The formula for the volume of this rectangular prism is:

V = x 3 + 5x 2 - 4x - 20

The length is x+5; the width is x+2; the height is unknown. Find an expression for the height.

Show all steps of your work for full credit.

Answers

Answer 1

Answer:

Step-by-step explanation: Explanation:

If

L

,

H

and

W

represent the length, height and width of the prism, then the volume of the rectangular prism is :

V

=

L

.

H

.

W

............. (1)

Given :

V

=

x

3

+

11

x

2

+

20

x

32

;

............... (2)

W

=

(

x

1

)

;

   

H

=

(

x

+

8

)

.

Let

L

=

(

x

+

l

0

)

be the expression for the length, then the RHS of equation (1) becomes

L

.

H

.

W

=

(

x

l

0

)

(

x

+

8

)

(

x

1

)

,

   

   

   

   

=

(

x

+

l

0

)

(

x

2

+

7

x

8

)

   

   

   

   

=

(

x

+

l

0

)

(

x

2

+

7

x

8

)

   

   

   

   

=

x

3

+

(

7

+

l

0

)

x

2

+

(

7

l

0

8

)

x

8

l

0

..... (3)

Comparing this to the LHS of equation (1), we get the following set of equations to solve for

l

0

,

7

+

l

0

=

11

;

   

7

l

0

8

=

20

;

   

8

l

0

=

32

;

l

0

=

4

Therefore

L

=

(

x

+

4

)


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\frac{x}{300} \leq 15
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Answers

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Answer:

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Answers

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Answers

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Answers

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