SOLUTION: a circle of radius 6 units has half of its area removed by cutting off a border of uniform width find the width of the border

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Question 929900: a circle of radius 6 units has half of its area removed by cutting off a border of uniform width find the width of the border
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,



A = pi%2Ar%5E2

let x be the width of the border

%28pi%2A6%5E2%29%2F2+-pi%2A%286-x%29%5E2+=+0

%28pi%2A6%5E2%29%2F2+=+pi%2A%286-x%29%5E2+

 18 = (6-x)^2 = 36 - 12x +x^2

x^2  - 12x + 18 = 0

x = 1.75735931288072

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B18+=+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=%28-12%29%5E2-4%2A1%2A18=72.

  

  Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+72+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+10.2426406871193

    x%5B2%5D+=+%28-%28-12%29-sqrt%28+72+%29%29%2F2%5C1+=+1.75735931288072

    

    Quadratic expression 1x%5E2%2B-12x%2B18 can be factored:

  1x%5E2%2B-12x%2B18+=+1%28x-10.2426406871193%29%2A%28x-1.75735931288072%29

  Again, the answer is: 10.2426406871193, 1.75735931288072.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B18+%29