SOLUTION: The height of waves in a storm depends on the speed of the wind. Assuming the wind has no obstructions for a long​ distance, suppose the maximum wave height H for a wind spee

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Question 1065943: The height of waves in a storm depends on the speed of the wind. Assuming the wind has no obstructions for a long​ distance, suppose the maximum wave height H for a wind speed x can be approximated by H = 0.05x^2+2x−15​, where H is in feet and x is in knots​ (nautical miles per​ hour). For what wind speed would the maximum wave height be 10 ​ft?
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
10=0.05 x^2+2x-15
Multiply by 20 to remove the decimal point.
200=x^2+40x-300
x^2+40x-500=0
(x+50)(x-10)=0
x=10 knots.
10=100(0.05)+10(2)-15=10

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
H = 0.05x^2+2x−15​
:
We are given H = 10 and asked to solve for x
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10 = 0.05x^2+2x−15​
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subtract 10 from both sides of =
:
0.05x^2+2x−25 = 0
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Divide both sides of = by 0.05
:
x^2 +40x -500 = 0
:
(x + 50) * (x - 10) = 0
:
x = -50 and x = 10
:
We reject the negative value for x
:
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For a max height of 10 foot waves,
we have a wind speed of 10 knots
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