Recent content by riskybeats

Hello, trying to figure out exactly what is going on in this question. Homework Statement (a) If P(z) is a nonconstant polynomial, show that |P(z)| > |P(0)| holds outside some disk R |z| ≤ R for some R > 0. Conclude that if the minimum value of |P(z)| for R z ≤ |R| occurs at z_o...

Okay that makes sense. Thanks for your help.

Actually I get what you mean, and that would work with the conditions of the algorithm as well. But how do we know that the set preceding the set which has the pairs satisfying a + b contain the pair (a,b)? Ps. This is a great way to practice talking about this stuff correctly (or at least...

Sorry for the confusing wording, I meant preceding. That makes more sense, but I am still not sure why there is the condition that x + y = a + b - 1. For the set of paired numbers before the set containing (a,b), there are a + b - 2 members. For the set containing (a,b), there are a members...

Homework Statement Prove that N X N is denumerable and provide a bijective function (also prove that the function is bijective) Homework Equations Cantor's Diagonalization argument The Attempt at a Solution My teacher provided a full solution, but it is in coming up with the...

I'm doing this question right now, and I am wondering how to get 294 J/K as an answer. I don't understand why the final volume doesn't relate to the max volume, and how to use PV^gamma to get the correct ratio. Thanks.

Sorry but I'm not sure what you mean by the equation of the normal. Do you mean the vector equation of the tangent plane? <-3/2, 2, -1>\cdot<x + 3/4, y - 1/4, z> = 0? Although I do still have those other numbers a2 + 4b2. Would that influence the normal of my plane still? I am tired and...

The norm of my plane is influenced by a and b. This is what I have: 2a (X - a) + 8b (y - b) - z + a^2 + 4b^2 = 0 So if the vector is <3, -4, 2>, I could put the norm of my plane as <-3/2, 2, - 1> since that would be parallel? Hence a = -3/4 and b = 1/4 ?

I couldn't get to sleep because I kept on thinking this problem through. As far as I can see, if the plane's norm is the same as the vector <3, -4, 2>, then it must be perpendicular to it. I am not sure how to make the norm on the plane into that though based off of just of values of a and b...

a)Find the equation of the tangent plane to the graph z = x2 + 4y2 at the point (a, b, a2 + 4b2) b) For what values of a and b is the tangent plane perpendicular to the vector (3, -4, 2)? I figured you have to use the tangent plane equation z - zo = zx(a,b)(x-a) + zy(a,b)(y-b). This gave me...

That was a great explanation. Thanks a lot, it makes complete sense now. I can't believe I just discovered this site now, you guys are unbelievably helpful. Thanks again!

Hello hello. In class we went over the ''mini-chain rule'' once, and haven't gone over the real chain rule yet. I really want to understand how to go about solving this equation, and to really understand what is happening here. x=u3-3uv2 y=3u2v-v3 z=u2-v2 Define z as a function of x and...

Okay, the only reason I did 1.02 is because I thought of doing I could express is as a negative/positive percentage. This was obviously a bad move and doesn't make any sense. But I got it now. Thanks for the help everyone!

By approximately what percent would the volume of a right circular cylinder increase or decrease if the height were to increase by 2% and the radius of the base were to decrease by 1.5%? Partial differentials makes sense in this case, I am just stuck when I have no usable values. Volume of...

Great find! This site has 4 of my 6 courses in it! I am stoked, thanks!