# triple

1. ### Moment of Inertia of a Solid Cone

How to find the moment of inertia about the z axis of the top half of a solid cone using Spherical Coordinates? This what I did! I = ∫ R^2 dm where I is the moment of inertia and R is the perpendicular distance from the axis of rotation to the slant height of the cone changing dm with...
2. ### Triple Integrals; Volume of Solids within Boundaries

Hello, everyone. So here is the problem in question with their respective answers: Let W1W1 be the solid half-cone bounded by z=x2+y2−−−−−−√z=x2+y2, z=3z=3 and the yzyz-plane with x≥0x≥0, and let Let W2W2 be the solid half-cone bounded by z=x2+y2−−−−−−√z=x2+y2, z=5z=5 and the xzxz-plane with...
3. ### triple integral

i was told that the ſ ſ ſ dzdxdy = volume , however , if i have ſ ſ ſ z(dzdxdy) , is it still volume ?
4. ### triple integral in polar coordinate

why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z .......
5. ### limit of triple integrals

how to get the limit of theta in this question ? in this question , the author found that the linit of theta is from 0 to pi/2 what i did is : since we know that , x= r cos theta , so 1 = 1 cos theta , so , theta = 2pi is the working correct ?
6. ### calculating volume using double or triple integral

which is correct ? i have 2 notes below . Which way is correct ?
7. ### Volume triple integrals

I need to calculate the volume formed by z=1 and x^2+y^2=8z. Y used cylindrical coordinated and I got r^2=8z and z=1. Is this OK? r from 0 to Sqrt 8 Theta from 0 to 2Pi z from r^2/8 to 1 Thanks
8. ### Triple integral volume

I need to calculate the volume formed by the cone x2+y2=3z2 and the cylinder x2+y2=4y. I drew both figures and with cylindrical coordinates I got this triple integral: I don't know if I got the right triple integral. Assuming the triple integral is right, the answer I got is 128π/(3√3). I...
9. ### Check these two Triple Integrals (cylindrical and spherical)

Sphere Work (the picture I drew is an xy trace of the sphere, if that isn't clear) http://i.imgur.com/WMWUp1D.jpg?1 The sphere problem asks you to find the volume of the region bounded by the plane z=1/2 and a ball with radius 1 centered at the origin using spherical coordinates. I'm not even...
10. ### Triple Integral

How would the first step be accomplished, changing the limits of integration of the most inner limits of integration? \sqrt{200 - x^{2} - y^{2} and x^{2} + y^{2} I understand that a conversion formula is needed, but the Cartesian coordinates given are not single numbers, but are square roots.
11. ### Primitive Pythagorean triple

Prove that for any primitive Pythagorean triple (a, b, c), exactly one of a and b must be a multiple of 3, and c cannot be a multiple of 3. My attempt: Let a and b be relatively prime positive integers. If $a\equiv \pm1 \pmod{3}$ and $b\equiv \pm1 \pmod{3}$, \$c^2=a^2+b^2\equiv 1+1\equiv 2...
12. ### Set up triple integrals in Cylindrical and Spherical coordinates

I have no idea to set this integral, please help: 1, the first octane bounded above by z=x and x2+y2 = 4 for triple integral in Cylindrical coordinate: This is what i have (1st integral) 0 to pi/2 (2nd integral) 0 to 1 (3rd integral) rcos(theta) to (1-r2) then r dz dr dtheta 2, Triple...
13. ### Triple Integral

Hello Can you help to solve this triple integral wich is in the attachment as well Intg ntg intg z*(x^2+y^2)^(1/2) dxdydz over the area A which is (x,y,z): x^2+(y-1)^2 >= 1 and 0<=z>=2 By using cylindrical coordinates Thanks
14. ### order of integration, triple integral

Hi I am struggling to get going on the following problem: V is the region bounded by surfaces x=0 and x=9-y^2 -9z^2 express the integral int int int f(x,y,z)dV as an iterated integral in two orders: (i) dx dy dz and (ii) dy dx dz I am having trouble trying to figure out the region V so I can...
15. ### Solving triple integral by switching to cylindrical coordinates

Hello, everyone. This is me posting for the first time here, so have mercy (haha). Recently I have come across an integral that's been bugging me ever since. The problem is to calculate the integral where the region D represents the intersection of two...
16. ### Find the value of k from a triple equation system

Hello, I would like to get some help to solve a problem I have to do for my Math course. Any help will be much appreciated. Here how it goes... I have to find all values of "k", for which one the system will have a not null solution. Here is the system: kx + 5y + kz = 0 x - ky - z = 0 2x -...
17. ### Vector Calc- Maximizing the Domain of a triple integral

What domain D in space maximizes the value of the integral . Justify your answer and find the maximum value of the integral.
18. ### Evaluating triple integral - undefined point?

I'm looking at the following triple integral: https://www.symbolab.com/solver/step-by-step/%5Cint_%7B0%7D%5E%7Bb%7D%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5Cint_%7B0%7D%5E%7B%5Cfrac%7Bz%7D%7Ba%7D%7D%5Cleft%28r%5E%7B3%7D%5Cright%29drd%5Ctheta%20dz/?origin=button When evaluating the part from 0 to 2pi for...
19. ### Improper triple integral - Vector Calc

I tried changing this into spherical coordinates, but I ended up with the p3/2sin(phi)/(cos(phi)+p2(1/2) which I can't figure out. I'm not sure if I did something wrong when switching coordinate systems, or if there's just an alternate way to solve, but I'm stuck. Any suggestions would be really...
20. ### Triple loan

A Bank approves 3 loans for a customer: L#1, L#2 and L#3. L#1: 2 years (24 months), rate of 12% annual cpd. monthly. L#2: 3 years (36 months), rate of 9% annual cpd. monthly. L#3: 4 years (48 months), rate of 6% annual cpd. monthly. Amount borrowed of L#2 is twice that of L#1...