1.Read the passage given below.

Mathematics

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expeople1 [14]2 years ago

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Find the average value of f over region

SVETLANKA909090 [29]

$D$ 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

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

The denominator is just the area of $D$ , which we already know. The average value is then simplified to

$\displaystyle\frac74\iint_Dxy\,\mathrm dA$

In the $x,y$ -plane, we can describe the region $D$ as all points $(x,y)$ that lie between the lines $y=0$ and $y=8x$ (the lines which coincide with the triangle's base and hypotenuse, respectively), taking $0\le x\le1$ . So, the integral is given by, and evaluates to,

$\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx$
$=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx$
$=14x^4\bigg|_{x=0}^{x=1}$
$=14$

3 0

3 years ago

Please answer i need help

skad [1K]

1. 72 to 50 points
50/72 = 69%
100-69= 31% decrease

2. 14 to 40 books
14 / 40 = 35%
100-35= 65% increase

3. 10 plus 30% increase
10 * 0.3 = 13

8 0

2 years ago

Read 2 more answers

If I got a 28% on a test and my grade is an 88% he would that affect my grade?

OlgaM077 [116]

If its from one test it doesnt always affect your grades but if you are continuously getting 28% then it will badly affect your grades

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