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

Answer:

51.9914 or 52 hrs.

Step-by-step 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

Answer:

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

Step-by-step 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,

$h=\frac{-(-160)\pm\sqrt{(-160)6-4(6)(7900)}}{2(6)}$

$h=\frac{160\pm\sqrt{188640}}{12}$

$h=\frac{160+\sqrt{188640}}{12},\frac{160-\sqrt{188640}}{12}$

$h=49.52,-22.8$

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.