The maximum weight allowed per car on The Twister carnival ride is 263 pounds. Your friend weighs 86 pounds. To be able to ride
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See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius 
and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given , i.e. 
.
The volume is then
The volume is then
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Work out the parenthesis.
Combine like terms.
Subtract 9 from both sides.
Subtract 4x from both sides
Divide both sides by -9
Work out the parenthesis.
Combine like terms.
Subtract 9 from both sides.
Subtract 4x from both sides
Divide both sides by -9