1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Which angles are in the exterior ​
Andre45 [30]

Answer:

a, b, f, and h

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Kentucky teens which one is the best completes the statement or answers the question
vampirchik [111]

i’m not from kentucky but it’s A

lmk if you need me to explain

7 0
3 years ago
Moneda más de la palabra insoportable
schepotkina [342]
Huhhhhhhhhhhhhhhhhhhhhhh
6 0
3 years ago
Can someone help me?
sineoko [7]

Answer:

x=4

Step-by-step explanation:


4 0
3 years ago
Devon earns a base salary of $600.00 per month, plus a 4% commission on his sales. Last month he brought in $15,000.00 in sales.
Thepotemich [5.8K]

Answer:

Total compensation = 600 + 0.04 * s  and a total last month of $1200

(which agrees with the second answer shown in the provided list)

Step-by-step explanation:

Total compensation comes from the addition of base salary ($600) plus 4% (0.04) of the sales (s). That means:

Total compensation = 600 + 0.04 * s

and since last month he brought $15000 in sales, he got from sales:

0.04 * 15000 = $600

which added to the base salary gives:

$600 + $600 = $1200

6 0
2 years ago
Other questions:
  • In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A. 22° 38° 142° 158°
    8·1 answer
  • Use substitution to solve the linear system of equations.
    10·1 answer
  • Use the information given to enter an equation in standard form. Slope is -6, and (7, 5) is on the line.
    11·1 answer
  • Round each number to the nearest 10 5,389
    12·2 answers
  • Jimmy spent $121.60 on shirts. Tee shirts cost $9.10 and long sleeve shirts cost $14.20. If he bought a total of 10, how many of
    9·1 answer
  • Which expression is equivalent to
    5·1 answer
  • It says choose all of the multiple choice answers that are true about the diagram
    12·1 answer
  • A clothing company is interested in the relationship between the number of sales per month for its employees (y) and price. Base
    10·1 answer
  • Solve x^2 +3x=0 by factoring
    7·1 answer
  • Find the measure of each angle indicated 12,13,14
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!