SOLUTION: A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of

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Question 635815: A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 2 inches, how wide will the border be? Use 3.14 to approximate Pi. Express your solution rounded to two decimal places. (1 cubic yard= 27 cubic feet)
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width of the border
volume=pi%2A%285%2Bx%29%5E2%2A2-pi%2A5%5E2%2A2=27
volume=pi%2A%2825%2B10%2Ax%2Bx%5E2%29%2A2-pi%2A5%5E2%2A2=27
volume=157%2B62.8%2Ax%2B6.28%2Ax%5E2-157=27
6.28%2Ax%5E2%2B62.8%2Ax-27=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6.28x%5E2%2B62.8x%2B-27+=+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=%2862.8%29%5E2-4%2A6.28%2A-27=4622.08.

Discriminant d=4622.08 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-62.8%2B-sqrt%28+4622.08+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2862.8%29%2Bsqrt%28+4622.08+%29%29%2F2%5C6.28+=+0.412888605663785
x%5B2%5D+=+%28-%2862.8%29-sqrt%28+4622.08+%29%29%2F2%5C6.28+=+-10.4128886056638

Quadratic expression 6.28x%5E2%2B62.8x%2B-27 can be factored:
6.28x%5E2%2B62.8x%2B-27+=+6.28%28x-0.412888605663785%29%2A%28x--10.4128886056638%29
Again, the answer is: 0.412888605663785, -10.4128886056638. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6.28%2Ax%5E2%2B62.8%2Ax%2B-27+%29

The border should be .41 inches wide.