Group+B+Period+6

Welcome Group B!! You are to complete problems 2, 8 and 14 from Section 4.6 on this page. Feel free to use the discussion forum to bounce ideas off each other. Each member of the group should contribute!!

2. **Surface Area** The radius //r// and surface area //S// of a sphere are related by the equation //S = 4//π//r//². Write an equation that relates //dS/dt// to //dr/dt// //S = 4//π//r//² - the surface area changes as the radius changes dS/dt=4π(2r)(dr/dt) - find the derivative dS/dt=8πr(dr/dt) - this equation shows that the rate the surface area changes equals 8πr times the rate the radius changes

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 plates's area increasing when the readius is //50cm.// //A =// πr² | area of a circle dA/dt = 2πr(dr/dt) | find derivative dA/dt = 2π(50)(.01) | plug in given radius and the rate at which the radius increases
 * dA/dt = π cm²/sec**

14//.//**Flying a Kite** Cabrera 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? //a//² + b² = c² | Pythagorean theorem 300² + b² = 500² | plug information provided b² = 160000 | solve for b b=400 | 300² + x² = y² | 2x(dy/dx) = 2y (dy/dx) | find derivative x(dy/dx) = y (dy/dx) | simplify 400(25) = 500(dy/dx) | plug in rates provided
 * dy/dx = 20 ft/sec | solve! : D**