If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by:
[tex]h = (x+1)-\dfrac{4}{(x^3+3x^2+8)}[/tex]
Given :
Volume of rectangular prism [tex]= x^4+4x^3+3x^2+8x+4[/tex]
Base Area of a rectangular prism = [tex]x^3+3x^2+8[/tex]
[tex]\rm Volume = Base \;Area\times Height[/tex] ---- (1)
Solution :
The volume of prism is the amount of space a prism occupies. It has two same faces and other faces that resemble a parallelogram.
Let the height of the prism be h.
Now, substitute the value of base area and volume of the rectangular prism in the given equation (1).
[tex](x^4+4x^3+3x^2+8x+4) = (x^3+3x^2+8)\times h[/tex]
[tex]\dfrac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}=h[/tex]
[tex]h = \dfrac{((x+1)(x^3+3x^2+8)-4)}{(x^3+3x^2+8)}[/tex]
[tex]h = (x+1)-\dfrac{4}{(x^3+3x^2+8)}[/tex]
If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by:
[tex]h = (x+1)-\dfrac{4}{(x^3+3x^2+8)}[/tex]
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https://brainly.com/question/15861918