The coordinates of a moving point satisfy the equation

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The coordinates of a moving point

(x,y)

satisfy the equation

\dfrac{x^{2}}{a(t)^{2}}+\dfrac{y^{2}}{9}=1

, where

a

is a positive function of time

t

measured in seconds. At the instant when

a = 5

and is increasing at

0.5

units per second, the point is at

(x,y) = (3,y)

with

y>0

and its

x

–coordinate is decreasing at

1.2

units per second. Determine

dy/dt

at that instant, including units.