anonymous
  • anonymous
The volume in cubic feet of a box can be expressed as V(x)=x^3-5x^2+6x or as the product of three linear factors with integer coefficients. The width of the box is 2 – x. a. Factor the polynomial to find linear expressions for the height and the width. b. Graph the function. Find the x-intercepts. What do they represent? c. Describe a realistic domain for the function. d. Find the maximum volume of the box.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Callisto
  • Callisto
Do you know how to factorize a polynomial?
anonymous
  • anonymous
x(2 + -1x)(3 + -1x)
anonymous
  • anonymous
for the height

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anonymous
  • anonymous
? 2 + -1x for the width
anonymous
  • anonymous
Your addition signs are redundant. Just write:\[V(x)=x(2-x)(3-x)\]
anonymous
  • anonymous
ok for the height
anonymous
  • anonymous
and the width 2-1x
anonymous
  • anonymous
and the width 2-1x
anonymous
  • anonymous
You know 2-x is the width. Now the length is either x or 3-x. Which one makes sense? Can we decide this with the information we are given
anonymous
  • anonymous
x
anonymous
  • anonymous
dont I just need to find the height and width
anonymous
  • anonymous
I don't see a way to determine this. We can pick 3-x as the length, making x the height. Or we could call 3-x the height and then x is the length. It is arbitrary which one we assign to each dimension since the volume comes out the same regardless of the labels we choose.
anonymous
  • anonymous
I have to head work...good luck!
anonymous
  • anonymous
is this calculus or pre calc?
anonymous
  • anonymous
factors as \[x(x-3)(x-2)\] no need for the minus sign. reasonable domain would be something like \(0
anonymous
  • anonymous
to graph, i would use this http://www.wolframalpha.com/input/?i=x^3-5x^2%2B6x+domain+0..2

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