SOLUTION: I'm not sure on how to start the following: When mineral deposits formed a coating 1mm thick on the inside of a pipe, the area through which the fluid can flow was reduced by 20%.

Question 174611This question is from textbook Algebra and Trigonometry Structure and Method Book 2
: I'm not sure on how to start the following:
When mineral deposits formed a coating 1mm thick on the inside of a pipe, the area through which the fluid can flow was reduced by 20%. Find the original inside diameter of the pipe.
It also gives me the equations for area of a circle and diameter.
Help is appreciated.
Thank you. This question is from textbook Algebra and Trigonometry Structure and Method Book 2

Found 2 solutions by checkley77, Alan3354:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
The formula for the area of a circle is pir^2
Thus:
.8pir^2=pi(r-1)^2
.8*3.14r^2=3.14(r^2-2r+1)
2.514r^2=3.14r^2-6.28r+3.14
3.14r^2-2.514r^2-6.28r+3.14=0
.626r^2-6.28r+3.14=0
Using the quadratic equation we get 9.504 mm. for the original inside radius of the pipe.
Proof:
.8*3.14*9.504^2=3.14*(9.504-1)^2
2.512*90.326=3.14*8.504^2
226.9=3.14*72.318
227~227
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
When mineral deposits formed a coating 1mm thick on the inside of a pipe, the area through which the fluid can flow was reduced by 20%. Find the original inside diameter of the pipe.
---------------
Reduced by 20% --> 80% remaining, or 0.8 of the original area.
-------------------------

Divide by pi

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=80 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.47213595499958, 0.52786404500042. Here's your graph:

Sub r for x, the solver always uses x.
The second answer is less than 1, so it is extraneous. Ignore it.

r = apx 9.472 mms
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