# Search results

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
16. ### Find mass and center of mass of ice cream cone

Homework Statement A toy manufacturer wants to create a toy ice cream cone by fitting a sphere of radius 4 cm inside a cone with a height of 8 cm and radius of the base of 3 cm. The base of the cone is concave, but the rest of the cone is solid plastic so that with the sphere attached...
17. ### Ball launched at an angle

Hi, thank you for the response! I made an effort to plug in t and I did not receive the correct answer. 7=vo*sin(50)(4/(vo*cos(50)))-(1/2)*(9.8)*((4/(Vo*cos(50)))^2 does this look correct? I plugged it into wolfram and ended up with a result of +-(9.21823 i)
18. ### Ball launched at an angle

Homework Statement A ball is launched from the origin at an angle of inclination of 50 degrees above the xy plane. If the ball lands at coordinates (4,7,0), find the initial velocity of the ball. Homework Equations x=(voCos(50)Cos(theta))t y=(voCos(50)Sin(theta))t The Attempt...