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Studentka2010 [4]
3 years ago
7

Angie packed same-size cubes into a rectangular prism. Image shows a base of cubes 3 units long, 2 units wide, and with a column

of cubes 1 cube wide and 7 cubes tall. Which expression could be used to find the number of cubes that would fill the prism? A. ( 3 + 2 ) + 7 B. ( 3 × 2 ) × 6 C. ( 3 × 2 ) + 7 D. ( 3 × 2 ) × 7
Mathematics
2 answers:
Anestetic [448]3 years ago
4 0

Answer:

I believe it's C. (3 x 2) + 7!

sergejj [24]3 years ago
4 0

Answer:Hey im the only one right here i guess its d

Step-by-step explanation:

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Work Shown:

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I'm have some issues with the problem shown in the screenshot and would love some help.
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The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

  • Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

  • Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let <em>x </em>represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, <em>V</em>, of the box is therefore;

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By differentiation, at the extreme locations, we have;

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Which gives;

\frac{d V }{dx}  =12\cdot \:  {x}^{2}  -  212\cdot \:  {x} + 630 = 0

6•x² - 106•x + 315 = 0

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When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

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Answer:

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