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) (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) (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
:
10 = 0.05x^2+2x−15
:
subtract 10 from both sides of =
:
0.05x^2+2x−25 = 0
:
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
:
**********************************
For a max height of 10 foot waves,
we have a wind speed of 10 knots
**********************************
:
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