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Gnesinka [82]
2 years ago
12

A rectangular box is designed to have a square base and an open top. The volume is to be 500in.3 What is the minimum surface are

a that such a box can have?
Mathematics
1 answer:
mr_godi [17]2 years ago
5 0

The minimum surface area that such a box can have is 380 square

<h3>How to determine the minimum surface area such a box can have?</h3>

Represent the base length with x and the bwith h.

So, the volume is

V = x^2h

This gives

x^2h = 500

Make h the subject

h = 500/x^2

The surface area is

S = 2(x^2 + 2xh)

Expand

S = 2x^2 + 4xh

Substitute h = 500/x^2

S = 2x^2 + 4x * 500/x^2

Evaluate

S = 2x^2 + 2000/x

Differentiate

S' = 4x - 2000/x^2

Set the equation to 0

4x - 2000/x^2 = 0

Multiply through by x^2

4x^3 - 2000 = 0

This gives

4x^3= 2000

Divide by 4

x^3 = 500

Take the cube root

x = 7.94

Substitute x = 7.94 in S = 2x^2 + 2000/x

S = 2 * 7.94^2 + 2000/7.94

Evaluate

S = 380

Hence, the minimum surface area that such a box can have is 380 square

Read more about surface area at

brainly.com/question/76387

#SPJ1

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Jonah found that the equation -2|8-6|-6=-12
svetoff [14.1K]

Answer:

False equation:   -2|8 - 6| - 6 = -10

Step-by-step explanation:

-2|8 - 6| - 6 = -12                True or false?

-2 | 2| - 6 = -12                    Substract 8 - 6 = 2

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7 0
3 years ago
Please help me?<br><br> please and thank you!
JulsSmile [24]

Answer:

-1/12

Step-by-step explanation:

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7 0
2 years ago
Part B
ziro4ka [17]

The linear equation that has a slope of -7 and crosses the x-axis at (3, 0) is:

y =  -7x + 21

<h3>How to find the linear equation?</h3>

A general linear equation is:

y = a*x +b

Where a is the slope and b is the y-intercept.

The slope must be equal to the limit found in part a, and you say that it is equal to -7, so the slope is -7. And for how is written the problem, I understand that it crosses the x-axis at x = 3.

Then we will have:

y = -7*x + b

Such that, when x = 3, y = 0, then:

0 = -7*3 + b

21 = b

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If you want to learn more about linear equations:

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