Mathematics

Problem

A point moves along the expanding ellipse

\dfrac{x^{2}}{a(t)^{2}}+\dfrac{y^{2}}{16}=1

, where

a(t)

is the time–dependent semi–major axis. At the moment when

a=6\text{ cm}

and

\dfrac{da}{dt}=0.30\text{ cm/s}

, the point is located at

(3\sqrt{3}\text{ cm},\,2\text{ cm})

and its

x

–coordinate is decreasing at

2\text{ cm/s}

. What is

\dfrac{dy}{dt}

(in cm/s) at that instant? a) Approximately

1.3

b) Approximately

2.6

c) Approximately

-2.0

d) Approximately

2.3