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Pavel [41]
3 years ago
7

On a certain hot​ summer's day, 557 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for

adults. The receipts for admission totalled $1146.75. How many children and how many adults swam at the public pool that​ day?
Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
7 0

Answer:

Adults:193

children:295

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512\ \text{in}^2

Step-by-step explanation:

x = Length and width of base

y = Height of box

Volume of the box is 16384\ \text{in}^3

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Surface area is given by

s=x^2+4y\\\Rightarrow s=x^2+4\times \dfrac{16384}{x^2}\\\Rightarrow s=x^2+\dfrac{65536}{x^2}

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Equating with 0 we get

0=2x^4-131072\\\Rightarrow x=(\dfrac{131072}{2})^{\dfrac{1}{4}}\\\Rightarrow x=16

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at x=16

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So the function is minimum at x = 16

y=\dfrac{16384}{x^2}=\dfrac{16384}{16^2}\\\Rightarrow y=64

The material required is

s=x^2+4y=16^2+4\times 64\\\Rightarrow s=512\ \text{in}^2

The minimum amount of material required is 512\ \text{in}^2.

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