Recent content by theno1katzman

But that wouldn't give you the same answer for part a and b... Why would that give y=x for the boundary. I looked it over again with my calculator, that upper boundary line (hypotenuse) is y=-x+1 however integrating that you end up with 2, which is still not the same as part a.

Homework Statement Find the simple closed integral of (x+xy-y)(dx+dy) counterclockwise around the path of straight line segments from the origin to (0,1) to (1,0) to the origin... a)as a line integral b)using green's theorem Homework Equations Eq of line segment r(t)=(1-t)r0+tr1 Greens...

Here is the solution that uses the base areas properly. I drew a diagram for this area as well. Arrows point to surfaces and the surfaces are using drawn with arrows pointing to the pyramids apex. m=1/120 I hope I have it now. This problem has been bugging me for some time ha-ha.

Thanks here is a second attempt at the problem, please let me know if what I did here is right.

Homework Statement Find exactly the volume in the first octant under the planes x + z =1 and y + z =1. Find the mass if the density is p(x,y,z)=xyz. The Attempt at a Solution This is a pyramid in shape, so for the volume, rather than constructing a double integral, I used the formula...

Well I'm not sure I understand everything you wrote there, I think the problem was simpler when converted to polar coordinates. Thanks for your help and suggestion to convert to polar coordinates. Here is the problem worked out once more. t is theta when converted to polar coordinates...

If V=xyz and g(x,y,z) = x +y + 4z =4 Then to maximize the volume of the box, you would use three partial derivatives tied to each by the Lagrange multipliers. Vx= lambda*gx yz= lambda Vy= lambda*gy xz= lambda Vz= lambda*gz xy=...

I'm going to go back and fix those silly errors but other than that I presume the calculus to be correct? The lengths of the sides of the rectangular box come from geometry and looking at the object. If you draw that plane x +y+4z=4 it intersects the y-axis at (0,4,0) and that gives the length...

Ok there is another way to get the volume of that box. The volume is going to be V=lwh. Length of the box is going to be 4-x. Width 4-y. And height 1-z. V= (4-x)(4-y)(z-1) = 16z-4xz-4yz +xyz-16+4x +4y -xy The three partial derivatives set equal to zero Vx =-4z +yz+4-y = 0 Vy =-4z +xz...

Ok here is the problem worked out again. The vertex on the box that is located on the plane can be found by the graph if you were to draw this situation. pt (4-x,4-y,1-z) using simple geometry. Now the distance from the origin to this point is going to be the diagonal of this box, cube the...

Answer: min value would be 0 and max value would be 1

Homework Statement Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + y + 4z = 4 Homework Equations Volume of a box with L being the length of a diagonal in that box = L3/(3sqrt3) Shortest...

The radius for the domain boundary is actually [sqrt]2. Some more work I tried using this method the textbook showed me, however the textbook was easier and had a different equation for the surface. 4 points to try on the domain where one of the values of the function is zero are (0,sqrt...

Homework Statement Find the maximum and minimum values of f(x,y) = (xy)2 on the domain x2 + y2 < 2. Be sure to indicate which is which Homework Equations I am not sure what to put here. I solved this problem a different way, and I am not confident I did it correctly. The Attempt at a...

Thank you, I wish my professor would have clarified that in class.