# short

1. ### why does this short cut work?

I am curious to understand why the following short cut seems to work for finding the length of the side of an inscribed square. It seems that Ø ÷ 1.41 gives a similar result to following step 1 (see attached pic). Why would this be so? Thanks in advance.
2. ### Recursion, short question

The recursion theorem In set theory, this is a theorem guaranteeing that recursively defined functions exist. Given a set X, an element a of X and a function , the theorem states that there is a unique function (where denotes the set of natural numbers including zero) such that for any...
3. ### they didn't really drug test me in really short s double burger

you know were taking donations I they didn't really drug test me in really short s double burger junior answers from other people but they basically got a bunch of lack her what they're No2 Extreme Surge doing I know the organization's want to cooperate so they pretty much shut down so I'll...
4. ### Selections. Why am I short?

Hi everyone, This is a spin off from another question. 4 letters are chosen and repetition is allowed so there are $26^4= 456976$ selections possible. Now I am going to split this up. Letters all different = 26∗25∗24∗23=358800 letters 2 the same= 26∗1∗25∗24∗4C2=93600 letters 3 the...
5. ### Two short, multiple-choice questions about singular points of a differential equation

Hello everyone. I am trying to do the following problem (and another one that is similar), but I don't know how to do parts (ii) and (iii), and I was hoping that someone could tell me the thought process that I must have when answering those parts, since I don't even know how to start.Any help...
6. ### Exact Sequences and short exact sequences - basic question

In Dummit and Foote Section 10.5 Exact Sequences (see attachment) we read the following on page 379: "Note that any exact sequence can be written as a succession of short exact sequences since to say X \longrightarrow Y \longrightarrow Z [where the homomorphisms involved are as...
7. ### Short run average and marginal costs help

Microeconomics: Short run average and marginal costs help please! Hey, I'm doing a microeconomics assignment and I need some help on this question please! Explanations would also be very helpful. Thanks 1) What effect would each of the following have on the short run average and marginal costs...

A square wave of period 2L is a step function which is equal to 1 for x from 0 to L, then is equal to -1 for x from L to 2L. A square wave can be approximated by this Fourier Series expansion: infinity f(x )=(4/pi) ?((1/n)sin(npix/L)) n=1,3,5.... I need to...
9. ### Help!!! Interval inequalities question really short need answer asap!

-22<x+3<334 Solve the interval inequality above
10. ### How do I predict how a number will evolve based on its evolution in a short span?

Greetings, First of all I am sorry if this has been posted before [I have tried searching] and/or if it seems like a beginner's question. Now on with the question: Let's say we have a number X, we monitor it for 10 time units, in these 10 time units, the number changes value [based on user...
11. ### Abstract algebra, short problems

I have a test Wednesday and I'm working on the practice test, just wanna know if these are right, I've done them all 1) a)list all of the elements of z30that have order 10 answer: {3, 9, 21, 27} b)let g be a group, x ϵ G, with order of x = 40. List all elements of <x> with order 10. answer: x4...
12. ### short time Fourier transform

Hey, I have a question about localization a signal in time domain by windowing. would anyone explain to me these phrases: 1) The basis functions sin(ωt) and cos(ωt) are not localized in time!(support region in frequency = 0) 2) The δ(t) is not localized in frequency! (support region in time = 0)...
13. ### Can anyone suggest a good book for Calculus short tricks?

hi, Im preparing for a quick multiple choice test in mathematics. I'd get about a minute for each question. Is there any book where i'd find quick rules, tricks, methods, to solve my questions. (like say, Le Hospital Rule was a quick method of solving "some" functions). The Chapters...
14. ### About a short exact sequence of relative homology groups.

Let x be a point in X. My question is about the following short exact sequence: 0 \to H_1(X) \to H_1(X,\{x\}) \to H_0(\{x\}) \: \xrightarrow{i_\ast} \: H_0(X)\to H(X,\{x\})\to 0, where i_* : H_0 (\{ x \} ) \to H_0(X) is the homomorphism induced by the obvious inclusion. I am told that i_* is...
15. ### Cant work out how someone goes from one step to next in short mod arithmetic problem

Ok so we have: 3+4s=1(mod5) 4s=3(mod5) from there to there is fine obviously, but then after they do this.... 4*4s=4*3(mod5) s=2(mod5) Can someone explain simply what is going on to get to s=2(mod5) Thanks!
16. ### Short proof ?

Let x1, x2, . . . , xk be real numbers such that the set A = {cos(nπx1)+cos(nπx2)+ · · ·+cos(nπxk) | n ≥ 1} is finite. Prove that all the xi are rational numbers. Apparently, it requires use of the pigeonhole principle, but I can't seem to figure out where or how to apply it
17. ### Any short method of solving these two equation

Plz solve this equation in a shortest way X+root Y=7 root X+Y+11
18. ### Short exact sequences

I am claiming the following is not a short exact sequence 0\rightarrow Z\stackrel{i}{\rightarrow} Z \oplus Z \oplus Z \stackrel{j}{\rightarrow} Z \rightarrow 0 I am thinking of it this way: If it was a short exact sequence, then i would be injective and j would be onto. Also, (Z \oplus Z \oplus...
19. ### Two short questions on vectors

Hi The following question i am having problems with: 1) Find the equation of the plane normal to the vector 2i+j-3k 2x+y-3z = d |d|=5 d= 5 or -5 so P = \frac{5}{\sqrt{14}} or \frac{-5}{\sqrt{14}} so 2x+y-3z = \frac{5}{\sqrt{14}} or 2x+y-3z = \frac{-5}{\sqrt{14}} book's answer says...
20. ### Short essay to compare and contrast chi-squared and correlation

I'm writing a paragraph or two comparing 'chi-square test' and 'correlation' in terms of their application, calculation, interpretation and usefulness, especially related to environmental sciences. Could anyone give me any pointers as to their features, and how they are alike and different...