Question

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? PLEASE COMMENT, I Can't SEE ANSWERS CAUSE OF A GLITCH

Answer 1

Answer:

x + 1 - ( 4 / x³ + 3x² + 8 )

Step-by-step explanation:

If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area $*$ the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area  $*$ height, and hence we can solve for the height by dividing the volume by the base area.

Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = $\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}$ = $x+\frac{x^3+3x^2+4}{x^3+3x^2+8}$ = $x+1+\frac{-4}{x^3+3x^2+8}$ = $x+1-\frac{4}{x^3+3x^2+8}$ - and this is our solution.

Answer 2

Answer:

$x +1 - \frac{4}{x^3 + 3x^2 + 8}$

Step-by-step explanation:

$volume=base \: area \times height$

$height=\frac{volume}{base \: area}$

$\mathrm{Solve \: by \: long \: division.}$

$h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}$

$h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}$

$h=x +1 - \frac{4}{x^3 + 3x^2 + 8}$