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Andrews [41]
3 years ago
12

Simplify 7N - 2N + 3P + 2P. (a) 5N + 5P (b) 10N + 10P (c)10NP

Mathematics
2 answers:
Yakvenalex [24]3 years ago
7 0
<span>7N - 2N + 3P + 2P

Combine like terms: 
7N-2N=5N 

3P+2P=5P 

Put them together to get :
5N+5P

Final answer: 
A</span>
aleksklad [387]3 years ago
3 0

I believe the answer to your question is 5N + 5P. I apologize in advance if the answer I gave you is incorrect.

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We can express b in function of a as:

2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a

Then, the area become:

A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2

To maximize the area, we derive and equal to zero:

\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36

Then, b is:

b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68

3 0
3 years ago
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