Recent content by ilikephysics

Question: A card is selected from a shuffled deck of cards. What is the probability that it is either a king, or a club? What is the probability that it is both a king and a club? Answer: There are 52 cards in a deck. Four kings and 13 clubs. So the probability of chosing a king or a club...

question How did you get the endpoint (3,5)? How would I right the sqrt(34) and arctan(3/5) as a vector? Did I do #2 right?

The problem is: Write the vector V=i+j+k=(1,1,1) at the point (x,y,z)=(1,1,1) in cylindrical polar coordinates. What is the gradient of the function phi=x(x^2+y^2)z at this point? Answer: I don't know how to write the vector in cylindrical polar coordinates. I know that the coordinates...

1. Write out the vector V=2i+3j at the point (x,y) = (1,2) in terms of the unit vectors in plane polar coordinates. Do this again for the same vector at the origin. Are your results different? Why? Answer: From my notes, I see that x,y = (r, theta) and x=r cos theta, y=r sin theta. So...

Can someone help Can someone please help me? I tried #1. Is it right? Am I on the right track?

am i doing #1 right? I'm still a bit confused of how to do legendre polynomials. For #1, I have to expand the function sin(x) in a series of legendre polynomials Pn(x) on the interval x E [-1,1]. Would I do this like the taylor series, x-x^3/3!+x^5/5!-x^7/7!+... So would P0(x) be x...

The instructions for the attached homework instructs us to use maple for both problems. I really don't know how to use it. I've never really used it. Can someone help please?

I know that legendre polynomials are solutions of the differential equation is (1-x^2)d^2y/dx^2 - 2x dy/dx+l(l+1)y=0 where l is an integer. The first five solutions are P0(x)=1, P1(x)=x, P2(x)=3/2x^2-1/2, P3(x)=5/2x^3-3/2x, P4(x)=35/8x^4-15/4x^2+3/8 The problem is that I don't understand what...

Find the value of ln(-e), (-1)^i, and (2i)^1+i in rectangular x+iy form, using the principal value of the logarithm. This is what I'm doing for each one: ln(-e)= e^ln(-e) (-1)^i= e^(i)(ln(-1)) (2i)^1+i= e^(1+i)ln(2i) If this is right, where do I go from here?

Express the sines and cosines in exponential form and integrate to show that (integral from -pi to pi) sin(3x)cos(4x)dx=0 What I'm thinking is that I should use sin x=e^x-e^-x/2 and cos x=e^x+e^-x/2. And I should multiply sin times 3 and cos times 4 and integrate. And get something like this...

eigenvectors Are these the eigenvectors? For a-b, -1 c-a-b For c-b, a-c-b 1

Find the eigenvalues and eigenvectors of the general real symmetric 2 x 2 matrix A= a b b c The two eigenvalues that I got are a-b and c-b. I got these values from this: (a-eigenvalue)(c-eigenvalue)-b^2=0 (a-eigenvalue)(c-eigenvalue) = b^2 (a-eigenvalue)= b = a-b...

here are the matrices 1 2 (1) 3 4 2 3 5 6 (2) 12 15 26 33 (product matrix)

What is the following question asking? Question: Prove that the determinant of the product of two general 2x2 matrces is the product of their determinants. What I think is that I should come up with two 2x2 matrices. 1 2 2 3 12 15 3 4...

please help me will someone please help?