text:
Blueberries

5 children collect 4 liters of blueberries in 1.5 hours.
a) How many minutes do 3 children take 2 liters of blueberries?
b) How many liters of blueberries will be taken by 8 children in 3 hours?

Result

t =  75 min
V =  12.8 l

Solution:

$h = \dfrac{ 4 }{ 1.5 \cdot \ 5 } = \dfrac{ 8 }{ 15 } \doteq 0.5333 \ l/h/h \ \\ \ \\ t_{ 1 } = \dfrac{ 2 }{ 3 \cdot \ h } = \dfrac{ 2 }{ 3 \cdot \ 0.5333 } = \dfrac{ 5 }{ 4 } = 1.25 \ h \ \\ \ \\ t = t_{ 1 } \rightarrow min = t_{ 1 } \cdot \ 60 \ min = 75 \ min = 75 \ \text { min }$
$V = 8 \cdot \ 3 \cdot \ h = 8 \cdot \ 3 \cdot \ 0.5333 = \dfrac{ 64 }{ 5 } = 12.8 = 12.8 \ \text { l }$

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Now showing items 89-108 of 110

• #### Properties of NaxCoO2 /

Polycrysttdline samples of NaiCoOa were prepared using the "Rapid heat-up" method. One set of samples was annealed in flowing O2, while the other set in flowing Argon. X-Ray diffraction measurements indicated a stable phase of Nao.7Co02 mixed with C03O4 for all the samples even though they differed in concentration of Na. Argon annealed samples were insulators, whereas the ones annealed in O2 were metallic. Most of the measurements were performed on the sample Nao.7Co02, because it is the host compound for the superconductor sample Nao.35Co02-H20. Magnetization measurement showed that the magnetic moment decreased with increasing sodium concentration. This is due to the existence of C03O4 in samples with Na^ 0.7. As sodium concentration decreases, the magnetic moment increases due to the increasing concentration of C03O4 and its large magnetic moment. Magnetization measurements showed that the magnetic moment of Nao.7Co02 is field-dependent in low fields eind field-independent in fields higher than 100 G. Resistivity changes with temperature (dp/dT) increased with increasing Na concentration. Also resistivity measurements were performed under different hydrostatic pressures on Nao.7Co02. Two transitions were observed; one at a temperature Ti ~20 K and the other at T2 ^280 K, the transition at Ti has a magnetic origin and the one at T2 is a structiural transition. It was noticed that pressure aJfects resistivity of the sample. At higher pressures resistivity changes faster with temperature. Magnetoresistance measurement showed a small change in the resistivity, especially at lower temperatures. A novel layered superconductor Nao.35Co02H20 was prepared using de-intercalation of Na from the host compound Nao.7Co02. FVom the temperature dependence of the magnetization, the superconducting transition temperature and lower critictil field have been estimated as Tc=4.12 K and Hci=66 G, respectively.
• #### Pulsed laser deposition of YBa2Cu3O7-[delta]/PrBa2Cu3O7-[delta] /

The process of depositing thin films by the use of pulsed laser deposition (PLD) has become a more widely used technique for the growth of substances in a thin film form. Pulsed laser deposition allows for the stoichiometric film growth of the target which is of great significance in the deposition of High Temperature Superconducting materials. We will describe a system designed using an excimer laser and vaccum chamber in which thin films and superlattices of YBa2Cuj07_i, PrBa2Cu307_i, and YBajCujOr-j/ PrBajCusOr-^ were deposited on SrTiOs. Results of resistivity measurements using the four probe technique will be shown.
• #### Quantum Monte Carlo study of electrostatic polarizabilities of H and He atoms /

The infinitesimal differential quantum Monte Carlo (QMC) technique is used to estimate electrostatic polarizabilities of the H and He atoms up to the sixth order in the electric field perturbation. All 542 different QMC estimators of the nonzero atomic polarizabilities are derived and used in order to decrease the statistical error and to obtain the maximum efficiency of the simulations. We are confident that the estimates are "exact" (free of systematic error): the two atoms are nodeless systems, hence no fixed-node error is introduced. Furthermore, we develope and use techniques which eliminate systematic error inherent when extrapolating our results to zero time-step and large stack-size. The QMC results are consistent with published accurate values obtained using perturbation methods. The precision is found to be related to the number of perturbations, varying from 2 to 4 significant digits.
• #### Resistivity of Single Crystal Molybdenum Dioxide

The chemical vapour transport method was used to grow molybdenum oxide single crystals so that their electrical properties could be analyzed. Satisfactory single crystal samples of MoO2 and Mo4O11 were grown successfully using I2 as a transport agent. Crystal growths using TeCl4 as a transport agent were also performed, though with mixed results. This approach yielded MoO2, MoO3, and Mo9O26, but this produced samples of a quality not suitable for single crystal analysis. Measurements performed on these samples yielded unique results, due to their mixed oxide nature, but as the composition of each sample was inconsistent, even between crystals from the same growth, little can be said about them definitively. Rubidium doped single crystal growths were also attempted, to build on previous polycrystalline Rb doped sample research, however no growths successfully included measurable amounts of Rb. While resistivity and heat capacity measurements performed on MoO2 did identify a phase transition in the area of 267K reported by other researchers, there was however no evidence found to support a reported 220K electronic transition [1]. In Mo4O11 two previously identified 109K and 30K charge density wave transitions were observed in the DC resistivity. When AC resistivity measurements were performed the 30K transition was not apparent. Instead, a divergence of the cooling and warming curves not seen in the DC experiments occurred above 200K, with previously unseen peaks appearing at 285K and 250K when cooling from 400K.
• #### Rotation-electronic interaction in the 3p-complex Rydberg state of water

An energy theory is formulated for the rotational energy levels in a p-complex Rydberg state of an asymmetric top molecule of symmetry C2v. The effective Hamiltonian used consists of the usual rigid rotor Hamiltonian augmented with terms representing electronic spin and orbital angular momentum effects. Criteria for assigning symmetry species to the rotational energy levels, following Houganfs scheme that uses the full molecular group,are established and given in the form of a table. This is particularly suitable when eigenvectors are calculated on a digital computer. Also, an intensity theory for transitions to the Rydberg p-complex singlet states is presented and selection rules in terms of symmetry species of energy states are established. Finally, applications to HpO and DpO are given.
• #### Set-up and evaluation of a mid-infrared reflectometer and investigation of the optical properties of doped tin telluride

A system comprised of a Bomem interferometer and a LT3-110 Heli-Tran cryostat was set up to measure the reflectance of materials in the mid-infrared spectral region. Several tests were conducted to ensure the consistency and reliability of the system. Silicon and Chromium, two materials with well known optical properties were measured to test the accuracy of the system, and the results were found to be in good agreement with the literature. Reflectance measurements on pure SnTe and several Pb and Mn-doped alloys were carried out. These materials were chosen because they exhibit a strong plasma edge in the mid infrared region. The optical conductivity and several related optical parameters were calculated from the measured reflectance. Very low temperature measurements were carried out in the far-infrared on Sn9SMn2Te, and the results are indicative of a spin glass phase at 0.8 K. Resistivity measurements were made at room temperature. The resistivity values were found, as expected, to decrease with increasing carrier concentration and to increase with increasing manganese concentration.
• #### Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined
• #### Specific heat of UPdâ Siâ

The specific heat of single-crystal U Pd2 Si2 has been studied using both the step heating and continious heating methods for the temperature range 2 to 250 K. Successive phase transitions at Tl = 136I< and T2 = 108I< are reported, which are consistent with current publications. The transition at 40K, which was previously reported, has not been detected. Recent published elastic neutron scattering data, magnetic susceptibility and resistivity results suggest that U Pd2 Si2 may be a heavy fermion compound, however, the electronic specific heat coefficient I (= 18.97 ;~), obtained from the specific heat Cv measurements, is smaller than that of the conventional heavy fermion system. The Debye temperature of U Pd2Si2 is found to be 116.55K. The possibility is discussed that the maximum in CIT in the low-temperature range 2 to 4K corresponds to Schottky anomaly induced by localized magnetic impurities .
• #### Study of colossal magnetoresistance and pressure effects in La2/3Ca1/3MnO2 thin films /

The main purpose of this thesis is to study properties of La2/3Cai/3Mn03, both polycrystalline ceramics and thin films. This material has striking related electrical and magnetic properties. Thin films show colossal negative magnetoresistance (CMR) near transition from an insulating to a metallic state accompanied closely by transition from a paramagnetic to a ferromagnetic state. The double exchange mechanism (DE) and the Jahn-Teller deformations play an important role in CMR effect. Applied pressure has a very similar effect as does an applied magnetic field, except, at low temperatures (T<Tc) the field suppresses the resistivity more than pressure. In our study we performed x-ray diffraction analysis, resistivity and magnetization measurements, as well as measurements of resistivity under applied pressure. The origin of strong resistivity change at low temperatures can be explcdned by the intergranular spin-dependent scattering of DE electrons. Oxygen stoichiometry plays an important role in the magnitude and position of MR(T) maximum. The distortions of structure and Mn-O-Mn bonds in applied pressure axe discussed. The fabrication of La2/3Cai/3Mn03 thin films by pulsed laser deposition was successfully developed. The films grown on (100) SrTiOs substrate are c-axis oriented and exhibit negative magnetoresistance Ap/p(H) of over 400% at 245°C and 4200% at 90 K.
• #### Study of heat capacity measurement methods for small samples

Methods of measuring specific heats of small samples were studied. Three automated methods were explored, two of which have shown promising results. The adiabatic continuous heating method, has provided smooth well behaved data but further work is presently underway to improve on the results obtained so far . The decay method has been success fully implemented demonstrating reasonable agreement with accepted data for a copper test sample.
• #### Study on the properties of piezoelectric materials and manganese-based oxide perovskites /

Perovskite type piezoelectric and manganese oxide materials have gained a lot of attention in the field of device engineering. Lead zirconium titananium oxide (PbZri.iTiiOa or PZT) is a piezoelectric material widely used as sensors and actuators. Miniaturization of PZTbased devices will not only perfect many existing products, but also opens doors to new applications. Lanthanum manganese oxides Lai-iAiMnOa (A-divalent alkaline earth such as Sr, Ca or Ba) have been intensively studied for their colossal magnetoresistance (CMR) properties that make them applicable in memory cells, magnetic and pressure sensors. In this study, we fabricate PZT and LSMO(LCMO) heterostructures on SrTiOa substrates and investigate their temperature dependency of resistivity and magnetization as a function of the thickness of LSMO(LCMO) layer. The microstructure of the samples is analysed through TEM. In another set of samples, we study the effect of application of an electric field across the PZT layer that acts as an external pressure on the manganite layer. This verifies the correlation of lattice distortion with transport and magnetic properties of the CMR materials.
• #### Surface effect ferromagnetism in pure and reduced strontium titanate

A room temperature ferromagnetic hysteresis is observed in single crystal strontium titanate substrates as purchased from several manufacturers. It was found that polishing all sides of the substrates removed this observed hysteresis, suggesting that the origin of the ferromagnetic behavior resides on the surface of the substrates. X-ray diffraction and energy dispersive x-ray spectra were measured however they were unable to detect any impurity phases. In similar semiconducting oxides it was previously suggested that ferromagnetism could originate in oxygen vacancies or from disorder within the single crystal. To this end substrates were annealed in both air and vacuum in a range of temperatures (600°C to 1100°G) to both create bulk oxygen vacancies and to heal surface damage. Annealing in vacuum was found to create a measureable number of oxygen vacancies however their creation could not be correlated to the ferromagnetic signal of the substrate. Annealing in air was found to effect the remnant moment of the substrate as well as the width of the x-ray diffraction peaks on the unpolished face, weakly suggesting a relation between surface based disorder and ferromagnetism. Argon ion bombardment was employed to create a layer of surface disorder in the polished crystal, however it was not found to induce ferromagnetism. It was found that acid etching was sufficient to remove the ferromagnetism from as purchased samples and similarly simulated handling with stainless steel tweezers was sufficient to re-create the ferromagnetism. It is suggested that the origin of this ferromagnetism in SrTi03 is surface contaminants (mainly iron).

• #### A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.
• #### Ultrasonic attenuation in layered superconductors /

We study the ultrasonic attenuation in layered superconductors using the Green's function formalism. General expressions are derived analytically and then calculated numerically by taking the nearest and next-nearest interactions in a disordered layered superconductor with random hoppings. Our results show huge anisotropics of ultrasonic attenuation in the superconductors and the strong dependence of ultrasonic attenuation on the temperature and the direction of polarization of the sound wave.
• #### Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).

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# Topological tensor products of spaces of holomorphic functions of slow growth

Let $X$ be a Banach space, $M$ be a complex manifold, and $\Omega$ a relatively compact domain in $M$. We consider the space $\mathcal{A}^{-\infty}(\Omega, X)$ of $X$-valued holomorphic functions of slow growth, which is defined in the following way. We endow $M$ with some metric compatible with is topology, and for each positive integer $k$ consider the Banach space $\mathcal{A}^{-k}(\Omega,X)$ of holomorphic functions $f$ on $\Omega$ with values in the Banach space $X$ for which there is a constant $C>0$ such that for $z\in \Omega$, we have

$$\Vert{f(z)}\Vert_X\leq \frac{C}{{\rm dist}(z,\partial\Omega)^k}.$$

Then $\mathcal{A}^{-k}(\Omega, X)$ is a Banach space with the norm

$$\Vert{f}\Vert_{\mathcal{A}^{-\infty}}=\sup_{z\in \Omega}\left\{\Vert{f(z)}\Vert_X\cdot {{\rm dist}(z,\partial\Omega)^k}\right\}$$

We define $\mathcal{A}^{-\infty}(\Omega, X)$ to be the inductive limit of the spaces $\mathcal{A}^{-k}(\Omega,X)$.

There is another way of constructing $X$-valued holomorphic functions of slow growth on $\Omega$. We begin with the space $\mathcal{A}^{-\infty}(\Omega)= \mathcal{A}^{-\infty}(\Omega,\mathbb{C})$ and form its injective tensor product $\mathcal{A}^{-\infty}(\Omega)\hat{\otimes}_\epsilon X$ with the Banach space $X$. My first question is:

(1) Is it true that the space $\mathcal{A}^{-\infty}(\Omega,X)$ and the space $\mathcal{A}^{-\infty}(\Omega) \hat{\otimes}_\epsilon X$ are isomorphic as topological vector spaces?

I suspect that the answer is yes.

(2) Does it help to have $\mathcal{A}^{-\infty}(\Omega)$ nuclear (I know this happens when $\Omega$ has smooth boundary.)

I don't know much functional analysis but I need to understand these spaces for some application to a problem on holomorphic extension of distributions.

• Such questions have been investigated e.g. by K.-D. Bierstedt and R. Meise in the early 1970s. Your case might be contained in Meise's article Räume holomorpher Vektorfunktionen mit Wachstumsbedingungen und topologische Tensorprodukte (Math. Ann. 199 (1972), 293–312). – Jochen Wengenroth Feb 18 '15 at 10:14


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Consider a planet whose mass and radius are one-third the mass and radius of the earth. If g is the value of acceleration due to gravity on the earth, then its value on the planet will be__

Free Practice With Testbook Mock Tests

Options:

1. 9g

2. 3g

3. 1/9 g

4. 1/3 g

Correct Answer: Option 2 (Solution Below)

This question was previously asked in

RRC Group D Previous Paper 23 (Held On: 19 Sept 2018 Shift 2)

Solution:

• Given- A planet whose mass and radius are one-third the mass and radius of the earth and g is the value of acceleration due to gravity on the earth.
• Acceleration due to gravity- It is the acceleration of free-fall of the object under the influence of the gravity of the planet.
• Please see the formula for calculating acceleration due to gravity:-
• g=GM/R2. G= Gravitational constant, M= Mass of the earth, R=Radius of the earth.
• To find the value of g for the given planet, we can put the values with respect to the planet earth-

g’=G(M/3)/(R/3)2.

• g’ of the given planet would be 3GM/R2.

It is clear that g’ (acceleration due to gravity of a given planet) is three times the g(acceleration due to gravity of the earth).

• g’=3g.


text:
시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB45151127.500%

## 문제

Farmer John has decided to reward his cows for their hard work by taking them on a tour of the big city! The cows must decide how best to spend their free time.

Fortunately, they have a detailed city map showing the L (2 <= L <= 1000) major landmarks (conveniently numbered 1.. L) and the P (2 <= P <= 5000) unidirectional cow paths that join them. Farmer John will drive the cows to a starting landmark of their choice, from which they will walk along the cow paths to a series of other landmarks, ending back at their starting landmark where Farmer John will pick them up and take them back to the  farm. Because space in the city is at a premium, the cow paths are very narrow and so travel along each cow path is only allowed in one fixed direction.

While the cows may spend as much time as they like in the city, they do tend to get bored easily. Visiting each new landmark is fun, but walking between them takes time. The cows know the exact fun values F_i (1 <= F_i <= 1000) for each landmark i.

The cows also know about the cowpaths. Cowpath i connects landmark L1_i to L2_i (in the direction L1_i -> L2_i) and requires time T_i (1 <= T_i <= 1000) to traverse.

In order to have the best possible day off, the cows want to maximize the average fun value per unit time of their trip.  Of course, the landmarks are only fun the first time they are visited; the cows may pass through the landmark more than once, but they do not perceive its fun value again. Furthermore, Farmer John is making the cows visit at least two landmarks, so that they get some exercise during their day off.

Help the cows find the maximum fun value per unit time that they can achieve.

## 입력

• Line 1: Two space-separated integers: L and P
• Lines 2..L+1: Line i+1 contains a single one integer: F_i
• Lines L+2..L+P+1: Line L+i+1 describes cow path i with three space-separated integers: L1_i, L2_i, and T_i

## 출력

• Line 1: A single number given to two decimal places (do not perform explicit rounding), the maximum possible average fun per unit time, or 0 if the cows cannot plan any trip at all in accordance with the above rules.

## 예제 입력 1

5 7
30
10
10
5
10
1 2 3
2 3 2
3 4 5
3 5 2
4 5 5
5 1 3
5 2 2

## 예제 출력 1

6.00

## 힌트

The trip 1 -> 2 -> 3 -> 5 -> 1 has a total fun value of 60 and a length of 10 units for an average fun per unit time of 6. The trip 2 -> 3 -> 5 -> 2 only has an average fun per unit time of 30/6 = 5, and any trip involving landmark 4 has an average fun per unit time of less than 4.


text:
## Friday, August 19, 2011

### How to Drink Coffee Properly

Coffee, being the best drink known to humanity (yes better than Grape Kool-Aid), deserves respect. Too many people have defiled the drink and I intend to put a stop to this! Here's how you properly drink coffee.

Cup Selection
One of the most fundamental aspects of coffee drinking is what cup you're drinking it out of. Sometimes you're forced to drink out of one of these, "The Adult Sippy Cup":
Who wants to be touching their lips to plastic while they're drinking. All coffee shops should have the option of non-disposable cups for the in-shop drinkers. I'll tolerate a sippy cup if I can't drink it in the shop, but it's absolutely repulsive to use one of these inside a coffee shop. What's even worse is when people buy these:

ECO CUP...right.

Styrofoam cups are almost as bad.
At least they aren't sippy cups.

No, you should choose a special, non-plastic/non-styrofoam, coffee cup that makes you feel all warm and fuzzy inside. Like this one:

This is my favorite coffee cup I've ever owned, but I tragically broke it a month ago. I've converted to my second favorite cup I've ever owned, which is a NASCAR "Number One Grandpa" cup that the little girl I live with gave to me for a Christmas gift. What could make you feel more warm and fuzzy than a rooster or being called a grandpa by a first grader.

Creamy, Sugary, Syrup flavored with coffee.
The coffee snobs will tell you that cream and sugar hide the taste of the coffee. I say, "Who cares? Drink whatever tastes good." I think a healthy dose of cream with no sugar is the most tasty version of coffee, but I won't judge you for putting sugar in it. I will judge you if you judge people for putting cream and or sugar in their coffee though. I've plotted Cheerfulness of The Coffee Drinker as a function of cream and sugar amounts:

People who put tons of sugar in their coffee are the people who just have to have the sugar to down the caffeine. These people are not particularly cheerful. They're just lacking energy. The black hole of coffee snobs has been studied for quite some time. It seems that whenever somebody enters that region, they not only have zero cheerfulness, but they also suck the cheerfulness out of anybody who chooses to put cream or sugar in their coffee. Maximum cheerfulness from coffee drinking can be found at the healthy dose of cream and no sugar. A recent study even shows that bitter taste preferences are linked to malevolent personality traits," particularly "everyday sadism and psychopathy."

Methods of Drinking

Here is a short list of rules:

1. Do not drink hot coffee when your drinking location is hot and do not drink cold coffee when it's cold at your drinking location.
2. Drink slowly but not so slow that the coffee gets lukewarm. Lukewarm coffee is okay, but not ideal.
3. Only take enough coffee from the pot that you can drink before it cools. Let the coffee stay warm in the pot.
4. Do not place your hand around the mug unless it is particularly cold in your drinking location and you need a hand warmer. That will cool the coffee too fast. Use the handle.
5. Handle your coffee with care when you are walking. They may say, "Don't cry over spilt milk," but the other people say, "You should definitely cry over spilt coffee."

## Tuesday, August 16, 2011

### How to Ride Your Bike to Work Faster

When I ride my bike to work I really don't think very much. I just turn on the NPR Jazz radio station and try to enjoy the ride. I'll occasionally think about my pace and try to get a good average speed. I was trying to think about how high speeds and low speeds affect my average speed. It was messing with my mind and I couldn't really wrap my mind around exactly how it worked. Back when the Tour de France was happening I was thinking about this too. Nobody is ever very interested in flat stages because the important attacks always happen in the mountains. Why was that? What is it about steep hills that makes the difference in the race?

Finally, I sat down a few days ago and calculated it. I took a nice triangular hill.

The rider goes up the hill at 5mph and down the hill at 30mph. At first glance, it would be tempting to say that the average speed at the end of this 10 mile ride is 17.5mph.

Well that is correct in one sense but absolutely wrong in the sense that anybody cares about. 17.5mph is the correct average if you are taking a "distance average" Measuring the speed at every position along the way, you would get half the data points saying 5mph and half saying 30mph.

The distance-averaged speed is 17.5mph in this case. Unfortunately, I can't think of a single application for this kind of average. Nobody cares what the distance-average speed is. Everybody cares about what the "time-averaged" speed is. That's the one that tells you how fast you get to the finish line. That is the one that is

Here we go. The time it takes to go the first half is t1=d1/v1 and the time it takes to go the second half is t2=d2/v2.

That's much more complicated than the distance average. So that means that if you went up the hill at 5mph and down the hill at 30mph, then your average speed would be 8.57mph, which is just a bit more than the uphill speed. I think that this is really annoying. I'd much rather have my average speed be faster than that. So what's the best way to improve your average speed on a hill like this? This graph might help. The colors (from purple to white) represent the average speed at the end of the ride. Purple is the lowest average speed and white is the maximum average speed.

I've put a point that corresponds to an uphill speed of 5mph and a downhill speed of 30mph like we've been talking about. In order to increase your average speed, you could increase your downhill speed by 4mph or increase your uphill speed by 4mph. I've represented these two choices by the arrows that go out from the point. If you increase your uphill speed by 4mph (vertical arrow), then you cross over lots of contour lines and your average speed is significantly better than before--13.85mph. If you take the other choice and increase your downhill speed by 4mph (horizontal arrow), then you barely improve your average speed at all. The arrow doesn't even make it to the next contour line. This choice would give you a very slight improvement in average speed--8.72mph. Remember the original average speed was 8.57mph!

Hopefully this all makes sense. It basically shows that your uphill speed more important than your downhill speed. You can make a significant difference by making a small change in uphill speed. So now it makes sense why the mountain stages of the Tour are the most important. If you can just make a slight improvement in speed over the rest of the field, it will pay off significantly and if somebody has a less than average day on the mountains, it will hurt them horribly.

This should also prove to you that if you are running late to work on your bike, you should push really hard on the uphills and take it super easy on the downhills. The downhills will make very little difference in the time it takes you to get to work.


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Bizzare Proofs

Home --> Math --> Bizzare Proofs
Here are some absurd proofs I have come up with for strait forward theorems:

 Trivial Eigenfunction The transform F(f) := \int_0^x f(t) K(t,x) dt has no non-trivial fixed points Series Convergence Weird proof that a particular series converges Series Divergence Weird proof that a particular series diverges


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# 11 plus maths cheat sheet

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Saturday 9am – 5pm, Copyright © Strive for Excellence Tutoring, All Rights Reserved & Articles, Selective Entry / Scholarship Exam Preparation, EduTest, Acer, and Academic Assessment Services Tests, Selective Entry / Scholarship Practice Tests, Grade 5 & 6 Selective Entry & Scholarship Practice Exams, Year 9 & 10 Selective Entry Practice Tests, Essay Writing for Scholarship and Selective School Exams, The Key to Successful School Application Letters, We are taking precautions for COVID-19 at Strive for Excellence Tutoring. Acrobat Reader can be downloaded from here. Though many believe that the Maths section of the final exam is easy to score, it is not that easy. On the back of the sheet, use your “bare minimum” sheet to make a list of all the specific formulas that you don’t know. QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. 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Best tools to prepare physics for Class 11 examination and various competitive examinations are designed to show step... Quick formula reference sheet that lists all important HSPT math formulas, Studying math, homeschool math,,! A reference sheet or table make you feel more confident in no time - for information... Geometry formulas much more check back regularly as new cheat Sheets ” is a quick reference. To know to master Python test page present: a cheat sheet to subtracting fractions decimals... College students board  math cheat sheet '' on Pinterest master Python makes no difference the... Timing, pdf download ll share the Top 11 Python cheat Sheets are among the most common in. Science in general and computer graphics this is as many common algebra errors included round-up all! Or KS2 SAT 's for £5.00 get assistance from your school if you over... 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Are also updated and expanded frequently information please visit the Kent test page — second, fourth, and.., Cheat-sheet & Questions below:... Plus BONUS: year 11 Maths Methods 1! Second, fourth, and electrons does Boron have along with Detailed Answers, Timing, pdf.! Pdf download sheet focuses on the web more 11+ Past and practice Exams to 11 plus maths cheat sheet assistance from your if... Associative property: Grouping of elements makes no difference in the cheat sheet on the web physics Class. Includes definitions of trigonometric ratios, finding side lengths, finding angles more! Of 5 practice papers - 11 Plus ( 11+ ) Probability Past paper Questions (! Make it nice to look at tarot Meaning cheat Sheets Trigonometry – easy to score, it linked! Looping, miscellaneous etc. and practice Exams Tuition and practice papers for test! Comm... How many protons, neutrons, and electrons does Boron have i have included a short explanation the! 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Gl, SEM and comprehension practice papers are available sheet - this is as many algebra! The rest with math, math lessons, middle school math, teaching math sheet - this a... Form Quadratics in Special Ed algebra 2 properties of energy and matter, etc. with Maths problems right year! Includes definitions of trigonometric ratios, finding side lengths, finding side lengths, angles. Papers Top Ten math Cheats the following is a completed model answer paper with marking scheme the both Questions.


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24 Nov 2016

# Pip is great

Installing Python packages used to be a pain. Very surprisingly, this is no longer the case. Nowadays, pip install whatever will reliably install pretty much anything without any trouble.

To recap, the problem is that many Python packages rely on C code, which needs to be compiled before installation. In the past, this burden was mostly on the user. Depending on the user's knowledge of C and compilers, and the user's operating system, this could become almost arbitrarily hairy.

This problem was solved, to some extent, using pre-compiled packages, first as binary installers on the package websites, then pre-packaged Python distributions, and later through third-party package managers such as conda.

This worked well, but it fractured the ecosystem into several different mostly-compatible package sources. This was no big problem, but users had to decide on a package-by-package basis whether to download an installer, use conda, or use pip.

But I am happy to announce that these dark days are behind us now. Pip now automatically installs binary Python packages called wheels, and most package developers do now provide wheels on PyPI. This is so obviously superior to the past that many high-profile packages don't even provide binary installers any more.

For me, this means I don't have to rely on conda any longer. I don't have to keep a mental list of which packages to install though conda and which packages to install through pip any longer. I can go back to using virtualenv instead of conda-envs1 again. I don't have to tell students to download pre-packaged Python distributions any longer. Pip is great!

## Footnotes:

1

Not because I dislike conda, just to simplify my development environment.

22 Nov 2016

# Soma

For a long time, I was afraid of picking up Soma, since it came from the developers who did Amnesia. Amnesia was the first game that scared me so thoroughly that I just couldn't bring myself to pick it up again after the first session. I admired it for its amazing world design, interactivity, and story, but it was too scary for me. I don't enjoy being scared.

I was thus of two minds when I heard about Soma: Soma was supposed to be less scary, and SciFi. But still, let me get this out of the way; This game scared me whitless. I had to use an online game guide to warn me of monsters and tell me how to evade them. I was too scared to figure this stuff out by myself, all alone in this creepy, nasty, underwater space station.

But at the same time, this game delivered one of the best stories I have ever seen in a video game. The story left me shaken and thoughtful for days, and the story was what dragged me back into the game even though I was really struggling with the monster sections. Even the delivery through conversations, environmental clues, and audio logs, was truly outstanding. I just love grimy Alien-style SciFi, and this is one of the very few video game stories that could fill more than a paragraph or two in a well-written book. I love it.

Apparently, if you like horror games, this is a very mild one. Boring even, if you can believe my favorite online critics. But believe me, it was right on the edge of what I was able to take. I still can't quite decide whether I would have preferred this game without the monsters, or whether the monsters were a necessary tool for evoking this intense sense of dread on the lonely SciFi ocean floor. Maybe the monsters lent some much-needed life and interactivity to the walk-em-up formula.

At any rate, I thoroughly enjoyed this experience, and can't wait for what this developer will create next. I wholeheartedly recommend this, as one of the best SciFi stories of this year, in any medium. ★★★★★

07 Sep 2016

# MATLAB Syntax

In a recent project, I tried to parse MATLAB code. During this trying exercise, I stumbled upon a few… unique design decisions of the MATLAB language:

## Use of apostrophes (')

Apostrophes can mean one of two things: If applied as a unary postfix operator, it means transpose. If used as a unary prefix operator, it marks the start of a string. While not a big problem for human readers, this makes code surprisingly hard to parse. The interesting bit about this, though, is the fact that there would have been a much easier way to do this: Why not use double quotation marks for strings, and apostrophes for transpose? The double quotation mark is never used in MATLAB, so this would have been a very easy choice.

## Use of parens (())

If Parens follow a variable name, they can mean one of two things: If the variable is a function, the parens denote a function call. If the variable is anything else, this is an indexing operation. This can actually be very confusing to readers, since it makes it entirely unclear what kind of operation foo(5) will execute without knowledge about foo (which might not be available until runtime). Again, this could have been easily solved by using brackets ([]) for indexing, and parens (()) for function calls.

## Use of braces ({}) and cell arrays

Cell arrays are multi-dimensional, ordered, heterogeneous collections of things. But in contrast to every other collection (structs, objects, maps, tables, matrices), they are not indexed using parens, but braces. Why? I don't know. In fact, you can index cell arrays using parens, but this only yields a new cell array with only one value. Why would this ever be useful? I have no explanation. This constantly leads to errors, and for the life of me I can not think of a reason for this behavior.

## Use of line breaks

In MATLAB, your line can end on one of three characters: A newline character, a semicolon (;), and a comma (,). As we all know, the semicolon suppresses program output, while the newline character does not. The comma ends the logical line, but does not suppress program output. This is a relatively little-known feature, so I thought it would be useful to share it. Except, the meaning of ; and , changes in literals (like [1, 2; 3, 4] or {'a', 'b'; 3, 4}). Here, commas separate values on the same row and are optional, and semicolons end the current row. Interestingly, literals also change the meaning of the newline character: Inside a literal, a newline acts just like a semicolon, overrides a preceding comma, and you don't have to use ellipsis (...) for line continuations.

## Syntax rules for commands

Commands are function calls without the parenthesis, like help disp, which is syntactically equivalent to help('disp'). You see, if you just specify a function name (can't be a compound expression or a function handle), and don't use parenthesis, all following words will be interpreted as strings, and passed to the function. This is actually kind of a neat feature. However, how do you differentiate between variable_name + 5 and help + 5? The answer is: Commands are actually a bit more complex. A command starts with a function name, followed by a space, which is not followed by an operator and a space. Thus, help +5 + 4 is a command, while help + 5 + 4 is an addition. Tricky!

## The more-than-one-value value

If you want to save more than one value in a variable, you can use a collection (structs, matrices, maps, tables, cell arrays). In addition though, MATLAB knows another way of handling more than one values at once: The thing you get when you index a cell array with {:} or assign a function call with more than one result. In that case, you get something that is assignable to several variables, but that is not itself a collection. Just another quirk of MATLAB's indexing logic. However, you can capture these values into matrices or cell arrays using brackets or braces, like this: {x{:}} or [x{:}]. Note that this also works in assignments in a confusing way: [z{:}] = x{:} (if both x and z have the same length). Incidentally, this is often a neat way of converting between different kinds of collections (but utterly unreadable, because type information is hopelessly lost).

26 Jun 2016

# P⋅O⋅L⋅L⋅E⋅N and Walk 'em ups

I like boring games. I like games that give me time to think. Like flight simulators, truck simulators, history simulators, and (don't call them walking simulators) walk 'em ups. And this weekend, this year's Steam Summer Sale started, and thus it was time to get some gaming done!

First, I played Everybody's Gone to the Rapture, a walk 'em up that got good reviews, and was especially praised for it's story. And it dutifully enraptured me, with its British landscapes, and personal story lines. But somehow it didn't quite connect. Maybe I'm not British enough, and I certainly didn't get all of the story. Still, this is well worth picking up, and visiting a digital Shropshire after just having visited the real one earlier this year was a real treat!

Second, I played P⋅O⋅L⋅L⋅E⋅N. It did not start well: The download took ages, I had to unplug all that fancy flight simulation gear to get it to recognize my controller, and performance was rather lackluster. Oh, and reviews were rather mediocre, too. (Also, here's a free tip for you if you games developers: putting fancy Unicode characters into your game title does not improve SEO).

But, I entirely fell in love with P⋅O⋅L⋅L⋅E⋅N! You arrive on Titan in your dinky near-future space capsule, take a short walk on the surface of the moon, and then explore the local space station. Of course, something went wrong, and the space station is deserted. Oh, and there is something about space bees.

What really worked for me here was the environmental story telling. This is a space station much in the tradition of 2001: A Space Odyssey and Alien. It's that perfect utilitarian and inhumanely sterile work place that human corporation always strive for, and human employees always mess up. The stark industrial bleakness of these space corridors is the perfect backdrop to make those little human irregularities really stand out.

There is no conflict, only light puzzles, and the story is developed only through voice diaries and environmental clutter. But in contrast to Rapture, it all makes sense. The futurist setting, the deep humanity of the people dealing with it. The creepiness of machines without operators. The struggle of the scientists and engineers against the forces of nature and greedy corporations. The nods —nay— genuflections to everything that has ever been great in Scifi. Even that Kubrick ending. I loved every inch of this! ★★★★★

21 Jun 2016

# Transplant, revisited

A few months ago, I talked about the performance of calling Matlab from Python. Since then, I implemented a few optimizations that make working with Transplant a lot faster:

The workload consisted of generating a bunch of random numbers (not included in the times), and sending them to Matlab for computation. This task is entirely dominated by the time it takes to transfer the data to Matlab (see table at the end for intra-language benchmarks of the same task).

As you can see, the new Transplant is significantly faster for small workloads, and still a factor of two faster for larger amounts of data. It is now almost always a faster solution than the Matlab Engine for Python (MEfP) and Oct2Py. For very large datasets, Oct2Py might be preferable, though.

This improvement comes from three major changes: Matlab functions are now returned as callable objects instead of ad-hoc functions, Transplant now uses MsgPack instead of JSON, and loadlibrary instead of a Mex file to call into libzmq. All of these changes are entirely under the hood, though, and the public API remains unchanged.

The callable object thing is the big one for small workloads. The advantage is that the objects will only fetch documentation if __doc__ is actually asked for. As it turns out, running help('funcname') for every function call is kind of a big overhead.

Bigger workloads however are dominated by the time it takes Matlab to decode the data. String parsing is very slow in Matlab, which is a bad thing indeed if you're planning to read a couple hundred megabytes of JSON. Thus, I replaced JSON with MsgPack, which eliminates the parsing overhead almost entirely. JSON messaging is still available, though, if you pass msgformat='json' to the constructor. Edit: Additionally, binary data is no longer encoded as base64 strings, but passed directly through MsgPack. This yields about a ten-fold performance improvement, especially for larger data sets.

Lastly, I rewrote the ZeroMQ interaction to use loadlibrary instead of a Mex file. This has no impact on processing speed at all, but you don't have to worry about compiling that C code any more.

Oh, and Transplant now works on Windows!

Here is the above data again in tabular form:

Task New Transplant Old Transplant Oct2Py MEfP Matlab Numpy Octave
startup 4.8 s 5.8 s 11 ms 4.6 s
sum(randn(1,1)) 3.36 ms 34.2 ms 29.6 ms 1.8 ms 9.6 μs 1.8 μs 6 μs
sum(randn(1,10)) 3.71 ms 35.8 ms 30.5 ms 1.8 ms 1.8 μs 1.8 μs 9 μs
sum(randn(1,100)) 3.27 ms 33.9 ms 29.5 ms 2.06 ms 2.2 μs 1.8 μs 9 μs
sum(randn(1,1000)) 4.26 ms 32.7 ms 30.6 ms 9.1 ms 4.1 μs 2.3 μs 12 μs
sum(randn(1,1e4)) 4.35 ms 34.5 ms 30 ms 72.2 ms 25 μs 5.8 μs 38 μs
sum(randn(1,1e5)) 5.45 ms 86.1 ms 31.2 ms 712 ms 55 μs 38.6 μs 280 μs
sum(randn(1,1e6)) 44.1 ms 874 ms 45.7 ms 7.21 s 430 μs 355 μs 2.2 ms
sum(randn(1,1e7)) 285 ms 10.6 s 643 ms 72 s 3.5 ms 5.04 ms 22 ms


text:
# Math Help - Tangent line to the curve.

1. ## Tangent line to the curve.

How do I do the following.

find the equation of the tangent line to the curve:

$xy^3+xy=14$

At point (7,1).

2. Originally Posted by Zanderist
How do I do the following.

find the equation of the tangent line to the curve:

$xy^3+xy=14$

At point (7,1).
$x(y^3+y)=14$

$x=\frac{14}{y^3+y}$

Now find $\frac{dx}{dy}$ at $y = 1$

3. Originally Posted by Zanderist
How do I do the following.

find the equation of the tangent line to the curve:

$xy^3+xy=14$

At point (7,1).
find $\frac{dy}{dx}$ in terms of $x$ and $y$, then sustitute $7$ for $x$ and $1$ for $y$ in the derivative expression to find the slope at that point.