Question

the equation $d = 6t + 210$ gives the distance $d$, in feet, from a reference point on the surface of mars to a mars rover, where $t$ is the number of minutes after the start of a period of observation. by how many feet does the mars rovers distance from the reference point increase over a period of 20 minutes?

a 330

b 230

c 120

d 6

Explanation:

Step1: Understand the problem

The equation \( d = 6t + 210 \) represents the distance \( d \) (in feet) of the Mars rover from a reference point at time \( t \) (in minutes). We need to find the increase in distance over 20 minutes. The increase in distance is the difference between the distance at \( t = 20 \) and the distance at \( t = 0 \) (or we can recognize that the coefficient of \( t \) is the rate of change, so over \( t \) minutes, the increase is \( 6t \)).

Step2: Calculate the increase

The rate of change of distance with respect to time is given by the coefficient of \( t \) in the equation \( d = 6t + 210 \), which is 6 feet per minute. So over 20 minutes, the increase in distance is \( 6\times20 \).

$$ 6\times20 = 120 $$

Answer:

C. 120