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Sav [38]
3 years ago
11

The total cost of c ounces of cinnamon if each ounce costs$.79

Mathematics
1 answer:
Anit [1.1K]3 years ago
8 0

The total cost of c ounces of cinnamon would be $0.79c

Since each ounce costs $0.79, just multiply this number by the number of ounces to get the cost.

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A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen
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Step-by-step explanation:

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If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}

The restriction is that the perimeter have to be 12 ft at most:

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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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