Question

Gia, a marine biologist, wants to monitor the temperature of the ocean at different depths along the continental slope. The speed of ocean current as a function of depth is given by S(d) = 3d + 1. Suppose that the depth of a research robot depends on time, t, according to the formula: d(t) = (1/27)t². What is the speed of the current at the depth of the robot after 9 seconds?

A) 10 m/s
B) 4 m/s
C) 7 m/s
D) 13 m/s

Answer 1

The speed of the current at the depth of the robot after 9 seconds is 28 m/s.

Step-by-step explanation:

The speed of the current at the depth of the robot can be found by substituting the depth function, d(t) = (1/27)t², into the ocean current function, S(d) = 3d + 1. After 9 seconds, the depth of the robot is d(9) = (1/27)(9)² = 9. Substituting this depth into the current function, we get S(9) = 3(9) + 1 = 28