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2 years ago

Compare the expressions. 40 -16 plus 10 ? -20 plus 18 plus 30

Mathematics

2 answers:

Harman [31]2 years ago

8 0

We just need to do come computation:

$40-16+10 = 40+(-16+10) = 40+(-6) = 40-6=34$

$-20+18+30 = -2+30 = 28$

So, we have 34>28

iragen [17]2 years ago

3 0

this answer is:

34>28

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A rectangular solid with a square base has a volume of 2,744 cubic inches. (Let w represent the length of the sides of the squar

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Answer:

For minimum surface area, the base length and height are equal in length and <u>equal to 14 inches.</u>

Step-by-step explanation:

Given:

Volume of rectangular solid (V) = 2744 cubic inches

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Height of solid = 'h'

We know that,

Volume = Area of base × Height

$2744=(w\times w)\times h\\\\2744=w^2h\\\\h=\frac{2744}{w^2}-----(1)$

Now, surface area of the solid is given as:

$Surface\ area=2\times (base\ area)+4(hw)\\\\Surface\ area=2w^2+4hw$

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$Surface\ area=2w^2+4\times\frac{2744w}{w^2}\\\\Surface\ area=2(w^2+\frac{5488}{w})$

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Differentiating both sides with respect to 'w' and equating it to 0, we get:

$\frac{dS}{dw}=0\\\\\frac{d}{dw}[2(w^2+\frac{5488}{w})]=0\\\\2w-\frac{5488}{w^2}=0\\\\2w=\frac{5488}{w^2}\\\\w^3=\frac{5488}{2}\\\\w=\sqrt[3]{2744}= 14\ in$

Therefore, the base length is 14 inches.

Now, from equation (1), the height is given as:

$h=\frac{2744}{w^2}\\\\h=\frac{2744}{14^2}=14\ in$

Therefore, for minimum surface area, the base length and height are equal in length and equal to 14 inches.

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