Assume that the temperature at all points in the cube Q = [-1,1]×[-1, 1] × [-1, 1] is proportional to the square of the distance from the origin. (a) What is the average temperature? (b) At which points of the cube is the temperature equal to the average temperature?

The volume V of an ice cream cone is given by V = where R is the common radius of the spherical cap and the cone, and h is the height of the cone. Use linearization to estimate the change in the volume when R changes from R = 1.5 inches to R = 1.7 inches, and h changes from h = 4 inches to h = 4.1 inches. Give your answer to two decimal places. R ----- h 6.20 |× in3

(D) Find the value of x (to the nearest thousand chips) that produces the maximum profit. Find the maximum profit (to the nearest thousand dollars), and compare it to the maximum revenue. The maximum profit occurs at x = million chips. (Round to three decimal places as needed.)