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December 20, 2014

December 20, 2014

Posted by **Anonymous** on Saturday, November 5, 2011 at 4:07pm.

What I have so far:

C = 1/2*pi*d, where d=x, or the width of the rectangle

P(rectangle) = 2y + x

So, the total perimeter:

P = 2y + x + 1/2*pi*x = 30ft

I'm not sure what to do next. How do I make this expression in terms of x?

Thank you

- Calculus -
**Damon**, Saturday, November 5, 2011 at 5:09pmarea = A = pi x^2/8 + x y

so

y = [A - pi x^2/8]/x

so

30 = 2 [A - pi x^2/8]/x + x + .5 pi x

30 x = 2 A - pi x^2/4 + x^2 + .5 pi x^2

(1+pi/4)x^2 - 30 x = -2 A

parabola, find vertex for max

1.785 x^2 - 30 x = -2 A

x^2 - 42 x = -1.12 A

complete square

x^2 -16.8 x + 70.6 = -1.12 A + 70.6

(x-8.4)^2= -1.12 A + 70.6

= -1.12 (A -63.3)

so x = 8.4 at vertex

and A = 63.3

so find y from

y = [A - pi x^2/8]/x

= [ 63.3 - pi 70.6/8] /8.4

=4.23

Check my arithmetic !

=

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