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
Ahat [919]
3 years ago
14

Electric charge is distributed over the rectangle 2 ≤ x ≤ 4, 0 ≤ y ≤ 2 so that the charge density at (x, y) is σ(x, y) = 2xy + y

2 (measured in coulombs per square meter). Find the total charge on the rectangle.
Mathematics
2 answers:
dybincka [34]3 years ago
7 0

Answer:

The total charge on the rectangle is 29.33C

Step-by-step explanation:

Given

σ(x, y) = 2xy + y²

For 2 ≤ x ≤ 4, 0 ≤ y ≤ 2

The total charge on the rectangle is calculated as follows.

Charge, q = ∫∫2xy + y² dydx {0,2}{2,4}

Integrate with respect to y

q = ∫xy² + ⅓y³ dydx {0,2}{2,4}

q = ∫(2²*x + ⅓*2³) dx {2,4}

q = ∫4x + 8/3 dx {2,4}

Integrate with respect to x

q = 2x² + 8x/3 {2,4}

q = (2(4)² + 8(4)/3) - (2(2)² + 8(2)/3)

q = 29.33C

jok3333 [9.3K]3 years ago
5 0

Answer: The answer is 29.33C

Step-by-step explanation:

From the question above, we have the following:

σ(x, y) = 2xy + y²

For 2 ≤ x ≤ 4, 0 ≤ y ≤ 2

The total charge on the rectangle will be calculated as follows.

Charge, q = ∫∫2xy + y² dydx {0,2}{2,4}

Now, we carry out integration with respect to y as follows:

q = ∫xy² + ⅓y³ dydx {0,2}{2,4}

q = ∫(2²*x + ⅓*2³) dx {2,4}

q = ∫4x + 8/3 dx {2,4}

Next, we carry out integration with respect to x as follows:

q = 2x² + 8x/3 {2,4}

q = (2(4)² + 8(4)/3) - (2(2)² + 8(2)/3)

q = (2(16) + 32/3) - (2(4) + 16/3)

q = (32 + 10.67) - (8 + 5.33)

q = 42.67 - 13.33

q = 29.34C

Therefore, the total charge on the rectangle is 29.34C

You might be interested in
Some students were surveyed to determine if they prefer soccer or baseball. The results are shown in the two-way table below. Ba
Arada [10]
60% add then divide them 

3 0
3 years ago
87-(36.5-11.5)*(-3)+9 simplify using order of operations
OLga [1]
Remember PEMDAS 
Do parentheses, results in 25. So whats left is 87-25*(-3)+9
Then you multiply -25 by -3, answer is 75.        87+75+9
Add all of them up.                                                171
The answer is 171!
5 0
3 years ago
Read 2 more answers
Molly earns a rebate each month on her movie tickets and books. She earns $0.25 for each movie ticket and $2 for each book. Last
Sliva [168]

The algebraic equation is 4(0.25)+2x=17

STEP 1: Simplify both sides of the equation

1+2x=17  or  2x+1

STEP 2: Subtract both sides

2x = 16

STEP 3: Divide both sides by 2

2x/2 = 16/2

x = 8

Molly purchased 8 books last month

7 0
3 years ago
If Tiva babysits for <br> hours, she will earn $32.
Viktor [21]

Answer:

true i think not 100% sure tho

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
HELP PLEASE! whats the height and base??
ddd [48]

Answer: 7.5

Step-by-step explanation:

Area of the bottom left triangle = 4x3/2 = 6

Bottom right = 6x3/2 = 9

Top right = 3x4/2 = 6

Top left = 6x3/2 = 9

6+9+6+9 = 30

Each square unit is 4

So the answer should be 30/4 = 7.5

Hope this is correct

8 0
2 years ago
Other questions:
  • 12=-4(-6x-3)
    8·1 answer
  • Factor completely 5b2+20ab+15a2
    14·1 answer
  • A) 90°<br><br> B) 180°<br><br> C). 6°<br><br> D). 86°
    9·2 answers
  • Divide (x^2-16/x-1)/x+4
    10·1 answer
  • What is the answer to this question
    10·1 answer
  • How do I determine the range. ​
    9·1 answer
  • What is the area of a rectangle with a length of 3 cm and a width of 4.5 cm?
    5·1 answer
  • Can anyone help me with this please .
    8·1 answer
  • An above ground pool with 17,100 gallons of water was draining. If the pool drained at a rate of 1,800 gallons per hour, how man
    6·1 answer
  • The wholesale price for a of shoes is $7.50. A certain department store marks up the wholesale price by 50%. Find the price of t
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!