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# C2 Differetiation Watch

1. Any chance I could get step by step instructions on how to simplify this:

40(40/(4+pi)) - 2(40/(4+pi))(40/(4+pi)) - 0.5pi(40/(4+pi))(40/4+ pi))

to get:

A = 800/4+pi ??

Ive been at it all morning - Im so annoyed that I cant seem to get the simple things like the best order in which to do things - I was trying ti di the BRACKETS FIRST followed by the exponents - like that bidmas thing This is for the following question.

A shape consists of a rectangular base with a semicircular top, as shown. Given that the perimeter of the shape is 40cm, show that its area, A cm^2, is given by the formula A=40r - 2r^2 – Pi r^2 / 2, where r cm is the radius of the semicircle. Find the maximum value for this area.

I have done the rest of it just cant simplify that last bit properly - coz apparently thats the answer - rather than it being a number which I am a bit confused about...as well!
2. 40(40/4+π) is expanded to get 1600/4+π

However, -2((40/4+π))((40/4+π)) - 0.5π((40/4+π)(40/4+π)) can be simplified into:

-2(40/4+π)^2 - 0.5π(40/4+π)^2

Now factorise this to get:
(-2-0.5π)(40/4+π)^2 which is the same as -(2+0.5π)(40/4+π)^2

So I think this should help to start from:

A = 1600/4+π - (2+0.5π)(40/4+π)^2 and simplify this to get A = 800/4+π

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Updated: April 17, 2016
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