Question

a cyclist pedals from the bottom to the top of a hill at a constant speed of 8 feet per second. during the climb, the distance from the cyclist to the top of the hill can be modeled by the formula ( a = b - 8c ).
for each quantity listed in the table, identify the variable in the formula which represents that quantity. select the correct circle in each row

quantity	a	b	c
the total distance, in feet, from the bottom to the top of the hill
the remaining distance, in feet, from the cyclist to the top of the hill

Explanation:

Step1: Analyze the formula \(a = b-8c\)

The formula \(a = b - 8c\) is a linear equation. Here, \(8\) is the speed (in feet per second).

Step2: Relate the variables to the quantities

• For the number of seconds since the cyclist began climbing the hill:

Since the cyclist is moving at a speed of \(8\) feet per second, and in the formula \(a=b - 8c\), \(c\) is multiplied by the speed. So \(c\) represents the number of seconds (time).

• For the total distance, in feet, from the bottom to the top of the hill:

When \(c = 0\) (at the start, when the cyclist has not climbed at all), \(a=b\). So \(b\) represents the total distance from the bottom to the top of the hill.

• For the remaining distance, in feet, from the cyclist to the top of the hill:

The formula \(a=b - 8c\) gives the value of \(a\) as the remaining distance. So \(a\) represents the remaining distance.

Answer:

Quantity	\(a\)	\(b\)	\(c\)
the total distance, in feet, from the bottom to the top of the hill		\(\bigcirc\)
the remaining distance, in feet, from the cyclist to the top of the hill	\(\bigcirc\)