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3 years ago

3 4 (2)t/3 = 9 Round your answer to the nearest hundredth. A) 1.62 B) 3.24 C) 8.26 D) 10.75

Mathematics

1 answer:

N76 [4]3 years ago

6 0

The answer is 10.75, or 10.7548875

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Answer:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

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Step-by-step explanation:

The question is

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

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we have

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$W=(10-2x)\ cm$

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substitute

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Find the domain for x

we know that

$(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm$

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

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