©Zarestky Math 151 Quiz 6 Version A NAME:_____KEY___________________________________ 1. (3 pts) Find D18 cos (5x ) . Establish a pattern: D cos (5x ) = (!sin5x ) "5 D 2 cos (5x ) = (!cos5x ) "52 D 3 cos (5x ) = (sin5x ) "53 D 4 cos (5x ) = (cos5x ) "54 So, D18 cos (5x ) will look like D 2 cos (5x ) with a different power of 5. D18 cos (5x ) = (!cos5x ) "518 2. (2 pts) For the following parametric equations, find x (t ) = 3t 6 ! 2t 4 +1 y (t ) = t 2 !6t dx = 18t 5 !8t 3 dt dy = 2t !6 dt dy dy 2t !6 = dt = so dx dx 18t 5 !8t 3 dt dy . dx 3/8/2010 ©Zarestky 3. Math 151 Quiz 6 Version A 3/8/2010 (5 pts) At noon, ship A leaves a port traveling South at 40 km/hr. At the same time, Ship B leaves the same port traveling East at 30 km/hr. At what rate is the distance between the ships changing after 30 minutes? For full credit, include a sketch. b Given: da db = 40 km/hr and = 30 km/hr. dt dt After 30 minutes, a = 20 km and b = 15 km so c= a 2 + b2 = 202 +152 = 25 Find dc by using the Pythagorean Theorem and Implicit Differentiation. dt A a 2 + b2 = c 2 da db dc 2a + 2b = 2c dt dt dt Substitute in the known values and solve for 2 (20)(40) + 2 (15)(30) = 2 (25) dc . dt dc dt dc 2500 = = 50 km/hr dt 50 Bonus: (1 pt) Simplify (n + 4)! n! . (n + 4)! (n + 4)(n + 3)(n + 2)(n +1) n! n! = n! a = ( n + 4)( n + 3)( n + 2)( n +1) (It is not necessary to multiply out the four terms.) c B