Question

The total cost c(x) of hiring a dump truck and an operator is described by the function c(x)=300+31x-3.90x^2 , where x is the number of hours worked. Find the number of working hours if c(x)=$220.

Answer 1

2.05hrs

Explanation:

Given he total cost c(x) of hiring a dump truck and an operator is described by the function c(x)=300+31x-3.90x^2 , where x is the number of hours worked. If c(x)=$220, then;

220 = 300+31x-3.90x^2

300+31x-3.90x^2 - 220 = 0

3.90x^2 + 31x - 80 = 0

x = -31±√31²-4(-80)(3.9)/2(3.9)

x = -31±√961+1.248/7.8

x = -31±47/7.8

x = -31+47/7.8

x = 16/7.8

x = 2.05

hence the number of working hours is 2.05hrs