Write the equation in spherical coordinates.

$$x^2-2x+y^2+z^2=0$$

Write the equation in spherical coordinates.

$$x+2y+3z=1$$

Change from rectangular to spherical coordinates. (-1,1,-2^1/2)

Change from rectangular to spherical coordinates. (0, -2, 0)

Change from rectangular to spherical coordinates. (0, -1, -1)

Express D as a region of type I and also as a region of type II. Then evaluate the double integral in two ways. double integral xydA, D is enclosed by the curves y=x^2, y=3x

Set up iterated integral s for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier. ∫∫ y dA, D is bounded by y = x - 2, x = y2 D

Use spherical coordinates. Evaluate triple integral (x^2+y^2+z^2)^2dV, where B is the ball with center the origin and radius 5.

Use spherical coordinates. Evaluate triple integral y^2dV, where E is the solid hemisphere x^2+y^2+z^2<=9, y>=0

A student performs a test of $H_{0}: p=0.5$ versus $H_{a}: p \neq 0.5$ and gets a P-value of 0.63. The student writes: "Because the P-value is large, we accept $H_{0}.$ The data provide convincing evidence that the null hypothesis is true." Explain what is wrong with this conclusion.

Use spherical coordinates to calculate the triple integral of f(x, y, z) over the given region.

$$f ( x , y , z ) = \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } ; \quad x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 2 z$$

The nutrition label on a bag of potato chips says that a one ounce (28 gram) serving of potato chips has 130 calories and contains ten grams of fat, with three grams of saturated fat. A random sample of 35 bags yielded a sample mean of 134 calories with a standard deviation of 17 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips? We have verified the independence, sample size, and skew conditions are satisfied.

Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by the coordinate planes and the plane 2x+y+z=4

Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of the equations. -Inside the hemisphere z = √16 - x² - y² and outside the cylinder x² + y² = 1