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3 years ago

Subtract. Write your answer using scientific notation

Mathematics

1 answer:

denis-greek [22]3 years ago

8 0

Answer: The correct answer is D

8.4282 * 10⁸

Step-by-step explanation:

(8.47 * 10⁸) - ( 4.18 * 10⁶)

= (8.47 * 10⁸) - (0.0418 * 10⁸)

= 8.4282 * 10⁸

Hope this helps

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2 years ago

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3 years ago

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