Recent content by Amcote

It was made clear by my instructor that we should "apply a normal approximation with a continuity correction" for this problem. But even if I ignore all that and do what you suggest (as it should work that way) I get: \Phi \left( \frac{ 0.1 n }{.433 \sqrt{n}} \right) = \Phi \left( 2.33 \right)...

Sorry I made a typo just in that sentence, I meant P(B(n,0.25)≤0.35*n)=0.99.

Homework Statement A multiple choice test consists of a series of questions, each with four possible answers. How many questions are needed in order to be 99% confident that a student who guesses blindly at each question scores no more than 35% on the test? Homework Equations So I know that...

Yeah that's what I ended up doing. And for case 3 I rearranged the boundary conditions so that y=\frac{a_2}{a_1}y\prime and similarly with the b2, b1 and was able to get it to zero. Thanks for your help guys.

A couple things I want to add General Sturm Liouville equation: \frac{d}{dx}p(x)\frac{dy}{dx}-s(x)y(x)+{\lambda}w(x)y(x)=0 from my understanding, in our problem p(x) = 1 and s(x)=0 and w(x)=1. and so the last bit of that integral for us is: [y_j(x)y{\prime}_m(x)-y_m(x)y{\prime}_j(x)]_a^b And...

Homework Statement Consider the following Sturm-Liouville Problem: \dfrac{d^2y(x)}{dx^2} + {\lambda}y(x)=0, \ (a{\geq}x{\leq}b) with boundary conditions a_1y(a)+a_2y{\prime}(a)=0, \ b_1y(b)+b_2y{\prime}(b)=0 and distinguish three cases: a_1=b_1, a_2{\neq}0, b_2{\neq}0a_2=b_2=0, a_1{\neq}0...

The reason I think it is wrong is because in the next part of the question it says: ii) Show that for the contour C illustrated below, the integral of \alpha(\omega)/\omega vanishes along the semicircular part of the contour as R goes to infinite. I've attached what the contour looks like but...

Homework Statement Locate the poles of the response function \alpha(\omega) in the complex plane for an LRC circuit. Homework Equations \alpha(\omega)=\frac{-i\omega}{L}\frac{1}{\omega_0^2-\omega^2-i\omega\gamma} \omega_0^2=\frac{1}{CL} \gamma=\frac{R}{L} The Attempt at a Solution So we've...

This is a series circuit. So what I have so far is that we are trying to find the frequency when |VR|=|VC| |VR|=IR |VC=I(1/wC) IR=I(1/wC), w=2πf Rearrange to get f=1/(2πCR), or w=1/(CR) Now to show that the peak voltage for the cap and the resistor at this frequency can be written as Vin/√2...

Homework Statement For the RC circuit shown in Fig. 1, at some frequency the peak voltage across the capacitor and resistor are equal. Find the frequency at which this occurs. Show that the peak voltage across the capacitor or the resistor at this frequency is given by Vin/ √ 2. How would this...

Further attempt for number 2: suppose d=gcd(a+b,a-b,ab), therefore d|a+b, d|a-b, d|ab and also d|(a+b+a-b)=2a and d|(a+b-[a-b])=2b So d|gcd(2a,2b) but since gcd(a,b)=1 --> 2*gcd(a,b)=2 --> gcd(2a,2b)=2 so from this d|2 and so d=1 or d=2 from here it is the "ab" that is bugging me and will...

Basically because for whatever you choose x,y,z and t to be, ab=cd will always be true.

Problem 1 Suppose ab=cd, where a, b, c d \in N. Prove that a^{2}+b^{2}+c^{2}+d^{2} is composite. Attempt ab=cd suggests that a=xy, b=zt, c=xz. d=yt. xyzt=xzyt. So (xy)^{2}+(zt)^{2}+(xz)^{2}+(yt)^{2}=x^{2}(y^{2}+z^{2})+t^{2}(z^{2}+y^{2})=(x^{2}+t^{2})(z^{2}+y^{2}) Therefore this is...

Thank you very much for your help, it's much appreciated. (:

Thank you for your quick response, Now using your idea: If a is prime, it will have the form either 6k+1 or 6k-1 so, 8(6k-1)-1 should be prime as well but, 48k-8-1=48k-9=3(16k-3) this is composite so the form 6k-1 does not work. but 8(6k+1)-1=48k+8-1=48k+7 is it sufficient to say that 48k+7...