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 .

Read the excerpt from the strange case of dr jekyll and mr. hyde what do dr. jekyll's thoughts reveal about him in this excerpt? [t]he inmates of my house were locked in the most rigorous hours of slumber, and i determined, flushed as i was with hope and triumph, to venture in my new shape as far as to my bedroom. i crossed the yard, wherein the constellations looked down upon me, i could have thought, with wonder, the first creature of that sort that their unsleeping vigilance had yet disclosed to he is jealous of those who can sleep through the night. he is revered for his scientific advances. he is interested in studying the movements of the stars he is proud and enthusiastic about his initial results.

Drag each tile to the correct box. not all tiles will be used. consider the recursively defined function below. create the first five terms of the sequence defined by the given function

Justin has 750 more than eva and eva has 12 less than justin together they have a total of 63 how much money did