A point moves in the first quadrant so that its horizontal and vertical distances…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A point

P

moves in the first quadrant so that its horizontal and vertical distances from the origin satisfy

x^2+y^2=s^2

, where

s

is the length of a movable cable. At a particular instant,

x=6\,

cm,

y=8\,

cm, the cable is being let out at a rate of

10\,\text{cm/s}

, and

y

is increasing at

4\,\text{cm/s}

. What is

\dfrac{dx}{dt}

at that instant? (a)

-\dfrac{16}{3}\,\text{cm/s}

(b)

-\dfrac{34}{3}\,\text{cm/s}

(c)

\dfrac{34}{3}\,\text{cm/s}

(d)

\dfrac{20}{3}\,\text{cm/s}