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Serga [27]
3 years ago
7

13. Find a cubic function with the given zeros. 7, -3, 2

Mathematics
1 answer:
emmainna [20.7K]3 years ago
5 0

\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y

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Step-by-step explanation:

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Step-by-step explanation:

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A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur
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Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

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L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in

substitute

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Convert to expanded form

V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x

using a graphing tool

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Remember that

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so

The maximum is the point (0.46,3.02)

see the attached figure

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