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kari74 [83]
3 years ago
15

The volume of the rectangular prism is 60x^3 + 145x^2 + 70x. Factor to find the possible expressions for length, width and heigh

t of the prism.
Mathematics
1 answer:
tester [92]3 years ago
4 0
The volume of the rectangular prism:
V=length\cdot width\cdot height=lwh

60x^3 + 145x^2 + 70x=5x(12x^2+29x+14)\\\\=5x(12x^2+21x+8x+14)=5x[3x(4x+7)+2(4x+7)]\\\\=5x(4x+7)(3x+2)\\\\Answer:\\length=5x\\width=4x+7\\height=3x+2
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Step-by-step explanation:

<h3><u>Part (a)</u></h3>

See attachment 1.  The line of best fit is shown in red.

<h3><u>Part (b)</u></h3>

The quantities the student should graph in order to produce a <u>linear relationship</u> between the two quantities are t² and D.

<h3><u>Part (c)</u></h3>

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\begin{array}{|l|l|l|l|l|l|}\cline{1-6} \rm t^2& 0.0196& 0.1024& 0.2116 & 0.3481& 0.3969\\\cline{1-6} \rm D & 0.10 & 0.50& 1.00 & 1.70 & 2.00\\\cline{1-6}\end{array}

<u>Plot</u> a graph of D against t² and draw a line of best fit (see attachment 2).

<h3><u>Part (d)</u></h3>

From inspection of the graph, the line of best fit passes through the origin (0, 0) and (0.1024, 5.0).  Therefore, use these two points to find the slope of the line:

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\rm \implies \dfrac{1}{2}g=4.8828125...\:\rm m/s^2

\rm \implies g=2 \cdot 4.8828125...\:\rm m/s^2

\rm \implies g=9.8\:\rm m/s^2\:(1\:d.p.)

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