Group+B+Period+8

Welcome Group B. You are to complete problems 2, 8, and 14. Each member of the group must contribute. Feel free to use the discussion board to bounce ideas off one another.

//dS/dt// to //dr/dt//. //S// = 4//πr²// //dS/dt// = 4//π (2r)// //dr/dt// __**//dS/dt// = 8//πr// //dr/dt//**__
 * 2. //Surface Area//** The radius //r// and surface area //S// of a sphere are related by the equation //S// = 4//πr².// Write an equation that relates

//A// = //πr²// //dA/dt =// 2//πr// //dr/dt// //dr/dt =// 2//π (//50//)// //dr/dt =// 100//π// //dA/dt = (//100//π) (//0.01//)// __**//dA/dt =// //π// cm//²///sec**__
 * 8. //Heating a Plate//** When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm/sec. At what rate is the plate's area increasing when the radius is 50 cm?

//x²// + 300//²// = //y²// //x²// + 300//²// = 500//²// //x²// + 90000 = 250000 //x²// = 160000 //x =// 400 //x²// + 300//²// = //y²// 2//x dx/dt// = 2//y dy/dt// //x dx/dt// = //y dy/dt// 400 //dx/dt =// 500 //dy/dt// 400 //(//25//)// = 500 //dy/dt// 10000 = 500 //dy/dt// __**//dy/dt =// 20 ft/sec**__
 * 14. //Flying a Kite//** Inge flies a kite at a height of 300 ft, the wind carrying the kite horizontally away at a rate of 25 ft/sec. How fast must she let out the string when the kite is 500 ft away from her?