Web Analytics
ashleywebb1228
Answered

The volume of water in a rectangular swimming pool can be modeled by the polynomial 2x^3-9x^2+7x+6. If the depth of the pool is given by the polynomial 2x + 1, what polynomials express the length and width of the pool?

Verified Answer :

bartdrinksmalk

The area of the base is given by
\(B=\frac{V}{h}\)

We are given
\(V=2x^{3}-9x^{2}+7x+6\) and \(h=2x+1\)
\(\rightarrow B=\frac{2x^{3}-9x^{2}+7x+6}{2x+1}\)
which we can solve with long division:
                     x^2 -5x+6
2x+1 | 2x^3-9x^2+7x+6
           2x^3+ x^2
          --------------------------
                -10x^2+7x
                -10x^2-5x
                 --------------------
                          12x+6
                          12x+6
                         -----------
                                  0

So \(B=x^{2}-5x+6\)
which can be factored as
\((x-2)(x-3)\)

So the length and width are \(x-2\) and \(x-3\).

Related Questions