# Recent content by Michels10

1. ### Substitution differential equation problem

Nevermind, solved it. Needed to substitute v=y^2. Thanks!
2. ### Substitution differential equation problem

Solve y' = y/x + 1/y I get a similar answer to the correct one but I believe I am making a substitution error. Here is my attempt: dy/dx = y/x + 1/y set v = y/x equation now becomes: v + x(dv/dx) = v + 1/(x*v) reduces to: dv/dx = 1/(x^2 * v) Now the equation is...
3. ### Find mass and center of mass of ice cream cone

There is, but the semester is over. The problems we have discussed/were in the book did not involve varying densities(not to mention the concavity at the top of the cone[irregular shapes]). We have done simple double or triple integrals of the equation for density*the density proportionality...
4. ### Find mass and center of mass of ice cream cone

Yes it bothers me. This assignment was due two days ago and clearly I do not understand it. My book examples don't help me at all and I've got nothing to go by. Intuition? As for the "back to the drawing board" -- I don't thinks so. These repeated attempts post due-date are just brewing...
5. ### Find mass and center of mass of ice cream cone

I am indeed using maple. I've already found the volume of the sphere,using triple integrals- int(int(int(vsp(rho, theta, Phi), rho = 0 .. 4), theta = 0 .. 2*Pi), Phi = 0 .. Pi) = 256Pi/3 for the mass of the cone and the center of mass i got: f := ((4-sqrt(7))*1.4)*r^3 mass:=Int(Int(f, r = 0...
6. ### Find mass and center of mass of ice cream cone

Okay, got that, now what should I do for the sphere? Finding the density of the sphere should be relatively easy... Its not just the triple integral of volume * density constant *radius?
7. ### Find mass and center of mass of ice cream cone

The center of mass of the cone is somewhere along the Z axis. This yields a problem when dealing with double integrals doesn't it? I cant substitute a Z into the equation when dealing with polar coordinates. I believe the equation is: 1/mass Int(Int((z*density)rdr)dtheta) edit: i've been...
8. ### Find mass and center of mass of ice cream cone

Okay very cool. I suppose now I have to find out how deep the cone is in the center (along the z axis) due to concavity. Thanks you for your help thus far. I am going to keep going at it! I'll post back soon with an update.
9. ### Find mass and center of mass of ice cream cone

Okay, I'm assuming it has something to do with the slope of the cone, and the increasing radius/size as you move up from the bottom of the cone... Since the radius is 3 and the height is 8, this gives us a slope of 8/3. I'm assuming that I need to use that 8/3 in my equation, I'm not sure...
10. ### Find mass and center of mass of ice cream cone

I think i've about given up on this one. I clearly have no idea what I'm doing. I was trying to rearrange the equations to fit my graph. I saw my professor, he gave me an equation of z^2 = 64/9 * x^2 + y^2 for the cone and said that the height from the center of the sphere to the bottom...
11. ### Find mass and center of mass of ice cream cone

Okay, then how about I change them... sphere- 16 = x2+y2+(z - (8+sqrt(7)))2 cone- x2 + (y-3)2 = (z-8)2
12. ### Find mass and center of mass of ice cream cone

I updated one of my last posts with some integrals... But back to the graph.. The cone has a height of 8. The total height from the bottom of the cone to the center of the sphere is 8+sqrt(7). And the radius is still 4 for the sphere, and still 3 for the cone
13. ### Find mass and center of mass of ice cream cone

i've attached a picture of the cone/sphere graphed.
14. ### Find mass and center of mass of ice cream cone

how do these equations look: cone- z2 = (64/9)(x2+y2) sphere- 4 = x2+y2+z2 Cone: Int(Int(Int(1.4*(64/9)(r2)*r,dr),d(theta)),dz) r=0 to 3 theta = 0 to 2pi z = 0 to 8 Sphere: Int(Int(Int(1.8*p2*sin(phi),d(p),d(theta)),d(phi)) p = 0..2 theta = 0..2pi phi = 0..pi
15. ### Find mass and center of mass of ice cream cone

Thanks for your reply Mark44! Dont I still have two unknowns? density and mass? I guess my problem now is finding the equation for density. Do I need to set the equations equal to and find out where they intersect? I've solved for both volumes: Vcone = 24*pi Vsphere = (32/3)*pi Thanks, Michels10