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
Phoenix [80]
3 years ago
6

Approximate the integral integral integral integral f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2),

and (0, 2) into eight equal squares and finding the sum Sigma 8 i = 1 f(xi, yi) where (xi, yi) is the center of the ith square. Evaluate the iterated integral and compare it with the approximation. Integral 4 0 Integral 2 0 (x + y) dy dx Sigma 8 i = 1 f(xi, yi) delta Ai = ___________ Integral 4 0 Integral 2 0 (x + y) dy dx = _____________
Mathematics
1 answer:
amm18123 years ago
7 0

Answer:

Step-by-step explanation:

Approximate the integral \int\int\limits_R {f(x,y)} \, dA by dividing the region R with vertices (0,0),(4,0),(4,2) and (0,2) into eight equal squares.

Find the sum \sum\limits^8_{i=1}f(x_i,y_i)\delta A_i

Since all are equal squares, so \delta A_i=1 for every i

\sum\limits^8_{i=1}f(x_i,y_i)\delta A_i=f(x_1,y_1)\delta A_1+f(x_2,y_2)\delta A_2+f(x_3,y_3)\delta A_3+f(x_4,y_4)\delta A_4+f(x_5,y_5)\delta A_5+f(x_6,y_6)\delta A_6+f(x_7,y_7)\delta A_7+f(x_8,y_8)\delta A_8\\\\=f(0.5,0.5)(1)+f(1.5,0.5)(1)+f(2.5,0.5)(1)+f(3.5,0.5)(1)+f(0.5,1.5)(1)+f(1.5,1.5)(1)+f(2.5,1.5)(1)+f(3.5,1.5)(1)\\\\=0.5+0.5+1.5+0.5+2.5+0.5+3.5+0.5+0.5+1.5+1.5+1.5+2.5+1.5+3.5+1.5\\\\=24

Thus, \sum\limits^8_{i=1}f(x_i,y_i)\delta A_i=24

Evaluating the iterate integral \int\limits^4_0 \int\limits^2_0 {(x+y)} \, dydx=\int\limits^4_0 {[xy+\frac{y^2}{2} ]}\limits^2_0 \, dx =\int\limits^4_0 {[2x+2]}dx\\\\=[x^2+2x]\limits^4_0=24.

Thus, \int\limits^4_0 \int\limits^2_0 {(x+y)} \, dydx=24

You might be interested in
D. AA<br><br> Help please !!!
mojhsa [17]
I think the answer is Not Similar 

6 0
3 years ago
The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0)
snow_tiger [21]
Vertex form is:

y = a(x - 1)^2 - 16  where a is a cosntant

at y intercept we have

-15 = a^2 - 16
a^2 = 1

so equation of the parabola is y = (x-1)^2 - 16

the equation of symmetry is x = 1  and both roots are same distance either side of the point (1,0) so the other x-intercept  is  1 - 4 =   (-3,0)   
4 0
3 years ago
I’m new on this !! Answer number 2 for me please !!!
kow [346]
The researchers used data from 10 trials so they could compare each trial or use the information in all, its better to use more than one so you can compare and see the difference.
4 0
3 years ago
Telia works and gets paid every two Fridays her pay check is $71.00 or more depends on how much clothes she tags. She want's to
Tomtit [17]

Answer:

1 month and 3 weeks

Step-by-step explanation:

Total amount Telia needs: 12.49 + 250 + 170 = $432.49

Total amount she has: $207

Amount needs to buy hoodie and braces: 432.49 - 207 = $225.49

Telia gets paid $71 every two Fridays.

Therefore, in one month, Telia gets $142 (71 + 71).

In one week, Telia gets $35.5 (71/2).

35.5 x 7 = $248.5

7 weeks is 1 month and 3 weeks.

Therefore, it will take Telia 1 month and 3 weeks to pay off her braces and buy a hoodie.

!!

5 0
3 years ago
The difference between a number and seven is less than or equal to -3.
ikadub [295]

Answer:

n ≤ 4

Step-by-step explanation:

"The difference between a number and seven is less than or equal to -3" translates into n - 7 ≤ -3. To solve, isolate the variable n.

n - 7 ≤ -3

n ≤ -3 + 7

n ≤ 4

5 0
3 years ago
Other questions:
  • What is the perimeter of rectangle ABCD on the coordinate plane? coordinate grid
    8·2 answers
  • Please help! 76/(-3.8)
    9·2 answers
  • I have almost like an out suffering with this one.please!help!
    12·2 answers
  • Suppose that $1200 is invested at 612%, compounded quarterly. How much is in the account at the end of 5 years?
    10·1 answer
  • Please Help!!! What is the end behavior of function h? h(x)=2(x-3)^2 As x approaches negative infinity, approaches negative infi
    6·1 answer
  • PLS!!!!!!! HELP ME!!!! PLS!!! I WILL MARK U!!!
    14·2 answers
  • Which system is represented by the graph?
    10·2 answers
  • Which is the best estimate for the mass of a desktop computer
    10·1 answer
  • Which graph represents the function f(x)=x2−49x+7?
    5·1 answer
  • 5. A monument casts a 78 ft. shadow at the same time that a vertical yardstick casts a 4.5 ft. shadow. How high is the monument?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!