SOLUTION: A machine has two wheels tangent to each other. The distance between centers is 9 in. The sum of the areas is 198 sq. in. Find radius of each wheel, to the nearest hundredth of

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Question 1105369: A machine has two wheels tangent to each other. The distance between centers is 9 in. The sum of the areas is 198 sq. in. Find radius of each wheel, to the nearest hundredth of an inch.
Area of circle; pi * r^2.
radius; d/2.
Let wheels = x and y.
Not sure how to solve. Non-homework.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A machine has two wheels tangent to each other. The distance between centers is 9 in. The sum of the areas is 198 sq. in. Find radius of each wheel, to the nearest hundredth of an inch.
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x + y = 9
pi*(x^2 + y^2) = 198
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x^2 + y^2 = 198/pi
y = 9-x
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x^2 + 81-18x+x^2 = 198/pi
2x^2 - 18x + 81-198/pi = 0
2x^2 - 18x + 17.9746 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-18x%2B17.9746425356094+=+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=%28-18%29%5E2-4%2A2%2A17.9746425356094=180.202859715125.

Discriminant d=180.202859715125 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+180.202859715125+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+180.202859715125+%29%29%2F2%5C2+=+7.85599146783708
x%5B2%5D+=+%28-%28-18%29-sqrt%28+180.202859715125+%29%29%2F2%5C2+=+1.14400853216292

Quadratic expression 2x%5E2%2B-18x%2B17.9746425356094 can be factored:
2x%5E2%2B-18x%2B17.9746425356094+=+%28x-7.85599146783708%29%2A%28x-1.14400853216292%29
Again, the answer is: 7.85599146783708, 1.14400853216292. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-18%2Ax%2B17.9746425356094+%29

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x & y are the 2 solutions, they're interchangeable.
The sum of the 2 is 9.