At a college, records show that the average persons grade point average, G, is a function of the number of hours he or she studies and does homework per week h. The grade point average can be estimated by the equation : G=0.01h^2 +0.2h+1.2
To obtain a 3.2 GPA how many hours per week would the average student need to study?
P.S. It already asked for the GPA if the student studied for 0 hrs i got 1.2 and also asked for the GPA if the student studied for 3 hrs and i got 1.89.
3.2 = .01 h^2 + .2 h + 1.2
.01 h^2 + .2 h - 2 = 0
h^2 + 20 h - 200 = 0
h = -10+/- 10sqrt3
h = 7.32 hr
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check h = about 7.3
.01 h^2 = .53
.2 h = .15
+ 1.2
= 3.2 ok, it works
To find out how many hours per week the average student would need to study to obtain a GPA of 3.2, we can set up the given equation as follows:
G = 0.01h^2 + 0.2h + 1.2
We need to solve this equation for h (the number of hours per week). Rearranging the equation, we have:
0.01h^2 + 0.2h + 1.2 = 3.2
Now, let's solve this quadratic equation. Subtracting 3.2 from both sides, we get:
0.01h^2 + 0.2h - 2 = 0
Next, we need to find the values of h that satisfy this equation. There are different methods to solve quadratic equations, and one common method is using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 0.01, b = 0.2, and c = -2. Substituting these values into the quadratic formula, we get:
h = (-0.2 ± sqrt(0.2^2 - 4(0.01)(-2))) / (2(0.01))
Simplifying further, we have:
h = (-0.2 ± sqrt(0.04 + 0.08)) / 0.02
h = (-0.2 ± sqrt(0.12)) / 0.02
Notice that the expression inside the square root is positive, so we can proceed. Evaluating the square root, we have:
h = (-0.2 ± sqrt(0.12)) / 0.02
h = (-0.2 ± 0.3464) / 0.02
Now, let's calculate both possible values:
h₁ = (-0.2 + 0.3464) / 0.02
h₁ ≈ 7.32
h₂ = (-0.2 - 0.3464) / 0.02
h₂ ≈ -27.32
Since the number of hours cannot be negative, we discard the solution h₂ ≈ -27.32.
Therefore, to obtain a GPA of 3.2, the average student would need to study approximately 7.32 hours per week.