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Katyanochek1 [597]
3 years ago
14

What is the volume of the rectangular prism?

Mathematics
1 answer:
Tamiku [17]3 years ago
5 0

Answer:

1 and 1/9 feet cubed

Step-by-step explanation:

You find the volume by multiplying the height by the width by the depth

So we need to find them

The height has 5 blocks so we multiply 1/3 by 5 to get 5/3

The width has 3 blocks so we multiply 1/3 by 3 to get 3/3 or 1

The depth has 2 blocks so we multiply 1/3 by 2 to get 2/3

Then to find the volume, we have to multiply all of the dimensions so:

5/3 * 1 * 2/3

= 5/3 * 2/3

= 10/9

= 1 and 1/9 ft^3

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Type the correct answer in each box. (____)
trapecia [35]

Answer:

1. -16; 2. +64; 3. 16

Step-by-step explanation:

The formula for the volume of a cylinder is

V = πr²x

Data:

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Calculations:

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Divide each side by π

1024 = x(x - 8)²  

1024 = x(x² - 16x  + 64)

1024 =    x³ - 16x² + 64x

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The general formula for a third-degree polynomial is

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Your polynomial is  

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a = 1; d = -1024

According to the <em>rational roots theorem</em>, the possible roots are

factors of d/factors of a

Factors of d = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

Factors of a = ±1

Potential roots are x = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

That's a lot of possibilities to check by trial and error. I will just use the one that works.

Try x = 16 by synthetic division.

16|1  -16   64  -1024

  <u>|     16     0   1024 </u>

   1     0   64        0

So,

(x³ - 16x² + 64x - 1024)/(x – 16) = x² + 64

and

(x - 16)(x² + 64) = 0

x - 16 = 0        x² + 64 =    0

     x = 16       x²         = -64

                       x          =  ±8i

There is only one real root: x = 16 mm

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3 years ago
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Step-by-step explanation:

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