SOLUTION: The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what spe

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what spe      Log On


   

Question 582171: The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag?
I tried this several ways and still came up with 199.32 miles per hour which my teacher says is wrong.
Please help.
Found 3 solutions by Alan3354, stanbon, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag?
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H=0.005s^2 + 0.007s - 0.031
0.005s^2 + 0.007s - 0.031 = 200
5s^2 + 7s - 31 = 200000
5s^2 + 7s - 200031 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B7x%2B-200031+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%287%29%5E2-4%2A5%2A-200031=4000669.

Discriminant d=4000669 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+4000669+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+4000669+%29%29%2F2%5C5+=+199.316724300744
x%5B2%5D+=+%28-%287%29-sqrt%28+4000669+%29%29%2F2%5C5+=+-200.716724300744

Quadratic expression 5x%5E2%2B7x%2B-200031 can be factored:
5x%5E2%2B7x%2B-200031+=+%28x-199.316724300744%29%2A%28x--200.716724300744%29
Again, the answer is: 199.316724300744, -200.716724300744. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B7%2Ax%2B-200031+%29

====================
Ignore the negative solution.
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I get the same answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag?
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200 = 0.005s^2 + 0.007s - 0.031
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Multiply thru by 1000 to get: 5s^2 + 7s - 31 = 200000
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5s^2 + 7s - 200031 = 0
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I graphed it and got s = 199.32
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Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+H+=+.005s%5E2+%2B+.007s+-+.031+
given:
+200+=+.005s%5E2+%2B+.007s+-+.031+
-----------------------------
Multiply both sides by +1000+
+200000+=+5s%5E2+%2B+7s+-+31+
+5s%5E2+%2B+7s+-+200031+=+0+
+5s%5E2+%2B+7s+=+200031+
Divide both sides by 5
+s%5E2+%2B+%287%2F5%29%2As+=+200031%2F5+
I'll try completing the square
+s%5E2+%2B+%287%2F5%29%2As+%2B+%287%2F10%29%5E2+=+200031%2F5+%2B+%287%2F10%29%5E2+
+s%5E2+%2B+%287%2F5%29%2As+%2B+49%2F100+=+200031%2F5+%2B+49%2F100+
+s%5E2+%2B+%287%2F5%29%2As+%2B+49%2F100+=+4000620%2F100+%2B+49%2F100+
+s%5E2+%2B+%287%2F5%29%2As+%2B+49%2F100+=+4000669%2F100+
+%28+s+%2B+.7+%29%5E2+=+%28+2000.1672%2F10+%29%5E2+
Take the square root of both sides
+s+%2B+.7+=+200.01672+
+s+=+200.01672+-+.7+
+s+=+199.31672+
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I'll check this
+H+=+.005%2A199.32%5E2+%2B+.007%2A199.32+-+.031+
+H+=+.005%2A39728.462+%2B+1.395+-+.031+
+H+=+198.642+%2B+1.395+-+.031+
+H+=+200.0063+
This seems very close to the right answer.
Are we both making the same mistake?
The other possibility is you copied the
problem wrong ( or your teacher did ).
Did anyone get the right answer?