Quiz 3

Justify all answers with neat and organized work. Clearly indicate your answers. 20 points possible.

1. (5 pts.) Find dy/dx by implicit differentiation.

8sinxcosy=5

2. (5 pts.) The normal line to a curve C at a point P is, by definition, the line that passes through P and is perpendicular to the tangent line to C at P. Find an equation of the normal line to the parabola y=2-3x² at the point (3,-25). Sketch the parabola and its normal line.

Recall that two lines with slopes m₁ and m₂ are perpendicular if and only if m₁ m₂=-1; that is, their slopes are negative reciprocals:

m2=- 1 m1

3. (5 pts.) A particle moves according to a law of motion

s=f(t)=t3-18t2+96t,       (t ³ 0)

where t is measured in seconds and s in meters.

(a) Find the acceleration at time t, and after 3 seconds.

(b) Graph the position, velocity, and acceleration functions for 0 £ t £ 8.

(c) When is the particle speeding up? When is it slowing down?

4. (5 pts.) A plane flying horizontally at an altitude of 2 miles and at a speed of 450 miles per hour passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 miles away from the station.