At time , a point satisfies the relation , where the semi‐major axis length is itself…

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

Problem

At time

t

, a point

(x,y)

satisfies the relation

\left(\dfrac{x}{a}\right)^{2}+\dfrac{y^{2}}{25}=1

, where the semi‐major axis length

a

is itself changing with time. When

a=10\text{ cm}

x=3\text{ cm}

y=4\text{ cm}

\dfrac{dx}{dt}=1.0\text{ cm/s}

, and

\dfrac{da}{dt}=0.20\text{ cm/s}

, determine

\dfrac{dy}{dt}

at that instant (include units).