Recent content by rayne1

Ok, then is it still possible to find a basis and dimension of V if it is not a subspace of ${P}_{2}$?

$$V = \{({x}^{2}-1)p(x) | p(x) \in {P}_{2}\}$$ show that V is a subspace of ${P}_{2}$I tried: $({x}^{2}-1)(0) = 0$ so 0 is in ${P}_{2}$ (axiom 1 is satisfied). If p(x) and q(x) are in ${P}_{2}$, then $({x}^{2}-1)p(x) + ({x}^{2}-1)q(x) = ({x}^{2}-1)(p(x)+q(x))$ and since $p(x)+q(x) \in...

Not sure if correct, but I got: yp(t) = 4^(-t)/(log^2(4)-4(log(4))+3)

I tried and it didn't work. Don't know if I made a mistake in differentiating but this is what I did: y = Cte^(-t) y' = Ce^(-t)-Cte^(-t) y'' = -Ce^(-t)-Ce^(-t)-Cte^(-t) When I plugged it back into the original equation, I got 0. Edit: Oh, Is y" supposed to equal -Ce^(-t)-Ce^(-t)+Cte^(-t), instead?

I'm supposed to use undetermined coefficients to find a general solution to: y" + 4y' +3y =4^(-t) I can't find an example online where f(t) is equal to an exponential function that does not have e as the base, so I have no idea how to solve it. So far, I found the general solution to the...

Oh, thank you! I got a bit lazy to try everything out.

What would be the k value?

Assume the population of bacteria in a culture increases at a rate proportional to the current population. The population increased by 2455 from t = 2 to t = 3 and by 4314 from t = 4 to t =5. Find the initial population and how many times does the population increase each unit of time? I don't...

Okay, but I'm still unclear on how to solve it.

Not sure :(

Problem: McBurger’s drive-thru has only one service window and serves an average of 2 customers every 5 minutes. 70% of customers order drinks from the drive-thru. The manager monitors the employee at the drive-thru for the next 3 hours. He will give the employee a raise if exactly 20 customers...

Matrix A: 0 -6 10 -2 12 -20 -1 6 -10 I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of: 1 0 0 | 0 0 1 0 | 0 0 0 1 | 0 So, how do I find the nonzero eigenvectors of the...

integral from 2 to infinity dx/(x^2+2x-3) I got this as the result: lim x to infinity (1/4)(ln|x-1|-ln|x+1|+ln|5|) Then I got (1/4)(infinity - infinity + ln|5|) so do I need to use l'hopital's rule for ln|x-1|-ln|x+1| or would the final answer be ln|5|/4? If not, I am unsure of how to...

Oh I did try that, so then I must have made a calculation error.

Given the PDF: f(x) = 1/12 , 0 < x <= 3 x/18, 3 < x <= 6 0, otherwise find the expected value, E(x). I know how to find the expected value if there was only one interval, but don't how to do it for two.