The curve is given by and for

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The curve is given by

x(t)=kt

and

y(t)=4t

for

0\le t\le 3

, where

k

is a positive constant. If the length of the curve on this interval is

15

, what is the value of

k

? (a)

5

(b)

1

(c)

3

(d)

\sqrt{21}