Question

A study found that a​ student's GPA,​ g, is related to the number of hours worked each​ week, h, by the equation g= −0.0006h^2 +0.016h +3.02 Estimate the number of hours worked each week for a student with a GPA of 2.23

Answer 1

51.9914 or 52 hrs.

Explanation:

-0.0006h²+0.016+0.79 (divide each term by -0.0006)

=h²-(80/3)h-(3950/3)

Using the quadratic formula

((80/3)+sqrt((-80/3)^2-4(1)(-3950/3)))/2(1)

= 103.9828/2

=52.9914

Aprroximation: 51.9914 or 52 hrs.

Exact: ((80/3)+sqrt(53800/3))/2

Answer 2

The number of hours worked each week for a student with a GPA of 2.23 is 50 hours.

Explanation:

Given : A study found that a​ student's GPA,​ g, is related to the number of hours worked each​ week, h, by the equation
`g= -0.0006h^2 +0.016h +3.02`

To find : Estimate the number of hours worked each week for a student with a GPA of 2.23 ?

Solution :

The equation representing situation is

`g= -0.0006h^2 +0.016h +3.02`

Now, Substitute g=2.23

`2.23= -0.0006h^2 +0.016h +3.02`

Solve,

`0.0006h^2-0.016h-0.79=0`

Multiply both side by 10000,

`6h^2-160h-7900=0`

Apply quadratic formula,

`h=(-(-160)\pm√((-160)6-4(6)(7900)))/(2(6))`

`h=(160\pm√(188640))/(12)`

`h=(160+√(188640))/(12),(160-√(188640))/(12)`

`h=49.52,-22.8`

Reject h=-22.8

Approximately the value of h is 50.

Therefore, The number of hours worked each week for a student with a GPA of 2.23 is 50 hours.