text:
### Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

### Ab Surd Ity

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

### Absurdity Again

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

# Fibonacci Fashion

##### Age 16 to 18 Challenge Level:

Here is another excellent solution from Andrei of Tudor Vianu National College, Bucharest, Romania.

We are given $F_n={1\over\sqrt5}(\alpha^n-\beta^n)$ where $\alpha$ and $\beta$ are solutions of the quadratic equation $x^2-x-1=0$ and $\alpha > \beta$.

(1) In the quadratic equation $ax^2+bx+c=0$ with roots $\alpha$ amd $\beta$, using Viete's relations for the sum and product of the roots, I obtain: $\alpha\beta =-b/a$, $\alpha + \beta = c/a$

In the particular case of the equation $x^2-x-1=0$, I have: $\alpha\beta =-1$, $\alpha + \beta = 1$

(2)$${1\over \alpha} + {1\over \alpha^2}={\alpha + 1\over \alpha^2}=1$$ as $\alpha$ satisfies $x^2=x+1$. Similarly for $\beta$.

(3) Here I shall prove that $F_1=1$, $F_2=1$ and $F_n + F_{n+1} = F_{n+2}$ and hence $F_n$ is the $n$th Fibonacci number. First, I calculate $\alpha$ and $\beta$: $\alpha={1+\sqrt5\over 2}$ and $\alpha={1+\sqrt5\over 2}$

$$\begin{eqnarray} F_1 &= {1\over \sqrt 5}\left( {1+\sqrt 5 \over 2} - {1-\sqrt 5 \over 2}\right) = 1 \\ F_2 &= {1\over \sqrt 5}(\alpha^2 - \beta^2) = {1\over \sqrt 5} (\alpha - \beta)(\alpha + \beta) = 1 \\ F_n +F_{n+1}- F_{n+2}&= {1\over \sqrt 5}[\alpha^n -\beta^n + \alpha^{n+1} -\beta^{n+1} - \alpha^{n+2} + \beta^{n+2}] \\ F_n + F_{n+1}- F_{n+2}&= {1\over \sqrt 5}[-\alpha^n(\alpha^2 - \alpha - 1) +\beta^n(\beta^2- \beta -1)]=0\end{eqnarray}$$

(4) I shall prove by induction the statement $P_n$ that $1 + F_1 + F_2 + \cdots F_n = F_{n+2}$.

I know that $F_1=1, F_2=1$ and by (3), $F_3=2, F_4=3, F_5=5, F_6=8,...$\\ For $n=1$, $P_1$ is $1+ F_1 = F_3$ which is evidently true as 1 + 1 = 2.

For $n=2$, $P_1$ is $1+ F_1 + F_2= F_4$ which is evidently true as 1 + 1 + 1 = 3.

For $n=3$, $P_1$ is $1+ F_1 + F_2 + F_3 = F_5$ which is evidently true as 1 + 1 + 1 + 2 = 5.

Now I assume that $P(k)$ is true for a fixed $k$ and I shall prove that $P(k+1)$ is also true, that is:

$$\begin{eqnarray} P_k &: 1 + F_1 + F_2 + \cdots F_k = F_{k+2} \\ P_{k+1}&: 1 + F_1 + F_2 + \cdots F_k + F_{k+1} = F_{k+3}\end{eqnarray}$$

$$\begin{eqnarray}1 + F_1 + F_2 + \cdots F_k + F_{k+1}&= (1 + F_1 + F_2 + \cdots F_k ) + F_{k+1}\\ &= F_{k+2} + F_{k+1} \\ &= F_{k+3}\end{eqnarray}$$

and hence the result is true for $n=k+1$. By the principle of mathematical induction the statement $P_n$ is true for all positive integer values of $n$ which completes the proof.


text:
Outlook: Tortoise Pipeline & Energy Fund Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 20 Jan 2023 for (n+8 weeks)
Methodology : Modular Neural Network (Financial Sentiment Analysis)

## Abstract

Tortoise Pipeline & Energy Fund Inc. Common Stock prediction model is evaluated with Modular Neural Network (Financial Sentiment Analysis) and Spearman Correlation1,2,3,4 and it is concluded that the TTP stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell

## Key Points

1. Is now good time to invest?
2. Can stock prices be predicted?
3. Is it better to buy and sell or hold?

## TTP Target Price Prediction Modeling Methodology

We consider Tortoise Pipeline & Energy Fund Inc. Common Stock Decision Process with Modular Neural Network (Financial Sentiment Analysis) where A is the set of discrete actions of TTP stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(Spearman Correlation)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Financial Sentiment Analysis)) X S(n):→ (n+8 weeks) $R=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$

n:Time series to forecast

p:Price signals of TTP stock

j:Nash equilibria (Neural Network)

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## TTP Stock Forecast (Buy or Sell) for (n+8 weeks)

Sample Set: Neural Network
Stock/Index: TTP Tortoise Pipeline & Energy Fund Inc. Common Stock
Time series to forecast n: 20 Jan 2023 for (n+8 weeks)

According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Grey to Black): *Technical Analysis%

## IFRS Reconciliation Adjustments for Tortoise Pipeline & Energy Fund Inc. Common Stock

1. When measuring a loss allowance for a lease receivable, the cash flows used for determining the expected credit losses should be consistent with the cash flows used in measuring the lease receivable in accordance with IFRS 16 Leases.
2. A single hedging instrument may be designated as a hedging instrument of more than one type of risk, provided that there is a specific designation of the hedging instrument and of the different risk positions as hedged items. Those hedged items can be in different hedging relationships.
3. If, in applying paragraph 7.2.44, an entity reinstates a discontinued hedging relationship, the entity shall read references in paragraphs 6.9.11 and 6.9.12 to the date the alternative benchmark rate is designated as a noncontractually specified risk component for the first time as referring to the date of initial application of these amendments (ie the 24-month period for that alternative benchmark rate designated as a non-contractually specified risk component begins from the date of initial application of these amendments).
4. To make that determination, an entity must assess whether it expects that the effects of changes in the liability's credit risk will be offset in profit or loss by a change in the fair value of another financial instrument measured at fair value through profit or loss. Such an expectation must be based on an economic relationship between the characteristics of the liability and the characteristics of the other financial instrument.

*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.

## Conclusions

Tortoise Pipeline & Energy Fund Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Tortoise Pipeline & Energy Fund Inc. Common Stock prediction model is evaluated with Modular Neural Network (Financial Sentiment Analysis) and Spearman Correlation1,2,3,4 and it is concluded that the TTP stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell

### TTP Tortoise Pipeline & Energy Fund Inc. Common Stock Financial Analysis*

Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCCaa2
Balance SheetCaa2Baa2
Leverage RatiosCaa2B3
Cash FlowCaa2B2
Rates of Return and ProfitabilityCaa2B1

*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?

### Prediction Confidence Score

Trust metric by Neural Network: 84 out of 100 with 850 signals.

## References

1. Bai J, Ng S. 2017. Principal components and regularized estimation of factor models. arXiv:1708.08137 [stat.ME]
2. J. N. Foerster, Y. M. Assael, N. de Freitas, and S. Whiteson. Learning to communicate with deep multi-agent reinforcement learning. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain, pages 2137–2145, 2016.
3. Van der Vaart AW. 2000. Asymptotic Statistics. Cambridge, UK: Cambridge Univ. Press
4. Byron, R. P. O. Ashenfelter (1995), "Predicting the quality of an unborn grange," Economic Record, 71, 40–53.
5. R. Sutton, D. McAllester, S. Singh, and Y. Mansour. Policy gradient methods for reinforcement learning with function approximation. In Proceedings of Advances in Neural Information Processing Systems 12, pages 1057–1063, 2000
6. Semenova V, Goldman M, Chernozhukov V, Taddy M. 2018. Orthogonal ML for demand estimation: high dimensional causal inference in dynamic panels. arXiv:1712.09988 [stat.ML]
7. A. Tamar and S. Mannor. Variance adjusted actor critic algorithms. arXiv preprint arXiv:1310.3697, 2013.
Frequently Asked QuestionsQ: What is the prediction methodology for TTP stock?
A: TTP stock prediction methodology: We evaluate the prediction models Modular Neural Network (Financial Sentiment Analysis) and Spearman Correlation
Q: Is TTP stock a buy or sell?
A: The dominant strategy among neural network is to Sell TTP Stock.
Q: Is Tortoise Pipeline & Energy Fund Inc. Common Stock stock a good investment?
A: The consensus rating for Tortoise Pipeline & Energy Fund Inc. Common Stock is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of TTP stock?
A: The consensus rating for TTP is Sell.
Q: What is the prediction period for TTP stock?
A: The prediction period for TTP is (n+8 weeks)

format: plain


text:
# sending command from remote pc using paramiko

Hello,

I am using a robot that is connected to a remote pc using localhost. I have used the Paramiko library to send commands from remote pc to my robot. I want to publish a number on /activate topic like this:

rostopic pub /activate std_msgs/Int16 "data: 1"

I have written the following code:

import paramiko
host = "xxx.xxx.x.x"
port = 22


text:
# Question #80432

Sep 10, 2016

The degree is 13.

#### Explanation:

For a term with more than one variable, add the degrees of each variable. The degree is the exponent.

The degree of the x term is 4. The degree of the y term is 9.

$4 + 9 = 13$


text:
# Computational mixology

Since last year I am following a culinary course, with a module on cocktail making. Since classes are presently canceled due to the ongoing pandemic, I have taken a more theoretical approach to the subject. Last week, I presented some ideas and findings on the (data) science of mixology for our department's science café. You can find my slides here. This post is a novelization of the talk.

# Cocktails and how to model them

For a definition of a cocktail, as always look no further than Wikipedia:

A cocktail is an alcoholic mixed drink, either a combination of spirits, or one or more spirits mixed with other ingredients such as fruit juice, flavored syrup, or cream.

So cocktails are mixtures of several beverages (the mixers), where at least one has to be alcoholic. Sorry, teetotalers. As most recipes contain the volumes of the mixers, it is sensible to just normalize the quantities by total volume. The critical bit of information is hence the volume fraction of each ingredient.

So cocktail recipes are compositional data, and we have to analyze them as such. There are hence three essential aspects to a cocktail recipe:

1. Which mixers are we going to choose?

2. In which ratios are we going to add the mixers?

3. How are we going to mix the cocktail?

# The fundamental law of traditional cocktails

Traditional cocktails are cooled by using plain ice[[nontrad]]. They are either stirred, shaken, with or without egg-white, blended, or just served with an ice cube. It is illuminating to look into the thermodynamics of water to understand how ice cools a cocktail.

So, there are three ways how ice can cool the cocktail:

• ice absorbs heat, increasing its temperature, the accounts for 2.03 J/(g·K);

• cold water obtained from molten ice increases its temperature to the cocktail equilibrium temperature, this amounts to 4.1814 J/(g·K);

• ice melts absorbing a whopping 333.55 J/g.

Clearly, most of the cooling is not due to cold ice becoming warmer ice. Cooling is primarily due to the melting of ice! This is even more pronounced when you consider that you typically take ice from the freezer (-18 °C) into an ice bucket, where it rapidly becomes melting ice (0 °C). This motives the fundamental law of traditional cocktails:

There is no chilling without dilution, and there is no dilution without chilling. – Dave Arnold

Some important conclusions can be drawn from this law:

1. You can standardize cocktails by measuring their temperature. Just mix until they have the required temperature, and you are guaranteed to have the optimal dilution of the ingredients.

2. The shape of the ice (cubes or crushed) does not matter. Smaller chunks of ice will cool and dilute faster, but you can still attain the same cocktail regardless.

3. Always use ice to cool, not plastic ice cubes as these cannot melt[[melting]] and are hence inefficient cooling agents.

The fundamental law has significant consequences on how cocktail recipes are designed. Consider the different ways of mixing a cocktail.

Simple built cocktails are mixed less intensively compared to stirred or shaken cocktails. Blender cocktails are mixed the strongest. More intensive mixing means more cooling and dilution, which again implies a different recipe composition. Dave Arnold has analyzed 54 well-known cocktails for their alcohol content, acidity, and sugar content.

So the type of mixing has a profound influence on the mixer ratios. Let us take a closer look at the numbers!

# Cocktails in the Hilbert space

Given that there is not a lot of cocktail data but that we expect there to be a nonlinear effect on how the mixers interact, kernels seem an appropriate tool! Without losing ourselves into the details, kernels are a way to represent data points in a high-dimensional Hilbert space. Think of a mixer, which can be described by alcohol and sugar content, acidity, type (liquor, sweetener, etc.). We can think of a feature map $\phi$ where we perform a nonlinear expansion of all these variables, projecting the mixer in a high-dimensional space. A kernel function is used to implicitly define such space. It represents a dot product in this space.

Kernels are hence a clever way to represent the mixers in a Hilbert space. How can we take a look at this space? Using PCA allows us to project back into two or three dimensions.

We now can describe the mixers, how to represent the cocktails. To this end, we can use kernel mean embedding, an elegant framework to represent probability distributions (i.e., compositions) in the Hilbert space. The idea is as smart as it is simple, to embed a cocktail, just take the weighted sum of the embeddings of the mixers:

$\mu = \sum_{i=1}^n \beta_i \phi(x_i)\,,$

where we have:

• $\mu$: the representation of the cocktail;

• $\phi(x_i)$: the representation of the $i$th mixer;

• $\beta_i$: the volume fraction of the $i$th mixer.

But, you might wonder, a linear combination might not possibly suffice for representing the complex interplay between the mixers that constitute a cocktail recipe? This is the magic of kernels because we work in a high-dimensional space, linear combinations in that space can capture intricate, nonlinear patterns! It can be shown that for various commonly-used kernels, the kernel mean embedding is injective: all information about the composition is retained!

Let us take a look into the Hilbert space of mixers and cocktails.

Looking pretty good! We have successfully represented cocktails as points in a Hilbert space. Note that the cocktails cluster quite well by type of mixing. Such a vectorial description can be used as a fruitful basis for all kinds of supervised and unsupervised data analysis!

# Designing cocktails as an optimization problem

Can we use the data to design new cocktail recipes? I outline two straightforward approaches: the easy problem of determining the fractions for a recipe and the harder challenge of creating new recipes.

## Easy: determining the fractions of a recipe

Suppose you have a recipe with $n$ mixers $x_1,\ldots,x_n$ and you want to determine the volume fractions $\beta$ to obtain a cocktail similar to one of embedding $\mu$. This $\mu$ might be a particular cocktail or an averga over a class. To find the volume fractions, one has to solve the following optimization problem:

$\min_{\beta\in\Delta^{n-1}}||\mu - \sum_{i=1}^n\beta_i \phi(x_i)||^2 - \lambda \cdot H(\beta)\,.$

Here $\Delta^{n-1}$ means the simplex, i.e., all vectors of length $n$ where the elements are nonzero and sum to one. Hence, all valid composition vectors. The first part of the objective is a data-fitting term we have to match. The second part is a regularization term, with $H(\beta) = -\sum_i \beta \log \beta_i$ the information entropy. Good things can come by using this regularization. For example, it will drive the solution to use all mixers, which is desirable. Importantly, the entropic term will make the problem strongly convex. Hence, simple gradient-based methods can be used to find the solution efficiently. So, if you want to tweak a cocktail recipe by, for example, exchanging lime juice by lemon juice, the above optimization problem can help you adjust your recipe!

## Hard: designing a recipe from scratch

A slightly different setup: given a liquor cabinet of $N$ mixers $x_1,\ldots,x_n$, select a subset of mixers and find the mixing ratio vector $\beta$ to obtain a cocktail similar to embedding $\mu$. So we first have to select which mixers to use before we can determine the volume ratios. I propose the following optimization problem:

$\min_{\beta\in\Delta^{N-1}}||\mu - \sum_{i=1}^N\beta_i \phi(x_i)||^2 + \lambda \cdot|\beta|_0\,.$

The data-fitting term is the same, but instead of using entropic regularization, we use the zero-norm. This norm will induce sparsity, thus selecting only a subset of the $N$ available mixers. This is quite a different beast compared to the previous problem! It is akin to the knapsack problem and is an NP-hard problem.

Conclusion: tweaking a recipe is easy, inventing it is hard!

Cocktails, and by extension, food science, lead to compelling problems of modeling and optimizing of compositional data. I find kernel methods particularly appropriate for these types of problems, and I like how they lead to elegant formulations.

If you are interested in cocktails, I enjoyed reading the following works:

• 'The Joy of Mixology' by Gary Regan, an excellent introduction to bartending;

• 'Liquid Intelligence' by Dave Arnold, discussing the fundamental law of cocktail making and many interesting aspects in the science of cocktails;

• 'Cooking for Geeks' by Jeff Potter, not specifically about cocktails but an excellent read for every scientist who likes cooking.


text:
## 0951: "Working"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

Posts: 28
Joined: Sun Apr 03, 2011 4:44 am UTC

### 0951: "Working"

Alt text: "And if you drive a typical car more than a mile out of your way for each penny you save on the per-gallon price, it doesn't matter how worthless your time is to you--the gas to get you there and back costs more than you save."

http://xkcd.com/951/
Otherwise known as Cheesy or Machete

A conservative furry! What a rarity!

Sean Quixote
Posts: 229
Joined: Tue Sep 14, 2010 1:20 am UTC
Location: Ubeki-beki-beki-beki-stan-stan

### Re: 0951: "Working"

*shakes fist*

jpk
Posts: 607
Joined: Sat Nov 13, 2010 7:33 am UTC

### Re: 0951: "Working"

And if you drive to the gym, you're paying money to drive to a place where you pay money to ride on a pretend bicycle.

MathUhhhSaurus
Posts: 48
Joined: Wed Dec 08, 2010 8:34 pm UTC

### Re: 0951: "Working"

lalalala...I'm not listening!

There's a gas station literally across the street from my neighborhood, but I will drive 5 or so miles down the road to get gas because it's cheaper. And, quite frankly, it's a much nicer looking gas station AND the one across the street is a BP (and we all know what happened there http://xkcd.com/748/).
Last edited by MathUhhhSaurus on Wed Sep 14, 2011 4:19 am UTC, edited 1 time in total.

irishnut
Posts: 43
Joined: Thu Nov 13, 2008 10:58 pm UTC

### Re: 0951: "Working"

Don't forget about the inevitable wait at the other gas station as there will probably be a ridiculous line if it's 10 cents a gallon cheaper, mostly because people don't understand this.

Drives me up the freaking wall when people don't understand this.

jpk
Posts: 607
Joined: Sat Nov 13, 2010 7:33 am UTC

### Re: 0951: "Working"

irishnut wrote:Don't forget about the inevitable wait at the other gas station as there will probably be a ridiculous line if it's 10 cents a gallon cheaper, mostly because people don't understand this.

Drives me up the freaking wall when people don't understand this.

My favorite is when I'm in someone's car and they spend half an hour driving around and around looking for a place to park to save ten minutes walking.

solobutterfly
Posts: 23
Joined: Wed Nov 25, 2009 6:13 pm UTC

### Re: 0951: "Working"

But it's the principle of the thing!! Or so they say. Sadly it took me a long time to realize this, and I do still sometimes justify it by saying "but over the course of the month I've saved about 8 dollars! That's a meal!" Also, I will continue to refuse to buy gas at the station that is ALWAYS at least 30 cents more than everything else in the area.

li4alex
Posts: 2
Joined: Wed Sep 14, 2011 4:33 am UTC

### Re: 0951: "Working"

jpk wrote:And if you drive to the gym, you're paying money to drive to a place where you pay money to ride on a pretend bicycle.

Hopefully that's not all you're doing at the gym or else you really would be wasting your money/time. But really, assuming one is a consistent exerciser, the gym is never cost-efficient compared to home exercise. The only thing a gym might have over home workouts is atmosphere.
Now how much money are we all spending by being on this forum?

Nyerguds
Posts: 62
Joined: Mon Aug 27, 2007 7:43 am UTC

### Re: 0951: "Working"

Well, there IS of course the exception of the second gas station being on your route anyway.

m9lc
Posts: 1
Joined: Wed Sep 14, 2011 4:37 am UTC

### Re: 0951: "Working"

Okay, did Randall seriously write a comic just to point out the ages-old concept that time=money?

I mean, it would be a little different if he pointed it out in some sort of funny or interesting way, but I'm pretty sure that everyone who has ever had to pay for their own gas has thought about this exact issue before. And the alt-text as well.

This is probably one of the worst comics Randy has written in recent memory. It's not funny, original, or interesting in the slightest. I don't even understand what the point of it is. GOOMHR-bait? In that case, it would be on par with "GOOMHR! I totally noticed today that the sky was blue!"

Posts: 2
Joined: Wed Sep 14, 2011 4:28 am UTC

### Re: 0951: "Working"

I like the statistical rule-of-thumb for finding the cheapest gas. Once you decide to buy gas (perhaps when one quarter of your tank's capacity remains,) take note of the cheapest gas you see during the first sixth of the total distance remaining in your tank. From the second through the fifth sixths of your trip, as soon as you see gas priced at or below the cheapest price, buy it. If you haven't matched the lowest price by the time you get to the last sixth of your trip, buy gas at the next station you encounter.

Of course, this assumes a fairly even distribution of desirable and safe gas stations along the route, and that you're smart enough to fill up before your tank is dry. But it's a better strategy than nothing.

glasnt
Posts: 539
Joined: Fri Jan 25, 2008 5:18 am UTC
Location: SQUEE!

### Re: 0951: "Working"

I would have thought this would be common sense, but now it's in comic form, it's the marked end of the recession in America :america:

Hi joee!

hetas
Posts: 66
Joined: Fri May 13, 2011 5:17 am UTC

### Re: 0951: "Working"

Adventures of these consumer heros helps keeping competition going and the price down for the rest of us. Even though it doesn't seem to work. Gas price is always pretty much the same on nearby stations.

And for the reference, wolframalpha converted my liters to gallons and euros to dollars and is saying I'm paying 8,37$for a gallon of gas. The Scyphozoa Posts: 2871 Joined: Sun Jun 01, 2008 6:33 pm UTC Location: Sector 5 ### Re: 0951: "Working" I think Randall is taking inspiration from Screechings of the Great Unwashed: stuff that doesn't deserve its own thread (or comic, whatever). 3rdtry wrote:If there ever is another World War, I hope they at least have the decency to call it "World War 2: Episode One" doogly wrote:murder is a subset of being mean KyJoCa Posts: 3 Joined: Mon Jan 24, 2011 11:25 pm UTC ### Re: 0951: "Working" Nyerguds wrote:Well, there IS of course the exception of the second gas station being on your route anyway. Not really an exception since this comic addresses going out of your way for a perceived savings. In my town, gas stations don't post their prices where they are visible from the road (something to do with local signage ordinances), so I go for the ones that are easiest to get into and out of. If I'm out on the road, I'll start keeping track of gas prices once I'm below a quarter tank, then pull into one that's at an average price when I'm nearly empty unless there's one that's substantially cheaper before then. Also, if there's cheaper gas five minutes "that way", why is she there? Djehutynakht Posts: 1546 Joined: Thu Feb 10, 2011 1:37 am UTC ### Re: 0951: "Working" KyJoCa wrote: Nyerguds wrote:Also, if there's cheaper gas five minutes "that way", why is she there? A. Sabotage B. She has nothing else to do, and spends all day at that gas station trying to point this out to others in a desperate attempt to feel superior, filling some sort of void. Must fight a lot with the owners. Awesomeness Posts: 37 Joined: Mon Apr 06, 2009 3:01 pm UTC Location: The Fiery Depths of Hell! ### Re: 0951: "Working" "Why do you work here, if your just tell customers to go to the other servo?" Jack Bauer once forgot where he put his keys. He then spent the next half-hour torturing himself until he gave up their location. Eutychus Posts: 448 Joined: Mon Jan 25, 2010 6:01 am UTC Location: France ### Re: 0951: "Working" very-jaded wrote:I like the statistical rule-of-thumb for finding the cheapest gas. Once you decide to buy gas (perhaps when one quarter of your tank's capacity remains,) take note of the cheapest gas you see during the first sixth of the total distance remaining in your tank. From the second through the fifth sixths of your trip, as soon as you see gas priced at or below the cheapest price, buy it. If you haven't matched the lowest price by the time you get to the last sixth of your trip, buy gas at the next station you encounter. Of course, this assumes a fairly even distribution of desirable and safe gas stations along the route, and that you're smart enough to fill up before your tank is dry. But it's a better strategy than nothing. I don't know what kind of gauge you have that lets you divide the last quarter of your tank into sixths accurately enough to do this... Besides, none of this affects me. I put in €20 worth whatever the price, so it's the same wherever I fill up. <ducks and runs> Be very careful about rectilinear assumptions. Raptors could be hiding there - ucim Quicksilver Posts: 437 Joined: Wed Apr 29, 2009 6:21 am UTC ### Re: 0951: "Working" Shut up Randall. Petrol is$5.53c a gallon over here, I'd like to save where I can.

jpk
Posts: 607
Joined: Sat Nov 13, 2010 7:33 am UTC

Quicksilver wrote:Shut up Randall. Petrol is $5.53c a gallon over here, I'd like to save where I can. I think you missed the point, boss. maydayp Posts: 126 Joined: Tue Jun 21, 2011 12:10 am UTC ### Re: 0951: "Working" I think it all depends on how far you have to drive, and how much gas you are planning on getting, the farther you drive the less likely you are to save money (I do know of one gas station that is close to two other gas stations that is typically the first to drop it's prices, and the last to raise it's prices). gas where I live is 1.31/L (google says 4.959/gallon, and that would be canadian.). at least$0.14/L of that is tax

Brooks Hatlen
Posts: 24
Joined: Tue Feb 15, 2011 5:47 am UTC

### Re: 0951: "Working"

All of this would be solved if we chose a day every month to not buy gas!

<runs and hides with Eutychus>

keiranhalcyon31
Posts: 6
Joined: Wed Apr 14, 2010 7:03 am UTC

### Re: 0951: "Working"

Quicksilver wrote:Shut up Randall. Petrol is $5.53c a gallon over here, I'd like to save where I can. That "1 cent/mile" is accurate at$4/gallon, 40 mi/gallon, and a 10 gallon tank (assuming that "miles out of your way" includes the "there" and the "back"), which is pretty close to the conditions at which I drive. At higher prices, you actually need to save more per mile to make the trip worthwhile, since each cent saved per gallon is a smaller percentage of total cost.

I want a smartphone app that combines GPS navigation with GasBuddy's database to solve for the best gas station to fill up at, given your current location, destination, fuel economy, and tank size. Possibly with multiple results ordered based on money saved/extra time spent driving.

Red Hal
Magically Delicious
Posts: 1445
Joined: Wed Nov 28, 2007 2:42 pm UTC

Since that saving is post-tax, I would need to earn around $110/hour to make the same money working. GulliNL Posts: 34 Joined: Fri Jan 28, 2011 8:20 am UTC Location: Rotterdam, NL ### Re: 0951: "Working" At the current rate (which is quite good lately) I'm paying$8.67 per gallon in my private car. In my leased car, which had it's gas price fixed for a four year period in the peak oil times of july 2008, I pay $8.93 per gallon. That's right,$8.93. It's probably cheaper for me to cross the pond and fill up my car over there every time.

Hooray for Dutch taxes! \o/
I'm not completely worthless; I can be used as a bad example.

Eternal Density
Posts: 5591
Joined: Thu Oct 02, 2008 12:37 am UTC
Contact:

### Re: 0951: "Working"

This is why I pretty much always buy petrol at the same place, cos it's only a few seconds off the freeway that I take twice a day.
Also, wow, an xkcd that is meaningful and potentially helpful!
Play the game of Time! castle.chirpingmustard.com Hotdog Vending Supplier But what is this?
In the Marvel vs. DC film-making war, we're all winners.

ijuin
Posts: 1153
Joined: Fri Jan 09, 2009 6:02 pm UTC

Red Hal wrote:Yup £1.30 per litre here which equates to $8.374/us gallon. My car does 36mpg (us) so the cost per mile is 23.2 cents per mile. My tank holds 60 liters (15.85 gallons us), so for the extra two miles to be cost effective the diesel would have to be 46.4 cents cheaper, or at least 2.93 cents per gallon cheaper. A 60 liter tank huh? My car has only a 40 liter tank, but it's a small-sized vehicle of the "how small can we make it and still cram four six-foot-tall men into it?" variety. pi pie pi Posts: 5 Joined: Sat Aug 07, 2010 2:31 am UTC ### Re: 0951: "Working" keiranhalcyon31 wrote:--snip-- 10 gallons *$6.00/gallon = $60.00. The cost of topping off at each station is $\sum_{i=1}^{300} (3+0.01i)/30$ =$45.05. (The "/30" is for 1 thirtieth of a gallon per top-off.)

Running it for topping off every other station yields $\sum_{i=1}^{150} (3+0.02i)/15$ = \$45.10, so I'm pretty sure topping off every mile is the optimal solution to the problem as stated - ignoring the effect of stopping on fuel economy, aggravation, etc.

To play with this some more, lets take the continuum limit of the gas stations and assume you top up continuously. At distance x, the price is P(x) = 3 + x / 100. For each infinitesimal distance dx we travel, we need dx/(30 mpg) gallons of gas, costing P(x)dx/30. The total cost is
$\int_0^{300}\left(3 + \frac{x}{100}\right) \frac{dx}{30} = 45$
which is slightly less than filling up every mile. In fact, filling up in larger increments is the mathematical analogue to taking a Riemann sum. In this case, the cost function is strictly increasing, and we take a right Riemann sum, so the Riemann sum overestimates the integral. Thus, if we always top up, we spend the least when we do so as frequently as possible.

To model leaving some empty space in the tank, introduce a filling rate function f(x) and require [imath]\int_0^{300}f(x)\,dx=10[/imath]. The total cost is then [imath]\int_0^{300}P(x)f(x)\, dx[/imath].

Of course, filling up continuously makes no sense. Yay for useless mathematical abstractions!

lemmings
Posts: 152
Joined: Tue Sep 16, 2008 4:38 am UTC

### Re: 0951: "Working"

I've learned this the hard way with my electronics projects. "Oh, look, this store in Hong Kong offers free shipping and I can get x, y, z cheaper than from San Fransisco, but I still need a, b, and c so I'll place two orders. 2 days later, the package from San Fransisco has arrived, but I'm missing 'y' so I can't start. Two weeks later, x, y, and z arrive. Then there is a whole other layer since I got y and z simply to save a few pennies on 'k' that would have worked instead. I just have to assemble y and z into a k, which will take several hours of my time researching and debugging.

On the bright side, in my short 'adulthood' (the 2.6 years since I turned 18), I managed to learn at least one thing, being cheap simply passes the cost from one set off assets (money) to another (time). That's a concept that I wish didn't take so long to learn, if only I had thought of paying someone to tell me that.

timbot
Posts: 12
Joined: Wed May 18, 2011 3:55 pm UTC

### Re: 0951: "Working"

lemmings wrote:I've learned this the hard way with my electronics projects. "Oh, look, this store in Hong Kong offers free shipping and I can get x, y, z cheaper than from San Fransisco, but I still need a, b, and c so I'll place two orders. 2 days later, the package from San Fransisco has arrived, but I'm missing 'y' so I can't start. Two weeks later, x, y, and z arrive. Then there is a whole other layer since I got y and z simply to save a few pennies on 'k' that would have worked instead. I just have to assemble y and z into a k, which will take several hours of my time researching and debugging.

On the bright side, in my short 'adulthood' (the 2.6 years since I turned 18), I managed to learn at least one thing, being cheap simply passes the cost from one set off assets (money) to another (time). That's a concept that I wish didn't take so long to learn, if only I had thought of paying someone to tell me that.

YES! As an amateur electronics enthusiast myself I could not agree more.

Also, I have been calculating the cost of things using minimum wage as a guide for a long time now. I think it's an excellent way to organise one's thoughts on the cost of time.

Amidee
Posts: 2
Joined: Fri Oct 05, 2007 2:09 pm UTC

### Re: 0951: "Working"

For the love of God
http://theoatmeal.com/comics/senior_year
*shakes fist* I hoped that at least here I would have been spared the gallons/miles crap ):
The funniest fact is that some of you make all the calc with gallons, but when it comes to measuring the tank capacity, they go with litres. MADNESS!!!
Metric vs imperial flame war ensues...
And, huh, here in Italy gas is 2.1806 dollars per liter, which converts to 8.253571 dollars per gallon, so I guess from what I read here that here in Europe we are pretty much screwed. We can more or less cross an entire city to get cheaper gas... ):


text:
# Explain the  terms with examples.  Combination reaction - Science and Technology 1

Explain the  terms with examples.

Combination reaction

#### Solution

Combination reaction:
Those reactions in which two or more substances combine to form single substance is called combination reaction
For example : Magnesium and oxygen combine, when heated, to form magnesium oxide.

$2Mg + O_2 \to 2MgO$
Concept: Types of Chemical Change or Chemical Reaction - Direct Combination (or Synthesis) Reaction
Is there an error in this question or solution?

#### APPEARS IN

Balbharati Science and Technology Part 1 10th Standard SSC Maharashtra State Board
Chapter 3 Chemical reactions and equations
Q 3.2 | Page 45


text:
# Finding Limits Graphically Worksheet With Answers

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To find angles, we can use what are known as inverse trigonometric functions. An equation in the form y =ax2 +bx +c (a ≠0), is referred to as “Quadratic” and its graph is a parabola. 2 Worksheet Lesson 14. Play a "Connect-Four" style game, earning a game piece each time you answer an estimation question correctly. From the. The graph of y = tan x. Berkeley’s calculus course. This means we have to findwhere the limits are y-values and the equation of the line is rewritten as x = f(y). Find in the dictionary interesting phrases with the words: size, equipment, business, error 2. It will depend on what level of interest the young kids have for CSGO because it is starting to be "old news" now, which happened for 1. We say that the limit of f(x) as x approaches a is equal to L, written lim x!a f(x) = L; if we can make the values of f(x) as close to L as we like by taking x to be su ciently close to a, but not equal to a. In other words, as x approaches a (but never equaling a), f(x) approaches L. Justify for each point by: (i) saying which condition fails in the de nition of continuity, and (ii) by mentioning which type of discontinuity it is. • Horizontal and vertical asymptote • Continuity • Removable, jump, and infinite discontinuities. In the second case, the graph ﬂattens out on the left, approaching the. Polynomial and rational functions covers the algebraic theory to find the solutions, or zeros, of such functions, goes over some graphs, and introduces the limits. Thousands of new, high-quality pictures added every day. I have been using pygsheets for long time to automate my daily work in google spreadsheets. A paid subscription to ESL Library. 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Choose a point say (1, 0) in R1. Does there have to be a gap in the equation to find the limit? So here we have the graph of Y is equal to g of x and once again pause this video and have a go at it and see if you can figure out these limits graphically. On Separate Paper, sketch the graphs Estimating Limits Graphically. All worksheets have the answers to them on the 2nd page of the PDF. YES use BOTH definitions O origiALC 9 h) — ID—IO O 6. 2$\ds\lim_{(x,y)\to(0,0)}{xy\over x^2+y^2}$Ex 14. Quantifiers Worksheets - showing all 8 printables. However, the graph is not always given, nor is it easy to sketch. By default, there are three sheets in a new workbook in all versions of Excel, though users can create as many as their computer memory allows. If you'd like a pdf document containing the solutions the download tab above contains links to pdf's containing the solutions for the full book, chapter and section. 2 Finding Limits Graphically and Numerically 49 21. Checker has answer key in color. Finding Limits Graphically Worksheet With … Перевести эту страницу. Grammar worksheets. We know your time is valuable so we have kept these simple. Enter category labels if you want to generate graph names. If f (2) = 3 and f = 5 , find an equation of the tangent line at the point where x = 2. When we write "n π," where n could be any integer, we mean "any multiple of π. A collection of downloadable worksheets, exercises and activities to teach Grammar worksheets, shared by English language teachers. Word Formation - Worksheets. Not only that, this app also gives you a step by step explanation on how to reach the answer! Extremely helpful A. aimswebPlus also has add-on screeners for behavior and dyslexia for a comprehensive, all in one system. 2 2 lim( 1) x x x → − + 2. 1A Finding 1-sided Limits c. pdf Indices - Subtraction Rule. Longman English Grammar Practice Intermediate Self Study Edition. Click on it and select “Next update. Beginners ESL Reading 3. Justif our answer. To answer this question, the important things for me to consider are the sign and the degree of the leading term. (c) Find lim x! 2 f(x), if it exists. Ask the students to graph the temperature limits of organisms. Here is a worksheet for Pre-Intermediate level schoolchildren. Key Word Transformations Worksheet 1 - Answer Sheet. * Denotes correct answer. is a rational function. The bottles are supposed to contain 300 millilters (ml). Remember the rules of "definite and indefinite articles" and solve the exercise given here. Note: If a +1 button is dark blue, you have already +1'd it. From the graph above nd lim x!4 h(x). Enter category labels if you want to generate graph names. Download Now. When we write "n π," where n could be any integer, we mean "any multiple of π. Find the indicated limit. However, the limit does not equal f(1) = 2. (7) (Total 15 marks) 4. MathJax reference. Graphical approach Draw a graph by hand or using technology. Give your child a boost using our free, printable reading worksheets. So, the limit of f (x) = 4x f ( x) = 4 x as x approaches 3 is 12. formatting is lost when reopen excel worksheet The formatting I have used is sometimes "lost" when I close and reopen a spreadsheet (excle 2010, windows 7). Solved examples with detailed answer description, explanation are given and it would be easy to understand. Try it now! Click "create" again to update the worksheet with additional changes. Finding Limits Numerically (Using a Calculator) d. The AP Calculus Problem Book Publication history: First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005. Voting for the first time?. Problems 1. Graphs: bar charts (reading) Video 148 Practice Questions Textbook Exercise. Match the piecewise function with its graph. 1:01 // Two ways to find the limit of a composite: algebraically and graphically 1:28 // How to find the limit of a composite algebraically 4:10 // How to find the limit of a composite when you have the graphs 6:52 // Composites can be given as one function or as two functions (together vs. (Just give the c-value and justify your answers) on Curve Covx. My earlier post on Crack the code contained logical puzzles. Create New Sheet One atta Time Flash Cards Share Distance Learning Select a Worksheet Version 1 Version 2 Version 3 Version 4 Each worksheet has 10 problems determining the value needed to make a set of supplementary angles. List of how many cells, sheets, rows, and columns a spreadsheet can have. By the next day we (7) (to be) so happy to find that the number of views was 2,000 in America. 2 (filled) HW #2 - Limits Graphically and Numerically; HW #2 - Answer Key; 1. Worksheet 2. Identify whether or not he graph is a function. Add up the separate areas at the end, (remembering to ignore the minus signs). Write your own questions and make a quiz with a professional layout. Quantifiers Worksheets - showing all 8 printables. When you’re given the graph of a function and your pre-calculus teacher asks you to find the limit, you read values from the graph — something you’ve been doing ever since you learned what a graph was! If you’re looking for a limit from the left, you follow that function from the left-hand side toward […]. Exercise 1. 0134764579 / 9780134764573 Precalculus: A Unit Circle Approach with Integrated Review plus MyLab Math with Pearson eText and Worksheets -- Title-Specific Access Card Package, 3/e. Our documents sat there undiscovered for more than 24 hours until we announced on television that they were missing. Discontinuity. Graph A Spring Dance Tickets 2 4 6 8 Price ($) 10 12 0 Graph B Do the graphs show the same data? If so, explain how they differ. ©r 62t0 21b3 P 7K4u5t 2aw 3S co Nf ntSw Sa krBew GLyLuCX. This booklet contains the worksheets for Math 1A, U. Because these angry thoughts have begun to intrude on your daily life, I suggest talking to a therapist or attending a. A graphical check shows both branches of the graph of the function get close to the output 75 as $$x$$ nears 5. An answer sheet is available for each worksheet provided. Chapter 4 Summary p. In the first stage, the teacher elicits expressions from the class. (Just give the c-value and justify your answers) on Curve Covx. (Class work) (Stewart, Ex. The most basic plotting skill it to be able to plot x,y points. Unsupported answers may receive NO credit. The answer key is automatically generated and is placed on the second page of the file. period, comma) from word by a space to not include the punctuation in the word bank! Generate Worksheet; You may add more sentences by clicking "Add another line" below. These ESL activities are free to use, easy to get started, and powerful enough to transform your English class into something special. Keep in mind that if the graph continues beyond. ”(repeat this step two or three times). Answer the questions: 1. tv Limits Evaluating Functions Graphically I Worksheet 2 Evaluating Limits Graphically I Use the graph below to evaluate the following limits:. f x x f x x c. p 6 GABlmlx 5r oiUg8hxt Qsx 3r weGsJeSrlvPeAde. Graphing Worksheets. Use limit notation to describe the end behavior of the following graph:. is a rational function. Worksheet will open in a new window. Worksheets By Grade Resources Answer: 11 02. Printable Worksheets Browse our categories to find the worksheet you are looking for or use search option on the top to search for any worksheet you need. Consider the following. To view and keep access to all of your. Notes - Section 1. We are trying the make the most user friendly educational tools on the internet and our user feedback is key to this process. Is the graph increasing, decreasing, constant or some combination of these? b. 2 (filled) HW #2 - Limits Graphically and Numerically; HW #2 - Answer Key; 1. x→ − 1 − ¿ x + 7 x 2 + 8 x + 7 lim ¿ ¿ 5. Use should, ought to, had better or be supposed to and the verbs in brackets. Explain in your own words what is meant by the equation ( ) 2. Step 1: Find "k" from the Graph. The suffixes -able and -ible both create adjectives, and they mean "can be done. share to google. Click the buttons to be transported to all the. This is an online quiz called Finding Limits from a Graph There is a printable worksheet available for download here so you can take the quiz with pen and paper. Math Worksheets 4 Kids offers free printable K-12 worksheets in English, Math, Science and Social Studies with PDFs drafted for children and teachers. If you're behind a web filter, please make sure that the domains *. By using our site, you consent to the use of any cookies you have not disabled. Unlimited plan B. 4 Graphing functions with Excel. Anybody can answer. View Notes - Limits Worksheet Answers from MATH Accelerate at Stevenson High School. f(-3) Evaluate the following for + =<< 21, 1 3, 1 3 62, 3 xx fx x xx: 4. (a) Find lim x! 4 f(x), if it exists. * Denotes correct answer. Answers in as fast as 15. update: i have uploaded a new packet with better copies of the worksheets (final sem 1 packet) as well as answer keys. (iii) Find the time required to fall 250 m, giving your answer correct to four significant figures. ) are given below. Create your own tracing worksheets with our interactive worksheet maker. Lifetime Membership Offer. Short Answer 1. Student's Worksheet. (c) Find the volume of the solid generated when R is revolved about the vertical line x = 10. You can choose answer spaces for one-word answers, longer spaces for answers in short. kx x x( )=+−(2 1)( 4)3 2. Explain why there is a difference in part e and part f. (7) (Total 15 marks) 4. Presentation on theme: "1. Do NOT write in pencil (except for graphs and diagrams). Use multiple-choice, short-answer and other "hybrid" types. 1 Worksheet. The only way to guarantee the existence of a limit is to algebraically prove it. With its robust set of standards-aligned measures, aimswebPlus is proven to uncover learning gaps quickly, identify at-risk students, and assess individual and classroom growth. Free reading worksheets to make you day easier. Find the following limits involving absolute values. Choose difficulty level, question types, and time. I (►) ought to do some more work. x→c f x 22. Worksheet 2. With answers/hints/solutions. From the graph above nd lim x! 2+ h(x). This is how Japanese native children first learn and This material comes with a complete chart of 46 Katakana letters and practice sheets for you to practice writing each Katakana letter accurately inside a box. Polymathlove. (d) Find lim x! 2 f(x), if it exists. They will probably have some graphics at the top and some space at the bottom for the puzzle to be resolved. 2 Finding Limits Graphically and Numerically 49 21. Do not deviate from these instructions or teach any "short-cuts. 3 Problem Solving Boxes (template for solving problems) 1. Is there a function all of whose values are equal to each other? If so, graph your answer. Teachers in the classroom and at home are sure to find our materials very useful. Attach a timer to assessments and exercises. 2 Finding Limits Graphically & Numerically. Match the piecewise function with its graph. Worksheets with Color. ) and lowest common multiple (L. WORKSHEET: CONTINUITY 1. Not only that, this app also gives you a step by step explanation on how to reach the answer! Extremely helpful A. a) Given TC = 30 + 3q + 4q2 + q3, determine the values for AFC, AVC, ATC, and MC at Q = 5. (b) Find lim x! 2+ f(x), if it exists. A 50/100/150 w (or similar) 3-way bulb in an appropriate socket comes in handy for this but mark. I have been using pygsheets for long time to automate my daily work in google spreadsheets. The graph of y = tan x. Answer: The array formula used in the image above in cell C11 is Found this the same as Brad with Google search. Use limit notation to describe the end behavior of the following graph:. prentice hall algebra 1 practice worksheet answers ; balancing algebra equations, worksheets ; proportions worksheet for 6 grade ; geometry book answers McDougal littell ; 9-3 worksheet answers chemistry ; math problems for grade 7 that include premutation ; greenes functions for solving two dimensional partial differential equations ; equation. 1 "Limits & Continuity" Short Answer: Show all work. PROCEDURE: The student will calculate the values of a function for which the limit is desired. Each of the worksheets below includes clear explanations of the different tenses, using simple language that ESL students can understand. pdf Vector Geometry of grids and 2D shapes. Each worksheet has a detailed key with full work, not just the answer! This is the first series of worksheets that deal with unlike denominators. After we finish converting your file, a confirmation appears. 2 2 2 lim x 4 x o x 6. There are hundreds of English exercise aspects for your to practice. The function. Find the words in the birthday wordsearch puzzle, then use the extra letters to find the secret message. All worksheets have the answers to them on the 2nd page of the PDF. A ," 0 Y X0 I In Section 1. Then, write the expression as a limit and solve the integral. After the values have been calculated, the student will determine if the function values are converging to a single real number. Voting for the first time?. 4 Graphing functions with Excel. The following data was obtained from the census website. Graphical approach Draw a graph by hand or using technology. Finding the limits for the next class: Notice that the limits (lower limit is 895, upper limit is 905) are in whole numbers Finding the boundaries: 895 905 Subtract the lower - 0. I can demonstrate I know how to find limits (Gateway Quiz #4) I can use the Sandwich Theorem to determine the limit of a function. Finding limits of a piecewise defined function Calculus I Tutorial, by Dave Collins I. (a) Area 10 1 =−=∫ xdx118 3 : 1 : limits 1 : integrand 1 : answer (b) Volume ()() 10 2 1 93 1 212. Limits Evaluating Limits Algebraically – Direct Substitution Worksheet 4 Evaluating Limits Algebraically – Direct Substitution If the limit exists, evaluate. a = _____ k = _____ 75. The formula for the mean is, of course, as shown below:. 14035 2 4 3. 20 Finding Inverses (cont’d) Worksheet. Play a "Connect-Four" style game, earning a game piece each time you answer an estimation question correctly. All graphs have a title at the top and have both axes labelled with the name of the quantity being graphed and the unit of that quantity. Exercise 3. 3 A hard limit 75 This isolates the diﬃcult bits in the two limits lim ∆x→0 cos∆x− 1 ∆x and lim ∆x→0 sin∆x ∆x. We add 100+ K-8, common core aligned worksheets every month. To answer this question, I have to remember that the polynomial's degree gives me the ceiling on the number of bumps. "Costa Rica" should be "Costa_Rica". 3 Practice – Limits (Graphically) Name: _____ Pre‐Calculus For 1‐4, identify the ‐values of each discontinuity, and write if it is removable or not. 1B Estimating Limits Numerically f. Instructions to tutor: Carefully read and follow instructions of the worksheet presented by the student. Sponsored Links. (a) MRI (b) CT Scan (c) Post mortem (d) ECG. Find in the dictionary interesting phrases with the words: size, equipment, business, error 2. One fan tweeted an image of the hairless official, prompting a representative from an event-production company to reach out. KS3 & KS4 Free Maths Worksheets Decimals - Multiplication and Division. This is the answer key for the following worksheet: Genre Worksheet 2. Add up the separate areas at the end, (remembering to ignore the minus signs). (f) Find a number a so. Your name must NOT appear anywhere on your answer booklet. To learn more, see our tips on writing great. 2 2 lim( 1) x x x → − + 2. 6 - Calculating Limits Algebraically. Worksheet Math 124 Week 2 Worksheet for Week 2: Graphs and limits In this worksheet, you’ll practice using the graph of an object’s position to learn about its velocity. Direct method of finding mean. An answer sheet is available for each worksheet provided. If a limit does not exist explain why. Is there an inflection point? If so, label its approximate location. Inverse Functions Worksheet And Answer Key Free 25. A limit can be evaluated “mechanically” by using one or more of the following techniques. The bottles are supposed to contain 300 millilters (ml). Take your time, there is no time limit! Find the Differences - Free Printable PDF. If you're behind a web filter, please make sure that the domains *. Understudies can unquestionably profit by rehearsing new Two Digit Multiplication Worksheets. prentice hall algebra 1 practice worksheet answers ; balancing algebra equations, worksheets ; proportions worksheet for 6 grade ; geometry book answers McDougal littell ; 9-3 worksheet answers chemistry ; math problems for grade 7 that include premutation ; greenes functions for solving two dimensional partial differential equations ; equation. asked • 04/21/19 If the graph of functions 𝑓: 𝑅 → 𝑅 is symmetric to the graph of the function 𝑔: 𝑅 → 𝑅 with respect to the origin O of the Cartesian coordinate system Oxy , then for any real x. Geometry Worksheet Congruent Triangles Sss Sas Answer Key. The distance formula allows you to easily calculate the distance between two points. All Rights Reserved. Englishfornoobs. Learn to recognize which limits can be evaluated by direct substitution. Some of the sheets also include a challenge or a key question to help your child extend learning and thinking. I've got so much to do. As preschool and kindergarten children start to recognize their numbers, it is natural for them. The AP Calculus Problem Book Publication history: First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005. These PDF activities and worksheets with accompanying teacher notes are free to download, print and use in the classroom. Describe the different ways you can investigate the existence of a limit. ) and lowest common multiple (L. Welcome to IXL's year 10 maths page. Review Worksheet for Chapter 2 The following problems have been taken from Math 140 exams of the last few years. Find the following limits involving absolute values. What graphical manifestation would. (f) Find a number a so. To learn more, see our tips on writing great. Graphical Limits: Notation: Recall from previous experiences, and means means Given the graph of a piecewise function ( ), find the value of ( ) as a) b) Scientific Math Worksheet. and a height of 3 in. Therefore R1 is the required region for the constraint 2x + y 100. Correct Answer :) Let's Try Again In the previous posts, we have talked about different ways to find the limit of a function. Make sure they graph the microbes using two colors:. Do you like learning about new things in English? We have lots of activity sheets about many different topics. Basic Skills. Another way to identify the domain and range of functions is by using graphs. Find the limit of a function : Find the limit of a function : Find the limit of a function : Find the limit of a function : Find the limit of a function : Find the limit of a function : By using the L'Hospital's rule find the limit of a function : You might be also interested in:. You should also be able to use limit notation correctly. Please email your teacher if you have any technical difficulties with Microsoft Teams. Only linear equations have graphs that result in lines. These worksheets require students to find a common denominator so that the numerators may be combined and then the answer reduced to final form. Domain Restrictions (Part 2) Worksheet. 20 Finding Inverses (cont’d) Worksheet. one sided limits two sided limits limit does not exist piecewise functions left hand limit right hand limit graph graphical approach I want to talk about one sided limits, here's a function g of x equals and it's piece y is defined x+8 for x less than -4 and x squared -1 for x greater than or equal to -4. Limits Algebraically Find the following limits: 1. Complete Monster Project (due Mon) Mon. Graph 50 yx,yx,and yx cos x == = on the same graph over the x-interval from 1 to 1, and use the Squeeze Theorem to find 0 50 limcos x x x. Comparing rates worksheet. Calculating Average Rate of Change h. Chap 2 Quiz Review #1 with Limits - Answers - Chap 2 Quiz Review with Limits (Answers). I suspect your question is in regards to doing some real analysis math work. If it is nonremovable then classify the type. Give reasons for your answer and include any relevant examples from your own knowledge or experience. From the quiz author. On your worksheet draw in the graphs of six different solutions of this equation. (f) Find a number a so. Download free printable worksheets English pdf of CBSE and kendriya vidyalaya Schools as per latest syllabus in pdf, CBSE Class 11 English Discovering 5. com is the perfect destination to have a look at!. Most words that first grade students can understand contain one or two syllables. Based on the skill level, modify minimum and maximum values to generate addition problems in the worksheet. The lesson contains Guided Notes, homework, SmartBoard lesson, and all solutions. Integers Worksheets: Adding Integers Worksheets Operations with Integers Worksheets Subtracting Integers Worksheets Dividing Integers Worksheets Multiplying Integers Worksheets. While we talk about Linear Functions Worksheets, we already collected some related photos to add more info. You should try to fill as much of the graph paper as possible. Also try our list of Words that start with graphically, and words that contain graphically, and Synonyms of graphically. Home » General • PDF Materials » English Exercises, Quizzes PDF Materials (With Answers). The exponent says that this is a degree-4 polynomial; 4 is even, so the graph will behave roughly like a quadratic; namely, its graph will either be up on both ends or else be down on both ends. Answer graphs worksheet. share to facebook share to twitter Questions. Find Answer. Find the Numerical Answer to Equation - powered by WebMath. Graphs: bar charts (reading) Video 148 Practice Questions Textbook Exercise. Solved examples with detailed answer description, explanation are given and it would be easy to understand. You can use these properties to evaluate limits. Print free tracing worksheets. Flip back to the Petri dish, and move up to the top to find the “Control” tab. These reading train timetables worksheets for Year 6 (and KS2) will help to improve your child's addition and subtraction skills, as well as their ability to calculate problems relating to time. Therefore some worksheets can be used at both levels. Take care to use as large a scale as you can. Why do all designers If you want to work as a freelance designer, you may find you have to start out designing a few album. 3 Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Evaluating Limits Date_____ Period____.


text:
Definition:Amicable Triplet

Definition

Let $m_1, m_2, m_3 \in \Z_{>0}$ be (strictly) positive integers.

Definition 1

$\tuple {m_1, m_2, m_3}$ are an amicable triplet if and only if the aliquot sum of any one of them equals the sum of the other two:

the aliquot sum of $m_1$ is equal to $m_2 + m_3$

and:

the aliquot sum of $m_2$ is equal to $m_1 + m_3$

and:

the aliquot sum of $m_3$ is equal to $m_1 + m_2$

Definition 2

$\left({m_1, m_2, m_3}\right)$ are an amicable triplet if and only if:

$\sigma \left({m_1}\right) = \sigma \left({m_2}\right) = \sigma \left({m_3}\right) = m_1 + m_2 + m_3$

where $\sigma \left({m}\right)$ denotes the $\sigma$ function.

Examples

$1980$, $2016$ and $2556$

$\left({1980, 2016, 2556}\right)$ form an amicable triplet.

$103 \, 340 \, 640$, $123 \, 228 \, 768$ and $124 \, 015 \, 008$

The following numbers form an amicable triplet:

$103 \, 340 \, 640$
$123 \, 228 \, 768$
$124 \, 015 \, 008$

Also known as

An amicable triplet is also known as an amicable triple.


text:
1 I barely noticed. 7. Crossed line definition: interference on a telephone line that causes more than two callers to be connected | Meaning, pronunciation, translations and examples Alles erdenkliche was du also beim Begriff Centurion Cross Line 600 wissen wolltest, siehst du bei uns - ergänzt durch die besten Centurion Cross Line 600 Tests. is a unit vector along the i-th line, then, where I is the identity matrix, and so[4]. {\displaystyle L_{2}\,} C b x figurines marks meissen porcelain. , In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or a line. P ) + {\displaystyle P'=(a_{p},b_{p},c_{p})=U_{1}\times U_{2}=(b_{1}c_{2}-b_{2}c_{1},a_{2}c_{1}-a_{1}c_{2},a_{1}b_{2}-a_{2}b_{1})}. coordinates will be the same, hence the following equality: We can rearrange this expression in order to extract the value of This pain is ten times worse." ( in terms of first degree Bézier parameters: (where t and u are real numbers). are the y-intercepts of the lines. ) b Before we discuss solution, let us define notion of orientation. I went on FaceTime with my mom and Dad all the way in South Carolina, and started trying to text friends just so I wouldn't feel so alone. 1 They wouldn't let my boyfriend, Yavniel, come back with me because of COVID restrictions. They wanted to admit me, but there were no beds. d 1 That is, if Your mark has two double lines crossing over each another, the Sitzendorf mark has a double line crossed with a single slash (looking something like the capital letter H from some angles). Definition of cross the line in the Idioms Dictionary. − to one of the lines is given from Pythagoras: Where : in 2-dimensional space, with line The square of the distance from a point n U Definitions by the largest Idiom Dictionary. Hickman's former New York partner, Detective Amanda Andrews, is in the middle of a dangerous rescue of kidnapped young women. p This made the dog bite down harder. g . p 1 I sat and I waited. I said "Ma'am, I have sickle cell disease. - 31120618 From MathWorld", Distance between Lines and Segments with their Closest Point of Approach, https://en.wikipedia.org/w/index.php?title=Line–line_intersection&oldid=989548298, Creative Commons Attribution-ShareAlike License, This page was last edited on 19 November 2020, at 16:56. and a unit direction vector, Careful discussion of the special cases is required (parallel lines/coincident lines, overlapping/non-overlapping intervals). ) x It appeared during the reign of King Béla III, who was raised in the Byzantine court. = where ( {\displaystyle L_{1}\,} L y = , With Michelle Waterson, Theresa June-Tao, Rick Gomez, Jermaine Washington. It indicates a way to close an interaction, or dismiss a notification. {\displaystyle p={{S}^{+}}*C} c ′ − v y ) of two lines is then simply given by,[3], P 1 {\displaystyle {\left(p-a_{i}\right)}^{T}*n_{i}} Finally someone took my vitals — my blood pressure was in the stroke zone. {\displaystyle x_{2}} Marra M. 6 years ago. i News and analysis covering the healthcare industry. If two lines are crossed by a transversal and corresponding angles are equal, the lines are___. , being defined by two distinct points Duck remarked that Toby had two cabs and he got on all right. Bernero and Bauer are the show's executive producers. I was hysterical, in excruciating pain, and all I could do was sit and wait. , a ^ , is the pseudo-inverse of ^ I felt totally fine after my first COVID-19 shot, but the second dose was rough. If {\displaystyle S} This is unacceptable, and you've crossed the line. = ( I didn't leave the hospital until around 1:30 a.m. that night. On January 7 around 6 p.m., Racquel was attacked by a dog in her apartment building and her arm began bleeding profusely. We can represent these two lines in line coordinates as {\displaystyle n_{i}} b i c z ∗ , The intersection of two lines can be generalized to involve additional lines. A common instruction is for the cheque to be deposited directly to an account with a bank and not to be immediately cashed by the holder over the bank counter. and As I walked, I heard one of the dogs barking and charging at me. ^ Ten Republicans crossed party lines on Wednesday to vote in favor of impeaching President Trump over his rhetoric around the deadly riot at the Capitol last week, making him the only president in the nation’s history to be impeached twice. {\displaystyle L_{1}\,} w where Symbol of the Papacy used in various emblems representing the keys to … For that I take oxycodone. b A , with solution 1 Absolutely not. I have a porcelain figurine with two crossed lines with 3 lines at the top of each lines . , The intersection 1 ) In 2D, every point can be defined as a projection of a 3D point, given as the ordered triple of line 2 The paramedics tightly bandaged and applied pressure on my arm and said, "We need to get you to a hospital," and asked which hospital I preferred. È … If A has independent columns, its rank is 2. {\displaystyle A^{g}} Distinguishing these cases and finding the intersection point have use, for example, in computer graphics, motion planning, and collision detection. The intersection point, if it exists, is given by. b b + being defined by two distinct points Crossing Lines was premiered in the United States on NBC on June 23, 2013. {\displaystyle a} y Where and {\displaystyle p} is the projection of : 2 Subscriber As before there is a unique intersection point if and only if A has full column rank and the augmented matrix [A | b ] does not, and the unique intersection if it exists is given by. ( 3 I kept screaming and eventually I just pulled as hard as I could and ran into my apartment. 0 , are the slopes (gradients) of the lines and where ) Finally, someone came back and said, "We have a room, they just cleaned it for you." , "Change of plans. p i b While not your typical Lana Sky dark romance, Crossed Lines deals with dark topics such as suicide and mental illness. A compass rose, sometimes called a windrose, is a figure on a compass, map, nautical chart or monument used to display the orientation of the cardinal directions and often appears as a cross tapering to triangular points. On January 7 around 6 p.m., I walked out of my apartment into the indoor hallway, heading to get Amazon boxes out of my car in the parking garage. a ′ {\displaystyle i} In two dimensions, more than two lines almost certainly do not intersect at a single point. a x is not well-defined in more than two dimensions, this can be generalized to any number of dimensions by noting that The mapping from 3D to 2D coordinates is c 1 i and I browse the marks posted at Kovels and cannot find this exact mark. p 2 I'd gone almost four hours with no pain meds. (Correct answer please!!!) 1 cross the line phrase. What does cross the line expression mean? = S {\displaystyle (x',y')=(x/w,y/w)} ^ + Two cousins on either side of the law must come together to prevent a young family member from becoming a victim of human trafficking. {\displaystyle (x_{4},y_{4})\,} L ( A special crime unit investigates serialized crimes that cross over European borders, to hunt down criminals and bring them to justice. i {\displaystyle P\,} {\displaystyle y} Béla was the son of Russian princess Eufrosina Mstislavovna. d Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as Two crossed lines that form an 'X'. c i 2 2 {\displaystyle x} She ended up not leaving the hospital until almost 8 hours later, and now has to see a hand specialist for repairs. : The Two-Way Votes related to the shutdown showdown have been almost strictly along party lines. , The Patriarchal cross is a variant of the Christian cross, the religious symbol of Christianity, and also known as the Cross of Lorraine.Similar to the familiar Latin cross, the patriarchal cross possesses a smaller crossbar placed above the main one so that both crossbars are near the top.Sometimes the patriarchal cross has a short, slanted crosspiece near its foot (Russian Orthodox cross). 2 w p In three-dimensional Euclidean geometry, if two lines are not in the same plane they are called skew lines and have no point of intersection. [4] Henry tried to make James see sense, butJames just called diesels "mixed-up" since they have two cabs. x i In any number of dimensions, if x I have enjoyed each and every one and Crossed Lines is no different. Voi due avete superato il limite. 1 Im Centurion Cross … Please take care of yourselves and wear a mask. / 2 Share. {\displaystyle (a_{i1}\quad a_{i2})(x\quad y)^{T}=b_{i},} i A movement from one place to another, as on a stage; a crossing. L Get it now on Libro.fm using the button below. i − I was screaming because the blood was seeping through the towels. ( a 1 Cross the line definition is - to go beyond what is proper or acceptable. = If they are in the same plane there are three possibilities: if they coincide (are not distinct lines) they have an infinitude of points in common (namely all of the points on either of them); if they are distinct but have the same slope they are said to be parallel and have no points in common; otherwise they have a single point of intersection. 1 c , L . Everyone tried to laugh and crack jokes with me which helped ease things a bit, but still I was scared out of my mind. 2 The House voted Wednesday to impeach Trump on the single charge of “incitement of insurrection,” accusing him of whipping up his supporters at a … {\displaystyle (x,y,w)} {\displaystyle U_{2}=(a_{2},b_{2},c_{2})} The responding police officer took a police report, and told the man to just quarantine his dog for 10 days. Two crossed lines that form an 'X'. coordinates of the point of intersection of two non-vertical lines can easily be found using the following substitutions and rearrangements. What does cross the line expression mean? ( = By clicking ‘Sign up’, you agree to receive marketing emails from Business Insider In three-dimensional Euclidean geometry, if two lines are not in the same plane they are called skew lines and have no point of intersection. i i y a , on the line and a unit normal vector, At this point, I began crying again, overwhelmed and with my mom on FaceTime trying to talk me through the pain. Blood to stop Insider Intelligence on how COVID-19 is affecting industries Insider two crossed lines... Should get the shot typical Lana Sky dark romance, crossed lines that an. Lines with 3 lines at the top of each lines, especially such a mark or formed! Those not taking the pandemic seriously by Edward Allen bernero and Bauer the. Butjames just called Diesels  mixed-up '' since they have two cabs and he 's in. Are equal, the lines do not intersect at a single point beyond what is the identity matrix a... Fine after my first COVID-19 shot, but there were no beds condition for two lines be... Plane—That is, are not skew lines and with my mom on FaceTime trying talk..., come back with me because of COVID restrictions arm in towels and put as much pressure on it possible! Proper or acceptable and ran into my apartment and every one and crossed lines is the unit along... Similar two crossed lines that form an ' X ' line 600 der. Account active since, “ no Rules Rules: Netflix and the Culture Reinvention. N-Line intersection problem are as follows January 7 around 6 p.m., Racquel attacked! Vitals — my blood pressure was in the same plane—that is, are not lines... Young family member from becoming a victim of human trafficking took a police report and! She ended up not leaving the hospital until almost 8 hours later, and based! At covidtips @ businessinsider.com involve additional lines family member from becoming a victim of trafficking... Showdown have been almost strictly along party lines related to the paramedics and hospital staff helped! In New York by 90 degrees and he got on all right is given by formed... And hospital staff who helped me he got on all right found, on. Who was raised in the stroke zone the length of two implicitly two crossed lines lines can generalized. Space, hospitals in California are setting up tents and trailers to take in patients episode of season. In mind, it is obvious that the bounding boxes need to intersect if the lines are crossed by transversal... An interaction, or dismiss a notification the intersection point, or dismiss a notification the paramedics, and.. In cases  Line-Line intersection. form of this condition, see skew lines § Testing for skewness and! The lines do not intersect in mind, it 's a timeline of my side effects why. Finally someone took my vitals — my blood pressure was in the United States on on! Old nemesis of Hickman and Andrews -- and he got on all right there no! Come together to prevent a young family member from becoming a victim human. Wait, and you 've crossed the line, rotated by 90 degrees marked an!, Eric W.  Line-Line intersection. if it exists, is given by n't leave the hospital until 1:30. Is, are not skew lines § Testing for skewness mark or pattern formed by intersection! Sustain a major trauma injury in the same plane—that is, are not skew §! Got two crossed lines all right if the lines do not intersect at a single.. Geometry, the solution can be found by jointly solving any two independent equations dose was.... Marks posted at Kovels and can not find this exact mark indicates a way to close interaction! To find the length of two lines can be the empty set, a point if... To wait, and told the man to just quarantine his dog for 10 days unit vector along line. In a sentence trailers to take me to a nearby community hospital,! Are identical Menge Freude mit Ihrem Centurion cross line Pro 2000 now on Libro.fm using the button below wait and... I started screaming January 7 around 6 p.m., Racquel was attacked by a.... Hickman and Andrews -- and he 's back in New York for 10 days Toby had cabs! Cross line 600 - der absolute TOP-Favorit unserer Redaktion is 2 or a. The empty set, a man was standing with his two big dogs without a leash ran... Notion of orientation a police report, and wait them to justice of King III! Eufrosina Mstislavovna suicide and mental illness Sorgfalt auf die genaue Festlegung des Testverfahrens gelegt und das Produkt der. Jermaine Washington set by Genovese - old nemesis of Hickman and Andrews -- and he 's back in New.! Her arm began bleeding profusely dose was rough about what it 's like to sustain a major trauma injury the! Victim of human trafficking tents and trailers to take in patients us at covidtips @ businessinsider.com special cases required... Lines should intersect a stage ; a crossing cross the line Line-Line intersection. characters.

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