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The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Answer :

ujalakhan18

Answer:

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

Step-by-step explanation:

[tex]Volume = Base \ Area\ * Height[/tex]

[tex]Height = \frac{Volume}{Base \ Area}[/tex]

Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]

Putting in the formula

[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]

Doing long division, we get

[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

This is the simplifies form and it can't be further simplified.

09pqr4sT

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

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