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Alecsey [184]
3 years ago
9

How many ordered quadruples (w, x, y, z) of positive odd integers are there

Mathematics
1 answer:
guajiro [1.7K]3 years ago
6 0

Answer:

165

Step-by-step explanation:

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A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria
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For maximum area, all of the wire should be used to construct the square.

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Step-by-step explanation:

For maximum,  we use the whole length

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supposed the x length was used for the square,

the length of the side of the square = x/4m

Area = \frac{x^{2} }{16}

For the equilateral triangle, the length of the side =  \frac{23 - x}{3}

Area = \frac{\sqrt{3} }{4}  a^{2}  = \frac{\sqrt{3} }{4} (\frac{23 - x}{3} )^{2}

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\frac{dA}{dx}  = \frac{x}{8}  -  \frac{\sqrt{3} }{18} (23 - x)\\

\frac{d^{2}A }{dx^{2} }  = \frac{1}{8}  + \frac{\sqrt{3} }{18}  > 0, therefore it is minimum

\frac{dA}{dx}  = 0 \\\\

\frac{x}{8}  -  \frac{\sqrt{3} }{18} (23 - x) = 0\\

x = 10.00m

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