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Svetach [21]
3 years ago
10

The solution to 7x = 42 is x = ___. A.4 B.5 C.6 D.7

Mathematics
2 answers:
uranmaximum [27]3 years ago
6 0

Answer:

the x value equals 6.

Step-by-step explanation:

When you are solving for x, divide the 42 by 7.

Sidana [21]3 years ago
3 0
C.6

7x = 42 => x = 42/7 = 6
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An open box with a square base is constructed so that it has a volume of 64in^3. The base needs to be made out of a material tha
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The volume of a box is the amount of space in the box

The dimensions that minimize the cost of the box is 4 in by 4 in  by 4 in

<h3>How to determine the dimensions that minimize the cost</h3>

The dimensions of the box are:

Width = x

Depth = y

So, the volume (V) is:

V = x^2y

The volume is given as 64 cubic inches.

So, we have:

x^2y = 64

Make y the subject

y = \frac{64}{x^2}

The surface area of the box is calculated as:

A =x^2 + 4xy

The cost is:

C = 2x^2 + 4xy --- the base is twice as expensive as the sides

Substitute y = \frac{64}{x^2}

C = 2x^2 + 4x * \frac{64}{x^2}

C =2x^2 +  \frac{256}{x}

Differentiate

C' =4x -  \frac{256}{x^2}

Set to 0

4x -  \frac{256}{x^2} = 0

Multiply through by x^2

4x^3 -  256= 0

Divide through by 4

x^3 -  64= 0

Add 64 to both sides

x^3 =  64

Take the cube roots of both sides

x = 4

Recall that:

y = \frac{64}{x^2}

So, we have:

y = \frac{64}{4^2}

y = 4

Hence, the dimensions that minimize the cost of the box is 4 in by 4 in  by 4 in

Read more about volume at:

brainly.com/question/1972490

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