Question

Explain Each Part please!!!

The cost C, in dollars , of building a concrete sidewalk varies directly with its lentgh , s, in meters
A.. find an equation relating C and s if 200m sidewalk costs $4500
B) what does the constant variation represent ?
C) use the equation to determine the cost of a 700m sidewalk

Answer 1

A) s=200 C=4500
To find the equation, we must find out how much a 1m sidewalk cost: 4500/200= 22.5 $/m
so the equation is s*22.5=C
B)The constant variation represent that every 1m is equal to $22.5
C) 700*22.5= $15,750

Answer 2

Constant of Variation has this formula for Direct Variation.
y = kx
Where y = cost in dollars; x = length in meters; k = constant

We will use the formula for direct variation because the problem states that the cost varies directly to the length.

In the problem we need to get the constant of variation.

k = y/x
k = $4500 / 200 meter
k = $22.50 cost per meter.

A.) The equation relating C and s is:

k = C/s
* i just substituted C for y and s for x.

B.) The constant of variation represents the additional cost that the company will pay for every meter in length they add. which is $22.50 per meter.

C.) y = kx ; substitute C and s to y and x respectively;

C = ks
C = $22.50 * 700 m
C = $15,750