift key. Step 4: Drawing Lines and Angles Accurately Year 5 Summer Block 2 Resources. More on this topic including lesson Starters, visual aids and investigations. Some of the worksheets for this concept are Drawing angles, Find the measure of each angle to the nearest, Reading protractor level 1 s1, A resource for standing mathematics qualifications, Measure draw and classify angles, Grade 4 supplement, Angles and angle measure date period. Our mission is to provide a free, world-class education to anyone, anywhere. [It is possible] to draw a straight line from any point to any point. A scoliosis is defined as a lateral spinal curvature with a Cobb angle of 10° or more 4. This example generates a L-system, which consists of many small rectangles that look like islands. DraftSight - Draw a line at an angle. This angle is ½ the corner angle, so multiplying by 2 will give you the corner angle. See the proof below for more details. Clockwise angles to 180° by 5° - horizontal base. If the trusses are not symmetrical, find the left-side base angle to produce the right-side base angle. [It is possible] to describe a circle with any center and radius. Select the Pen tool. Worksheets > Math > Grade 3 > Geometry > Using a protractor. , Please draw , Please name the angle Ms. MATH | GRADE: 4th, 5th. The angle symbol is a mathematical symbol that is placed ahead of characters, usually uppercase italic letters representing spatial points, to describe a geometric angle formed by the intersection of two lines, line segments, or rays. There are two common forms: degrees (°), arc minutes (′) and arc seconds (″), as well as decimal degrees. Angles in circles. Directly Measure Roof Pitch Angle and Calculate. This Maths planning tool, which is based on the UK National Curriculum APP levels, is fully searchable and categorised into different assessment focuses, including number, fractions, decimals, percentages, problem solving, shape, measures, time, angles and data handling. Constructing angles. Do one of the following to specify the length: Move the cursor to indicate the direction and angle, and enter the length, for example 6. It looks like this is a job for a for loop that runs from 0 to n (the number of sides), calculating the points for each vertex and drawing lines connecting them. Nov 27, 2012 - Fun art project to practice measuring and drawing angles! - Kids make a minimum of angles, measure them, and then create their design. However, if you do not have a compass, you can draw the triangle without using the circle guide by measuring each side carefully with a ruler. Perspective jaws: This is my favorite way of getting angles right. Worksheet 1; Worksheet 2; Perpendicular. So c is a right angle. Metric and Imperial. Thus, OC is the required bisector. B — An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Click along the second ray to complete the angle. Corresponding sides are opposite corresponding angles. , as long as the horizontal and vertical units are of equal length. Related Skills: Character Design Comic Comic Art Comics Drawing Figure Drawing Illustration Japanese Manga Sketching. This online calculator finds the reference angle and the quadrant of a trigonometric a angle in standard position. The rugged, all-purpose VZXF angle seat valve is ideal for any application requiring open-loop control of media flows—whether gaseous, liquid, or highly viscous. Subscribe to RSS Feed. Our employees located at our headquarters are all now working from home, including our Customer Care agents, and our warehouses are following social distancing protocol and other official directives. By lighter shafts and more upright lie angles. TrianCal is online calculator triangles that works with any combination of values including sides, heights, angles, the area or perimeter of any triangle, calculating it with the minimum possible value (typically three). ↓ Scroll down to check out our Video Lessons. Draw the components for any forces or acceleration that does not lie along the X or Y axis, and identify the angle that is given (or being looked for). Jerry's Artarama is committed to helping the artist community through the use of our extensive library of "How To" Free Art Lessons on Video. by National Hardware. Start by clicking on the cube along the left side; then, place cubes on the grid where you would like them. Measuring angles review. When dealing with trigonometric functions sine, cosine, tangent, cotangent, secant and cosecant, most of the time they give the identical value for the angle and its reference. Lesson 4 - Y6 Summer Block 1 WO7 Angles in a triangle - missing angles 2020. ToInt32(x1); int intY1 = Convert. A –570 degree angle on the coordinate plane. Use on interactive whiteboards, angles can be automatically shown or measured with a protractor. Grade 3 geometry worksheets. Drawing angles can be set at 1° intervals. Draw the line QR. Now, angles 1 and 2 and angles 3 and 4 are NOT vertical angles. The strong magnetized base lets you attach directly to any metal surface: tables, blades, car and. How to Use a Protractor to Measure and Draw Angles. On the Home tab, in the Tools group, click the arrow next to Rectangle, and then do one of the following: To draw a straight line, select the Line tool. Scribble suggests using fruit as a practice for still life drawing, allowing you to perfect your shapes, strokes, shadows, and highlights while the object of your study sits still and accessible to you. Studyladder is an online english literacy & mathematics learning tool. Follow the other ray to find the angle measurement. Units may be inches, feet, meters, etc. Measuring angles using a protractor. Using the approach outlined in this course, I was able to get a lot better at drawing portraits in just one month. Turn Feature: If you are unable to measure the Rise & Run measurements of an angle, Apex allows you to enter the actual angle directly into the line dimension string. A Euclidean construction. Start using draw. Identify these in two-dimensional. This fourth grade geometry lesson teaches the definitions for a line, ray, angle, acute angle, right angle, and obtuse angle. The angle bisector divides the given angle into two equal parts. Draw a Line at a Specific Angle. Because these angles are in quadrants two and three, we draw a “reference triangle” in each quadrant. , as long as the horizontal and vertical units are of equal length. If you really want to pracitce, try drawing the same fruit from different angles! 8. Trigonometry is the study of the relationship between the angles of triangles and their sides. Estimate angle measures. What is CAD drawing? CAD stands for computer-aided design and drafting and it refers to designing and documentating technical specs and plans in various engineering fields. Drawing angles - Studyladder Interactive Learning Games. Prime Factorization. Create an obtuse triangle. Save worksheet. Draw a square directly in the centre (note no sides should be visible). Draw a custom stickman and watch him come to life in this interactive stickman adventure. Angles in Shapes (Megan Lightup) DOC. This way a polyline would orient exactly the same way as the angle mentioned. Measuring And Drawing Angles - Displaying top 8 worksheets found for this concept. Recognize angles as geometric shapes formed wherever 2 rays share a common endpoint. Add a Solution. Example - Adding Forces. Looking to improve your Anime skills? Learn more!. What I want to Find. Answer sheet Include answer sheet. Chapter 11 - 01. See the proof below for more details. These include all aspects of the topics required for GCSE Foundation level, and provide plenty of practice with the essential techniques, plus many worded questions throughout. AutoCAD #20 - How to draw Line & Angle in Degree, Minutes & Seconds in AutoCAD | AutoCAD Basics - Duration: 10:49. The Hand-Free Tool is the most powerful drawing tool of Microsoft Word. Review the conformational analysis of alkanes (dihedral angle; staggered/eclipsed; anti/gauche) and cyclohexane (chair conformations, axial/equatorial bonds). Watchmakers and carmakers spent nearly a full year in development with the objective of reproducing Bugatti’s iconic 16. Calculator computes the diagonals of a parallelogram and adjancent angles from side lengths and angle. In this second grade geometry worksheet, your child will practice finding the line or lines of symmetry on a variety of different shapes. With you line still selected click on the Rotate button and in the drop-down menu click more rotation options. I wanted to make sure that the two diagonal lines at the bottom of my drawing were correct, so I matched my pencil to the angles that I saw in the still life, and then moved my hand (while keeping the pencil at the same angle) in front of my paper and made sure the angles that I drew lined up. What you will need is a compass, a pencil, a ruler and some basic knowledge about perpendicular lines, angle bisectors, equiangular triangles and duplicating an angle. This can be done using only a compass and straightedge. Triangle vertices are usually named A, B and C. Advertisement. You can use fewer or more, if you want—there's no rule for this! Take the ruler again and draw a line between the center and every mark, across the whole plan. Angles and Degrees. Click Home tab > Draw panel > Line. We have to pay special attention to what happens to standard proportions when we draw a figure from such an exaggerated point of view. What is CAD drawing? CAD stands for computer-aided design and drafting and it refers to designing and documentating technical specs and plans in various engineering fields. If you want to draw a perfect circle, you can hold Ctrl to constrain the shape as you draw it. 2D shapes: names Video 1 Practice Questions Textbook Exercise. The intersection of the two arcs is the third corner of the triangle. Recall that an equilateral triangle has all three interior angles 60 degrees. The calculator solves the triangle specified by three of its properties. You can manipulate the ruler by using your fingers. Polygon explorer to learn about the properties of regular polygons. (0 votes, average: 0. Terminology: An angle whose vertex is on the circle is called an inscribed angle. Measure angles in whole-number degrees using a protractor. Types of Angles. Angles are measured in degrees, the symbol for degrees is a little circle ° The full circle is 360° (360 degrees) A half circle or a straight angle is 180°(180 degrees) A quarter circle or a right angle is 90°(90 degrees). Understand concepts of angle measurement. These games include browser games for both your computer and mobile devices, as well as driving games apps for your Android and iOS phones and tablets. The ruler pivots to any position you want: horizontal, vertical, or any angle in between. Draw any Shapes Perimeter to Calculate it's Irregular Area. Drawing a circle or ellipse Before you draw a circle, it's helpful to understand how SketchUp creates circle entities:. Get the Answers. Conversion of drawing vector files. Inkydink, helps him figure out a way to tone it down. To help yourself visualise straight lines, extend your pencil in front of you to see the angles of the head more clearly. Picture the reflection in a drawing as it lands and creates shadows over everything shown in the mirror. Construct segment AB. Volume & Height. (ii) Draw the true lengths on a line PM inclined at 45° to. Sketch definition is - a rough drawing representing the chief features of an object or scene and often made as a preliminary study. Last 6 Months All Time Last Month Last Week. 6:30 PM-9:30. So to draw these angle, start at the point of the angle to draw the vertical line then restart from the same point for horizontal. These worksheets will help your classes to understand the difference between acute, obtuse, reflex and mixed angles. 3rd quadrant: reference angle = angle - 180 degrees. It’s all a matter of degrees! In this BrainPOP movie, Tim and Moby introduce you to the concept of angles and how to measure them. The classic trigonometry problem is to specify three of these six characteristics and find the other three. Components available in aluminum, bronze, stainless steel and nickel-silver. 45 'How to Draw' Video Lessons. A comprehensive database of more than 25 drawing quizzes online, test your knowledge with drawing quiz questions. When you are ready, you can learn the basics of drawing by taking a free online drawing class. Many different colleges a. Aluminum angle stock is available in full size and custom cut lengths. CIVIL Engineering Tutorials 7,921 views 10:49. All drawings have points, lines and angles. CAD Drawing Anywhere - Online or On Your Desktop. Pictorial drawing Perspective drawing Multi-view drawing Difficult to create Easy to visualize. Label the center A and a point on the circle B. Drawing is a skill you can master at any age. angles sum right angle. To link to this page, copy the following code to your site:. Khan Academy is a 501 (c) (3) nonprofit organization. The reference angle is defined as the acute angle between the terminal side of the given angle and the x axis. A protractor is a handy tool used to measure and draw angles. Drawing angles can be set at 1° intervals. Any help would be appreciated. Stop searching. io Diagrams in Confluence and Jira With numerous shape libraries offering hundreds of visual. If it says that the angle is 72-1/2 degrees (for example), it's giving you the complement, and you'll need to subtract it from 90:. Easy measure angles, using interactive whiteboard angle simulator. Online angle meter. Types of angles Acute Obtuse Reflex. Find: m?GHK. The angle bisector of a given angle is the line of symmetry which divides the angle into two. Learn to draw simply by following the sketching steps in each video tutorial. Practice: Estimate angle measures. Note: The process works well on the Microsoft Office Word 2013. Hands for Drawing - Posemaniacs. to draw-pentagon :length pd seth 126 repeat 5 [ fd :length rt 72 ] end Draws a pentagon "length" pixels on each side, with the turtle originating and terminating at the apex. There are six different types of angles: Acute Angle - between 0° and 90° degrees. - The type. Points, lines, circles, polygons, and rectangles are among the graphic shapes you'll use to highlight features in your data and draw cartographic elements on your layout. Estimation - visualize angle sizes. #N#Math is about practice! This arcade style geometry math game will. To draw accurate angled lines, please follow these steps: Use the Protractor tool to create a Guide Line entity at some angle. This is the number of points needed to name an angle. Straight angle: The angle that is 180° is a straight angle, ∠AOB in the figure below. To draw a quadrilateral at least 5-6 elements should be given. Central Angle 1. McMaster-Carr is the complete source for your plant with over 595,000 products. Complementary Angles - Two angles whose measures add up to 90 degrees. KS2 - KS4 Teaching Resources Index. Looking to improve your Anime skills? Learn more!. Matthew created Drawing Tutorials Online to provide artists with quality art instruction delivered at the college level, without the college costs. Enter Pitch, Angle or Grade and hit appropriate button to re-draw diagram. I begin this lesson by showing students how to draw an angle using a protractor. Circles are represented by ellipses. Keep playing until the problems seem easy and you can solve them quickly.


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### Conference/Proceedings

#### DISCRETE MODEL REDUCTION OVER DISC-TYPE ANALYTIC DOMAINS AND $\infty$-NORM ERROR BOUND

Author
Oh Do-Chang, Lee Kap-Rai, Um Tae-Ho, Park Hong-Bae
Publisher
제어ㆍ로봇ㆍ시스템학회 in 1996
Cited Count
0
Partners
KISTI
Category
Marine Studies > Zootechnics
Keywords
model reduction, analytic domain, Hankel singular value
##### Abstract

In this note, we propose the discrete model reduction method over disc-type analytic domains. We define Hankel singular value over the disc that is mapped by standard bilinear mapping. And GSPA(generalized singular perturbation approximation) and DT(direct truncation) are generalized to GSPA and DT over a disc. Furthermore we show that the reduced order model over a smaller domain has a smaller L$_{\infty}$ norm error bound..

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