Find the volume of the figure: a prism of volume 15 with a pyramid of the same height cut out.

The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.

Step-by-step explanation:

The given is,

                A prism of volume 15

                A pyramid of the same height cut out

               For the above question diagram is missing, so i attach the diagram.

Step:1

            Ref the attachment,

                   Volume of figure = Volume of Prism - Volume of Pyramid....(1)

Step:2

           From the given diagram,

           Formula for volume of prism,

                                     ......................(2)

          Where, w - Width of the prism

                        h - Height of prism

                         l - Length of prism

        From the given,

        Volume, V = 15 cubic units

                         l = a

                       w = b

                        h = c

         Equation (1) becomes,

                                    15 = abc

                                      c =

Step:3

          Volume of pyramid, ..........................(2)

          where,

                      w - Width of pyramid

                       h - Height of pyramid

                        l - Length of pyramid                              

           From the given,

                      l = a

                    w = b

                     h = c

         From the volume of prism, h = c =

         Equation (2) becomes,

                                                         = 5

                                          cubic units

Step:4

        Equation (1) becomes,

                         Volume of figure = 15 - 5

                                                       = 10 cubic units

Result:

        The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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