Comparison Definition and 393 Threads

Here there are two scenarios for comparison. Scenario 1: We move two connected masses which are Constantly 3 metres apart on a friction free surface using the same force and acceleration in a straight line. Scenario 2: We move two connected masses which are Constantly 3 metres apart over an...

I combined three maps of Chernobyl fallout: Cs-137 map, Sr-90 map and Pu-239 map. Map scales are the same. Lowest contour levels for Cs and Sr are the same (1 Ci/km^2), Pu contour is ten times lower (0.1 Ci/km^2). This visually demonstrates that Cs is about ten times more widespread fallout...

Homework Statement LHS (3y+2)/5 RHS y Which is greater? Homework Equations Equation is provided in the question The Attempt at a Solution let y=1: LHS= 1 RHS=1 So LHS & RHS are equal. 2ND try; LET Y=0 LHS= 0.4 RHS= 0 So LHS is greater. So Answer can't be determined using the information...

A little question about the appropriateness of a certain research subject... Would it be useful to make a study of the computational effectiveness of equivalent codes written with Matlab, Mathematica, R Code, Julia, Python, etc. in a set of typical computational engineering problems like...

This shows brains from several different (mostly primates and rodents) at the same scale. Obtained from here. The weight is listed in grams, the (purported) number of neurons is in millions(M). Estimates of neuronal numbers are difficult. Sadly they are not all pointing the same direction.

Homework Statement Use a comparison test to determine whether this series converges: \sum_{x=1}^{\infty }\sin ^2(\frac{1}{x}) Homework EquationsThe Attempt at a Solution At small values of x: \sin x\approx x a_{x}=\sin \frac{1}{x} b_{x}=\frac{1}{x} \lim...

Homework Statement \sum_{x=2}^{\infty } \frac{1}{(lnx)^9} Homework EquationsThe Attempt at a Solution x \geqslant 2 0 \leqslant lnx < x 0 < \frac{1}{x} < \frac{1}{lnx} From this we know that 1 / lnx diverges and I wanted to use this fact to show that 1 / [(lnx) ^ 9] diverges but at k...

Homework Statement http://www.continuummechanics.org/eccentriccolumnbuckling.ht In here , i was told that for the eccentrically loaded column , the column will fail due to before it buckles . How is that possible ? Homework EquationsThe Attempt at a Solution The column will start to buckle...

Homework Statement Determine whether the series converges or diverges. ∞ ∑ 1/n! n=1 Homework Equations If ∑bn is convergent and an≤bn for all n, then ∑an is also convergent. Suppose that ∑an and ∑bn are series with positive terms. If lim an = C n→∞ bn where c is finite number and c>o...

Under what condition would particle de Broglie wavelength be equal to the classical EM wavelength?

Hi again, probably this seems to be a simply question, but in last days i becomes a really strange one. We all know that there are many kinds of constants in physics, some of them, are found experimentally with great accuracy in too expensive projects, but no matter how accurate can be measured...

Homework Statement [/B] A nail is heated in a bunsen burner flame and is about to be dropped into a beaker of water at room temperature. a) Which of the two substances (nail or water) would you expect to initially have: i) the highest internal energy ii) the highest average kinetic...

Hi everyone, This is my first time posting here I am looking to get some help with Abaqus, I wish to compare two models and find the residual stress which causes a original model to deform to the other. The deflection between the two models can be calculated by other software. I plan to do...

I love physics/maths/ETC.. I'M considering physics and doing relevant preparation(Only in y11(15 years old))... Just wondering if there are any benefits to engineering in comparison? This include all aspects like satisfaction/pay/Amount of science involved/ETC...? Thanks

71. Use the Comparison Theorem to determine weather the integral $$\displaystyle I=\int\frac{{x}^{2}}{{x}^{5}+2} \, dx$$ is convergent or divergent. Comparison Theorem Suppose that $f$ and $g$ are continuous with $f(x) \ge \, g(x) \ge 0 $ for $x\ge a$ (a) if $\displaystyle \int_{a}^{\infty}...

Hello! We have a solid cylinder and then we take that and drill its core so that it becomes hollow. In which case the cylinder will be stronger? Thanks!

hello everyone, i am currently a physics undergraduate in europe and i am thinking about possible graduate studies either in usa or europe.i want to study theoretical particle physics(string theory,quantum fileds,cosmpology etc.). my first choice is a phd in usa. but as an alternative i am...

Consider a steel rod of diameter 'd'. If the same rod is broken up into strands and arranged parallel to one another so as to form a new rod of the same diameter 'd' ,Which will have a higher load bearing capacity?. Instead of being arranged parallel , If they are made into a rope of similar...

The limit comparison test states that if $a_n$ and $b_n$ are both positive and $L = \lim_{{n}\to{\infty} } \frac{a_n}{b_n} > 0$ then $\sum_{}^{} a_n$ will converge if $\sum_{}^{} b_n$ and $\sum_{}^{} a_n$ will diverge if $\sum_{}^{} b_n$ diverges. Does this rule also apply if $L$ diverges to...

I have this series: $$\sum_{k = 1}^{\infty} {4}^{\frac{1}{k}}$$ To solve this, I am trying to compare it to this series $$\sum_{k = 1}^{\infty} {4}^{k}$$ So, I can let $a_k = {4}^{\frac{1}{k}} $ and $b_k = {4}^{k}$ These seem to be both positive series and $ 0 \le a_k \le b_k$ Therefore...

I have $$\sum_{n = 2}^{\infty} \frac{{(\ln\left({n}\right)})^{12}}{n^{\frac{9}{8}}}$$ We can compare it to $ \frac{1}{{n}^{\frac{1}{8}}}$. $ \sum_{n = 1}^{\infty} \frac{1}{{n}^{\frac{1}{8}}}$ diverges because $p < 1$ in this case. So, if I can prove that $...

I have this integral $$\int_{1}^{\infty} \frac{1}{(x + x^2)^\frac{1}{3}} \,dx$$ I think this is smaller than $$\int_{1}^{\infty} \frac{1}{(x^2)^\frac{1}{3}} \,dx$$ The latter converges since $p = \frac{2}{3}$ which is greater than 1. Therefore, since the first integral is smaller than the...

Compare the numbers $2^{2016}$ and $3^{201}7^{604}$.

What is better for power? 5 parts air at 400 psi compression 10 inch bore by 30 inch stroke compared to 800 psi compression with 1 part air with 10 inch bore with 10 inch stroke? Same air fuel ratio in both With diesel? Which will be more power and which will be more efficient? And why?

Compare the numbers $X=(\log_2(\sqrt{5}+1))^3$ and $Y=1+\log_2(\sqrt{5}+2)$ and determine which is larger.

Prove that $8^{91}\gt 7^{92}$.

I'm trying to use LTSpice in order to fine tune LC circuits, but a road block I've hit is that when I run the simulation and generate a bode plot, the previous plot is overwritten, so I can't visually compare the effects of the L C changes. Some graphing programs have a function that let's you...

Hi everybody! I have another question about integrability, especially about the limit comparison test. The script my teacher wrote states: (roughly translated from German) Limit test: Let -∞ < a < b ≤ ∞ and the functions f: [a,b) → [0,∞) and f: [a,b) → (0,∞) be proper integrable for any c ∈...

Hello, I want to make sure I understand the following considering ideal gases. Assuming I have two different types of gases, say, O2 and H2 (each at thermal equilibrium), is it correct to say that the kinetic energy of the O2 gas equals to the kinetic energy of the H2 gas since they're both...

Determine, without the help of calculator, which of the following is bigger: 1016^{11}\cdot 3016^{31} versus 2016^{42}

According to Einsteins Theory of relativity if an object traveled at the speed of light, it's mass would become infinite, time would seem to stop relative to others and it length would become absolute zero. The same conditions were thought of at the Big Bang, when time didn't seem to have...

I am trying to compare a computer generated word to display the following however, when Quit is entered it produces the output "Hello". What is my error in the code? #include <stdio.h> #include <string.h> int main(void) { char userString[50]; strcpy(userString, "Quit"); /* Your...

I'll preface this with saying I'm an Industrial Designer, not an engineer. I also build workshop furniture as a hobby, which this question is in reference to. I'm building a motorcycle lift table. I'm curious, is there a chart that compares things like tubing material, size, strength and...

I am doing a lab which involves the determination of vapour pressure of a particular compound by Knudsen Effusion. Like other analytical methods it involves calibration but we are using the know vapour pressure of naphthalene because its in the accepted range. So we have an equation for the...

Hi Everybody! Just have read in the Report into the death of Alexander Litvinenko https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/493860/The-Litvinenko-Inquiry-H-C-695-web.pdf I'm very surpised to see that namely Gamma Spectrometry was used while only 1 in 100,000...

Hey, I am working on Calculus III and Analysis, I really need help with this one problem. I am not even sure where to begin with this problem. I have attached my assignment to this thread and the problem I need help with is A. Thank you!

Hi, my book says that $\lim_{{n}\to{\infty}} {n}^{p}U_n \rightarrow A \lt \infty, p \gt 1 $ means that $U_n \lt \frac{A}{{n}^{p}} $, which I can see But apparently $ \lim_{{n}\to{\infty}}n U_n = A \gt 0 $ means that $ U_n \gt \frac{A}{n} $ I know this is going to sound like a stupid...

I have a generic question on solution procedure. Suppose I consider a system of several point-like bodies interacting only via gravitation. I formulate PDE+ODE system, containing EFE and geodesic motion of the bodies. Since EFE do not define metric uniquely, I need to impose a particular...

Prove $\dfrac{3^{371}+5}{5^{247}+3}>\dfrac{2^{371}+3}{3^{247}+2}$.

Use the comparison test to see if \sum_{1}^{\infty}{\left[n\left(n+1\right)\right]}^{-\frac{1}{2}} converges? I tried n+1 \gt n, \therefore n(n+1) \gt n^2 , \therefore {\left[n(n+1)\right]}^{\frac{1}{2}} \gt n, \therefore {\left[n(n+1)\right]}^{-\frac{1}{2}} \lt \frac{1}{n} - no conclusion...

Let $x,\,y,\,z$ be positive real numbers such that $x+y+z=3$. Prove that $\dfrac{1}{x^2}+\dfrac{1}{y^2}+\dfrac{1}{z^2}\ge x^2+y^2+z^2$.

Homework Statement Suppose an object of length “l” is located a distance “r” from a gravitating object of mass “M.” From physics you will learn that the gravitational acceleration is GM/r^2. Derive the difference in gravitational acceleration between distance “r” and distance “r+l” from the...

Homework Statement use the comparison theorem to determine whether ∫ 0→1 (e^-x/√x) dx converges. Homework Equations I used ∫ 0 → 1 (1/√x) dx to compare with the integral above The Attempt at a Solution i found that ∫ 0 → 1 (1/√x) dx = 2 ( by substituting 0 for t and take the limit of the...

Let's say you've got two electric bicycles both powered by identical 250W motors. Both are fixed gear. Both weigh about the same and have riders of the same weight. Both riders contribute no force to pedalling - all the work is done by the motors. The only difference is the first bike has 20"...

Hello Everyone, I am performing comparisons between our obtained values with the values presented in the literature. These comparisons will be presented in our future paper. Usually, every relative error or a discrepancy below 10% is considered to be a "good" agreement in the Molecular Physics...

I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##: ##A'-\frac{m}{r}A=(\epsilon+1)B## and ##-B' -\frac{m+1}{r}B=(\epsilon-1)A## ##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...

Comparison Test Consider the two infinite series ##\sum a_n## and ##\sum b_n## with ##a_n,b_n \geq 0## and ##a_n \leq b_n## for all ##n##. If ##\sum b_n## is convergent so is ##\sum a_n##. If ##\sum a_n## is divergent so is ##\sum b_n##. Limit Comparison Test Consider the two infinite series...

What I understood from Quantum Entanglement (QE), is that measuring the spin of one of two entangled particles in one location gives the spin of the other particle in other location no matter how far is the later. What I can also understand is that the same concept is applicable in the classical...

I have the sum, $$\sum_{n=1}^{\infty} \frac{1}{n^{3}}\sin(n \pi x) \text{, where }0 \leq x \leq 1$$ I have to show that the series converges, so I'm going to use the Comparison Test. $$ \text{If }0 \leq a_n \leq b_n \text{ then}$$$$\text{If }\sum b_n \text{ converges then }\sum a_n \text{ must...

hello I have problems with the distance units used in cosmology: I wonder where is located a distant supernova at 48 "distance modulus", compared to the Hubble radius. Far much less? please use meters (x10^25 m) thank you in advance rachid