Johnny

Find the double integral over the region R of:

y / [ (x^2)(y^2) + 1 ] dA

R: 0 to 1 for x and 0 to 1 for y.

I started by integrating with respect to y, using u-sub:

u = (x^2)(y^2) + 1, du = 2(x^2)(y)dy, and dy = du / [ 2(x^2)y ]

Substituting gives:

(y / u) * (du / [ 2(x^2)y ]) --> Simplify and pulling 1 / [ 2(x^2) ] out from integral...

(1 / [ 2(x^2) ]) Integral from 0 to 1: du / u

Then I made this ln(u) and continued integrating with respect to x...am I on the right track? Can you finish it or correct if I'm not?

Thanks.

Integral from 0 to pi of [ sec (t) ]i + [ tan^2 (t) ]j + [ tsin (t) ]k:

I actually already integrated, my issue is regarding secant's domain. Secant has a vertical asymptote at pi/2, and this integral is crossing that asymptote, so is this an improper integral that I have to split into two integrals?

Say from 0 to pi/2 and another from pi/2 to pi...? Or is there another "easier" way to approach this?

Just in case, after integrating...this is what I get:

= ( ln | sec (t) + tan (t) | )i + ( tan (t) - t )j + ( tcos (t) - sin (t) ]k

I just haven't evaluated yet...since I am unsure about this being an improper integral...

Any help would be appreciated.

Find a plane through the origin that is perpendicular to the plane M: 2x + 3y + z = 12 in a right angle. How do you know that your plane is perpendicular to M?

I can see the normal vector to the plane is 2i + 3j + k, and I understand that I need to use the normal vector to the plane that passes through the origin...but, I don't know how to find that.

I understand the last part, if the normal vectors dot product is equal to 0, they for right angles.

How would I find the normal vector for the plane that passes through the origin? Especially since I'm only given 1 point.

Thanks!

Which is equivalent to the converse of a conditional sentence? The contrapositive of its inverse, or the inverse of its contrapositive?

Note: I believe they both are equivalent to the converse. But, I'm not 100% sure because of the phrasing.

The average stock price for companies making up the S&P 500 is $30. Assume the stock prices are normally distributed and the standard deviation is unknown.

(a) If 23% of the stock prices are more than $41.25, what is the variance?

Any help would be greatly appreciated. I understood every single problem except this one.

I started by saying mu = 30, but without the standard deviation, I'm not sure how to find the variance. I'm also not sure if n = 500 as my population? Help :)

The average stock price for companies making up the S&P 500 is $30. Assume the stock prices are normally distributed and the standard deviation is unknown.

(a) If 23% of the stock prices are more than $41.25, what is the variance?

Any help would be greatly appreciated. I understood every single problem except this one.

I started by saying mu = 30, but without the standard deviation, I'm not sure how to find the variance. I'm also not sure if n = 500 as my population? Help :)

The average stock price for companies making up the S&P 500 is $30. Assume the stock prices are normally distributed and the standard deviation is unknown.

(a) If 23% of the stock prices are more than $41.25, what is the variance?

Any help would be greatly appreciated. I understood every single problem except this one.

I started by saying mu = 30, but without the standard deviation, I'm not sure how to find the variance. I'm also not sure if n = 500 as my population? Help :)

The average stock price for companies making up the S&P 500 is $30. Assume the stock prices are normally distributed and the standard deviation is unknown.

(a) If 23% of the stock prices are more than $41.25, what is the variance?

Any help would be greatly appreciated. I understood every single problem except this one.

I started by saying mu = 30, but without the standard deviation, I'm not sure how to find the variance. I'm also not sure if n = 500 as my population? Help :)