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Thread: need help with quadratic relations

  1. #1
    ssj
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    need help with quadratic relations

    A square based prism has volume given by the expression 81x4 -1
    A) find the dimensions of the square based prism

    Square based side #1:____________________ Square Based side #2: ____________________ Height ________

    B) if we increased the square based by 1 cm and height remains the same. Write a factored expression for the volume of the new prisms.

    C) what is the difference between the volume of the new prisms?

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  2. #2
    MHF Contributor
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    Re: need help with quadratic relations

    Quote Originally Posted by ssj View Post
    A square based prism has volume given by the expression 81x4 -1
    A) find the dimensions of the square based prism

    Square based side #1:____________________ Square Based side #2: ____________________ Height ________

    B) if we increased the square based by 1 cm and height remains the same. Write a factored expression for the volume of the new prisms.

    C) what is the difference between the volume of the new prisms?

    The problem statement incorrectly uses the word "square" in describing the prism base ... the description "square" would mean Square based side #1 = Square Based side #2 ... the problem statement should state the prism has a rectangular base instead of a square base.

    $V = \color{blue}{L \cdot W \cdot H} = 81x^4-1 = (9x^2-1)(9x^2+1) = \color{blue}{(3x+1)(3x-1)(9x^2+1)} \implies$ base side #1 (the length) = $3x+1$, base side #2 (the width) = $3x-1$, and height = $9x^2+1$

    see if you can work out parts (b) and (c) yourself.


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