Recent content by JProgrammer

So I am trying to find the volume of a solid with this information given to me: 𝑥=0 𝑦=0 𝑦=−2𝑥+2 However, when I go to enter this information into a disk method calculator, I don't have enough information to enter into the calculator, such as the lower function and limits. My question is...

So I need to compare the results of the volume formula of a cylinder to the results of the integration. In geometry, you learn that the volume of a cylinder is given by V = πr2h, where r is the radius and h is the height of the cylinder. Use integration in cylindrical coordinates to confirm the...

I am trying to find the direction of steepest ascent of this function with this given point: f(x) = x^2 - 4y^2 - 9 (1,-2) I have the understanding that the steepest ascent or in some cases descent can be measured by the gradient. So in wolfram alpha I type in: gradient f(x) = x^2 - 4y^2 - 9...

It is (-x^2).

Thanks for your reply. I have heard of this before, but I wasn't sure if it would work for this problem because a needs to be even and b needs to be odd. This would work for this problem? Since this set has been proven to be countable, it needs to be proven to be infinite. How would I prove that?

So I need to use pigeon hole theory to solve these problems: 3. A man has 10 black socks, 11 brown socks and 12 blue socks in a drawer. He isn’t a morning person, so every morning he just reaches in and pulls out socks until he gets two that match. a. Use the generalized pigeonhole principle...

I am trying to prove how this set is countably infinite: q∈Q:q=a/b where a is even and b is odd a needs to be even and b needs to be odd, so I thought this would prove that it would be countably infinite: q = a/b + x/x, where x is any even number. a always needs to be even and b always...

Do you mean could x possibly be negative? No it cannot be negative. If x is plugged in as negative, then the other negative will cancel it out. If x is plugged in as a positive, even though there is a negative in front of the x, it will be squared to be a positive.

I chose x + 1 because x needs to be greater than or equal to 0. I chose x - 1 because x needs to be less than or equal to zero.

So I have to either prove that these functions are 1 - 1 or show a counter example to prove they are not. I believe that I have proven that these functions are 1 - 1, but I am not 100% sure: For each of the following functions, either prove that the function is 1 – 1 or find a counterexample...

Okay this all seems to make sense, but where does the 9 come from? - - - Updated - - - Ignore this, I understand now.

So I have the following: F = {(1,3)(2,2)(3,2)(4,2)(5,5)} G = {(1,1)(2,3)(3,4)(4,5)(5,2)} Am I right in saying that F o G would be: F o G = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)} If not, does F o G actually mean? Thank you.

I am trying to find the slope of the tangent line of this polar equation: r = 4 + sin theta, (4,0) I put the equation into wolfram alpha and it gives me a 3D plot. If someone could help me find the slope of the tangent line, I would really appreciate it. Thank you.

I am trying to convert this polar equation to Cartesian coordinates. r = 8 cos theta I type the equation into wolfram alpha and it gives me a graph, but no Cartesian points. If somebody could help me find the cartesian points, I would appreciate it. Thank you.

1 -1 correspondence means that the function is both 1 - 1 and onto.