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Ainat [17]
3 years ago
8

a) Estimate the volume of the solid that lies below the surface z = 7x + 5y2 and above the rectangle R = [0, 2]⨯[0, 4]. Use a Ri

emann sum with m = n = 2 and choose the sample points to be lower right corners.
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
7 0

In the x direction we consider the m=2 subintervals [0, 1] and [1, 2] (each with length 1), while in the y direction we consider the n=2 subintervals [0, 2] and [2, 4] (with length 2). Then the lower right corners of the cells in the partition of R are (1, 0), (2, 0), (1, 2), (2, 2).

Let f(x,y)=7x+5y^2. The volume of the solid is approximately

\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy\approx f(1,0)\cdot1\cdot2+f(2,0)\cdot1\cdot2+f(1,2)\cdot1\cdot2+f(2,2)\cdot1\cdot2=\boxed{164}

###

More generally, the lower-right-corner Riemann sum over m=\mu and n=\nu subintervals would be

\displaystyle\sum_{m=1}^\mu\sum_{n=1}^\nu\left(7\frac{2m}\mu+5\left(\frac{4n-4}\nu\right)^2\right)\frac{2-0}\mu\frac{4-0}\nu=\frac83\left(101+\frac{21}\mu+\frac{40}{\nu^2}-\frac{120}\nu\right)

Then taking the limits as \mu\to\infty and \nu\to\infty leaves us with an exact volume of \dfrac{808}3.

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5 3/5 divided 2 2/3 jlll
Naddik [55]

Answer:

7/1 or 7.

Step-by-step explanation:

<u>Turn 2 2/3 into an improper fraction:</u>

2\frac{2}{3} =\frac{3}{3} +\frac{3}{3}+\frac{2}{3}=\frac{8}{3}

<u>Turn 5 3/5 into an improper fraction:</u>

<u />5\frac{3}{5} =\frac{5}{5} +\frac{5}{5} +\frac{5}{5} +\frac{5}{5} +\frac{5}{5} +\frac{3}{5} = \frac{28}{3}

<u>Find the reciprocal (opposite) of 8/3, then multiply:</u>

<u />\frac{28}{3} \times\frac{3}{8} =\frac{84}{24}

<u>Divide 84/24 by 12:</u>

<u />\frac{84\div12}{12\div12} = \frac{7}{1}

Your simplified answer is 7/1, or 7.

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2 years ago
I need help with #4 please as soon as possible.
Rudik [331]

I know that A is no solution and C is infinity solution but not sure about B.


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3 years ago
What are two measurements are needed to calculate the velocity of an object
maria [59]

Answer:

C. Displacement and D. Time

I hope this helps and you have a great day!!

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Kamals bedroom has an area of 120 square feet the width of the room is 5/6 the length of the room what are the dimension of kama
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3 years ago
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The equation of a line is y = 2x + 3. What is the equation of the line that is parallel to the first line and passes through (2,
Masja [62]

Answer:

y = 2x - 5

Step-by-step explanation:

The slope for a parallel line is the same as the slope in the given equation.  Therefore the slope of the new line will be 2    m= 2

use that slope and (2, -1) to find b

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Plug m and b into y = mx + b

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8 0
3 years ago
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