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dangina [55]
2 years ago
6

Estimate the quotient by rounding the expression to relate to a one-digit fact. Explain your thinking in the space below. a. 432

÷ 73 ___________ b. 1,275 ÷ 588 ___________
Mathematics
1 answer:
erastovalidia [21]2 years ago
8 0

Answer:

5 remainder 50 and 2 remainder 100

Step-by-step explanation:

432 /73

432=400

73=70

70/400 = 005 Remainder 50

1275=1300

588=600

1300/600=2 remainder 100

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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

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\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
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=14x^4\bigg|_{x=0}^{x=1}
=14
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