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tatuchka [14]
3 years ago
13

The volume of a rectangular prism is (x4 + 4x^3 + 3x^2 + 8x + 4), and the area of its base is (x3 + 3x^2 + 8). If the volume of

a rectangular prism is the product of its base area and height, what is the height of the prism?
Mathematics
2 answers:
kap26 [50]3 years ago
6 0

V=x^4+4x^3+3x^2+8x+4\\\\B=x^3+3x^2+8\\\\V=BH\to H=\dfrac{V}{B}\\\\\text{Substitute:}\\\\H=\dfrac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}

Dovator [93]3 years ago
6 0

Answer:

Height = \frac{(x+3)(x^{3}+x^{2}+8)}{(x^{3}+3x^{2}+8)}

Step-by-step explanation:

The volume of a rectangular prism = (x^{4}+4x^{3}+3x^{2}+8x+4)

and the area of the base = ((x^{3}+3x^{2}+8)

We know the formula,

Volume of the rectangular prism = Area of the base × Height

Height = \frac{\text{Volume of the prism}}{\text{Area of the base}}

Now plug in the value of volume and area in the formula

Height = \frac{x^{4}+4x^{3}+3x^{2}+8x+24}{x^{3}+3x^{2}+8}

Further solving the fraction

Height = \frac{(x+3)(x^{3}+x^{2}+8)}{(x^{3}+3x^{2}+8)}

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