Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of 4.1 feet per second. Find a function, d(t) , which gives the distance Ken is from the streetlight in terms of time. Find a function, S(d) , which gives the length of Ken's shadow in terms of d. Then find S(d) . What is the meaning of $( S \circ d ) ( t )$
A) $( S \circ \mathrm { d } ) ( \mathrm { t } )$ gives the time in terms of Ken's distance from the streetlight.
B) $( S \circ d ) ( t )$ gives the distance Ken is from the streetlight in terms of time.
C) $( S \circ d ) ( t )$ gives the length of Ken's shadow in terms of time.
D) $( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } )$ gives the length of Ken's shadow in terms of his distance from the streetlight.

Question

Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of  4.1  feet per second. Find a function,  d(t) , which gives the distance Ken is from the streetlight in terms of time. Find a function,  S(d) , which gives the length of Ken's shadow in terms of d. Then find  S(d) . What is the meaning of $( S \circ d ) ( t )$
A) $( S \circ \mathrm { d } ) ( \mathrm { t } )$ gives the time in terms of Ken's distance from the streetlight.
B) $( S \circ d ) ( t )$ gives the distance Ken is from the streetlight in terms of time.
C) $( S \circ d ) ( t )$ gives the length of Ken's shadow in terms of time.
D) $( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } )$ gives the length of Ken's shadow in terms of his distance from the streetlight.

Quizplus · Accepted Answer

The composition $( S \circ d ) ( t )$ combines the function that gives Ken's distance from the streetlight as a function of time, $d(t)$, with the function that gives the length of Ken's shadow as a function of his distance from the streetlight, $S(d)$. Therefore, $( S \circ d ) ( t )$ gives the length of Ken's shadow as a function of time, not his distance from the streetlight or the time in terms of his distance.

Ken Is 6 Feet Tall and Is Walking Away from a Streetlight