MATHEMATICS HIGH SCHOOL

Awaste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 19y * d ^ 3 of debris. Find the dimensions of the dumpster that will minimize its surface area.

Answers

Answer 1

Answer:

Answer:

1.92 yd x 3.83 yd x 2.58 yd

Step-by-step explanation:

We have given a rectangular base, that its twice as long as it is wide.

It must hold 19 yd³ of debris.

Lets minimize the surface area, subject to the restriction of volume (19 yd³)

The surface is given by:

$S=2(w*h+w*2w+2wh)=2(3wh+2w^2)$

The volume restriction is:

$V=w*2w*h=2w^2h=19\n\nh=(9.5)/(w^2)$

replacing h in the surface equation, we have:

$S=2(3wh+2w^2)=6w((9.5)/(w^2))+4w^2=57w^(-1)+4w^2$

Derivate the above equation and set it to zero

$dS/dw=57(-1)w^(-2) + 8w=0\n\n57w^(-2)=8w\n\nw^3=57/8=7.125\n\nw=\sqrt[3]{7.124} =1.92$

The height will be:

$h=9.5/w^2=9.5/(1.92^2)=9.5/2.69=2.58$

Therefore,The dimensions that minimize the surface are:

Wide: 1.92 yd

Long: 3.83 yd

Height: 2.58 yd

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Answers

Answer:

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Step-by-step explanation:

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What is the common ratio for the geometric sequence below, written as a fraction?768, 480, 300, 187.5, …

Answers

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Answer:

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Step-by-step explanation:

Very fast please!

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Answers

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Answers

Answer:

The statement is false.

Step-by-step explanation:

For any vector 'r' we have

$\overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k}$

The magnitude is given by

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Answers

"The correct answer is 36.
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Answer:

Step-by-step explanation:

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Answers

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HELP NO EXPLANATION NEEDED :)