Answer:
B. The distance is decreasing at a rate of 120/√3 miles per hour.
Step-by-step explanation:
Use Pythagorean Theorem to find the distance between the car and the radar monitor.
d² = y² + ¼²
Take derivative with respect to time:
2d dd/dt = 2y dy/dt
d dd/dt = y dy/dt
Use the first equation to solve for y when d = ½:
½² = y² + ¼²
y = ¼√3
Now find dy/dt given that dd/dt = -60:
(½) (-60) = (¼√3) dy/dt
-30 = (¼√3) dy/dt
-120 = √3 dy/dt
dy/dt = -120/√3
The distance is decreasing at a rate of 120/√3 miles per hour.
