The average value of a function f(x, y, z) over a solid S is defined by 1 V (S) Z Z Z S f(x, y, z)dV, where V (S) is the volume of the solid S. Calculate the average value of f(x, y, z) = z 3 p x 2 + y 2 + z 2 over the solid S, where S is the solid hemisphere that lies above the xy−plane and has center the origin with radius a > 0. You may use, without proof, that the volume of a sphere with radius a is 4πa3 3 .

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

care to share were the trapezoid shown is ?

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.