Write the equation in spherical coordinates.

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

Show that the equation represents a sphere, and find its center and radius. 3x2 + 3y2 + 3z2 = 10 + 6y + 12z

Write the equation in spherical coordinates. $z=x^{2}+y^{2}$

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

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 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

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.

Verify the linear approximation at (0, 0).ex cos(xy) "approximately equal to" x + 1

Find the indicated partial derivative(s). z=u√v-w; ∂^3z/∂u∂v∂w

Find the force exerted by the biceps muscle in holding a 1.0 L milk carton (weight 9.9 N) with the forearm parallel to the floor. Assume that the hand is 35.0 cm from the elbow and that the upper arm is 30.0 cm long. The elbow is bent at a right angle, and one tendon of the biceps is attached to the forearm at a position 5.00 cm from the elbow, while the other tendon is attached at 30.0 cm from the elbow. The weight of the forearm and empty hand is 18.0 N, and the center of gravity of the forearm is at a distance of 16.5 cm from the elbow.

Find the volume of the solid that the cylinder r=a cos theta, cuts out of the sphere of radius centered at the origin.

Find the volume of the solid that the cylinder r=a cos theta, cuts out of the sphere of radius centered at the origin.