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
Task 7: In the triangle, AC = 10, CB = 7, and YZ = 4. Find the values:
Aleksandr-060686 [28]

Answer:

8 points????????? TYYYYYYYYYYYYYY

Step-by-step explanaI DONT KNOOOOOOOOOOOONIGAAAAAAAAAAAAAAxD

5 0
2 years ago
Someone will.be nice to plz help.me with this online math quiz plz
liq [111]
The answer is Orlando
5 0
3 years ago
Read 2 more answers
Multiply. Write in simplest form. Identify the two whole numbers between which the product lies.
True [87]
The answer is:
8 x 1/5 = 8/5
Five divides eight one time with a remainder of three.
The mixed number is 1 and 3/8, it is between 1 and 2.

~Hope this Helped~
5 0
3 years ago
Help me please !!!!!
Anuta_ua [19.1K]
You are correct!

90 would be the correct choice, here is why:

use the eqation: $20*30*15%

first times $20*30=600

now, 600 *15%= $90

therefore, your answer is 90 dollars
5 0
3 years ago
What is the equation of a line that is parallel to -3x+4y=4 and passes through the point (4,0)
Andrei [34K]

Answer:

y = 3/4x - 3

Step-by-step explanation:

If you write the equation in slope-intercept form, you will need the slope(m) and the y-intercept(b):

y = mx + b

To solve this, you first need to know the slope of the line in the given equation. In order to do this, change it to slope-intercept form for easy analyzation:

-3x + 4y = 4

= 4y = 3x + 4

= y = 3/4x + 1

Now, you know the slope(m) is 3/4, so you have this much of the slope-intercept equation:

y = 3/4x + b

At this point, you need to find the y-intercept. This can be done by plugging in the given point in the equation and solving for b:

using (4, 0) and y = 3/4x + b,

(0) = 3/4(4) + b

0 = 3 + b

b = -3

So, that means that the equation for the line is:

y = 3/4x - 3

6 0
2 years ago
Other questions:
  • Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 56°, a = 12, b = 14
    6·1 answer
  • What is the product?<br> 3 x [1 -4 5 -7]
    12·1 answer
  • Yolanda left for a youth retreat at 8:00 p.m. On Friday. She came home on Sunday morning at 10:00 a.m. How long was Yolanda away
    10·2 answers
  • Which graph represents an exponential function?
    5·1 answer
  • Alyssa starts with $40 and saves $10 each week. Bill has $24 and saves $12 each week. For numbers 5a. – 5c., determine whether e
    6·1 answer
  • Please help, i seriously don't understand how to solve this ;_;
    14·1 answer
  • Pls help. Write an equation to express y in terms of x.
    9·1 answer
  • Kathy is a scientist who is working in a remote part of Australia. She earns a salary of $86 840 plus a weekly allowance of $124
    14·1 answer
  • I need help do y’all know answer…..
    13·1 answer
  • After the first four games of a professional football season, three players scored a total of 80 touchdowns.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!