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ZanzabumX [31]
3 years ago
11

Find the distance and midpoint of the following points: (3, 2) and (8, 9)

Mathematics
1 answer:
azamat3 years ago
6 0

Answer:

Midpoint:

\frac{3 + 8}{2}  = 6.5 \:  \:  \:  \:  \frac{2 + 9}{2}  = 6.5 \\ (6.5 \: and \: 6.5) \\  \\ distance -  \sqrt{(8 - 3) {}^{2} + (9 - 2) {}^{2}  }   \\  \sqrt{25 + 49}  =  \sqrt{74}

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Answer:

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3 years ago
Find the average value of f over region
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D is a right triangle with base length 1 and height 8, so the area of D is \dfrac12(1)(8)=4.

The average value of f(x,y) over D is given by the ratio

\dfrac{\displaystyle\iint_Df(x,y)\,\mathrm dA}{\displaystyle\iint_D\mathrm dA}

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\displaystyle\frac74\iint_Dxy\,\mathrm dA

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\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx
=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx
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3 years ago
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vlabodo [156]
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Read 2 more answers
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<span>(x - 8) (x + 8)
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= x^2 - 64</span>
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4 years ago
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