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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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vampirchik [111]

Answer:

<em>There are 21 jelly beans in the jar.</em>

Step-by-step explanation:

Suppose, the number of jelly beans in the jar is  x

Two were off by 2, two were off by 3, two were off by 4. That means, the six guessed number will be:  (x+2), (x-2), (x+3), (x-3), (x+4), (x-4)

Given that, Alice guessed 25; Betty, 18; Clare, 23; Dotty, 19; Edith, 24; and Fran, 17.

So, the sum of all six guessed number will be:  25+18+23+19+24+17=126

Thus, the equation will be..........

(x+2)+(x-2)+(x+3)+(x-3)+(x+4)+(x-4)= 126\\ \\ 6x= 126\\ \\ x=\frac{126}{6}=21

So, the number of jelly beans in the jar is 21.


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2 years ago
What is the equation of a line with a slope of 7 and a point (1, 8) on the line?
Helen [10]

Answer:

y=7x+1

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

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m is the slope

b is the y-intercept

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m=7

point(1,8)

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8=7+b

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The equation of the line is equal to

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Use all 4 operations and at least one exponent to write and expression that has a value of 10
Yuki888 [10]

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15-5=10

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Rzqust [24]

Answer:

a). -65

b). -61

c). -20ab + 3bc +3ac

Step-by-step explanation:

According To the Question,

a). the sum of 72 − 104 + 5 and -32 + 4 - 10 .

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b). What should be added to 32 + 32 + 3 to get 3 + 3 , Let X be Added .

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c). Subtract  the sum of 12ab –10bc –18ac and 9ab + 12bc + 14ac from the sum of ab + 2bc and 3bc – ac.

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vlada-n [284]
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