Hi,
Set up the triple integral in spherical coordinates to find the volume bounded by z = \sqrt{4-x^2-y^2}, z=\sqrt{1-x^2-y^2}, where x \ge 0 and y \ge 0.
\int_0^{2\pi} \int_0^2 \int_{-\sqrt{4-x^2-y^2}}^{\sqrt{4-x^2-y^2}} r\ dz\ dr\ d\theta
The questions are close. So, not much difference in the answers.
You might want to simply prove that "if a> b and k< 0 then ka< kb" first. Then prove (a) by letting x= a, y= b, and prove (b) by letting x= b, y= a. This part I'm not understanding. I'd have to input values and the teacher says...
a.) Since x > y, so x - y is positive and k is negative.
Product of a negative and positive number is negative, kx - ky
Hence it follows that kx < ky.
b.) Since x < y, so x - y is negative and k is negative.
Product of two negative numbers is equal to a positive number.
Hence it follows...
Hi,
Are these correct?
Homework Statement
a.) Given that x > y, and k < 0 for the real numbers x, yand , show that kx < ky.
b.) Show that if x, y ∈ R, and x < y , then for any real number k < 0,kx > ky
2. The attempt at a solution
a.) kx > y...1
x > y x - y is +ve...2
k...
Homework Statement
Express x^4 + y^4 + z^4 - 2y^2z^2 - 2z^2x^2 - 2x^2y^2 as the product of four factors.
2. The attempt at a solution
(x-y-z)(-x+y-z)(-x-y+z)(x+y+z)