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
Nataliya [291]
3 years ago
11

Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

2 (measured in coulombs per square meter). Find the total charge on the disk.
Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

Required total charge is 256\pi coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

x^2=y^2\leq 16 so that the charge density at (x,y) is,

\rho (x,y)=2x+2y+2x^2+2y^2

To find total charge on the disk let Q be the total charge and x=r\cos\theta,y=r\sin\theta so that,

Q={\int\int}_Q\rho(x,y) dA                where A is the surface of disk.

=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA

=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta

=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta

=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta

=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta

=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi

=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi

=256\pi

Hence total charge is 256\pi coulombs per square meter.

You might be interested in
Use the multiplication property of equality to multiply both sides of the equation by 1/6 to get: (1/6)6x=(1/6)48.
zzz [600]
X= 8 because by multiplying the fraction with a whole number you had to to convert it to i a fraction and that equals one and then 1/6 times 48 is 8
5 0
3 years ago
What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
Firlakuza [10]

Answer:

(y-(-3))=4(x-(-1))

Step-by-step explanation:

formula for point slope form is:

y-y1=m(x-x1)

just plug in numbers from the point (-1, -3) for x1 and y1. The slope 4, would plug into m.

6 0
3 years ago
Suponha que uma variável assume os valores: 11 – 8 – 7 – a – 16 – 10 Determine a de modo que a média aritmética seja igual 11.
Elenna [48]

Answer:

a = 14  

Step-by-step explanation:

The mean is the sum of the values divided by the number of values.

\begin{array}{rcl}\text{Mean}&= &\dfrac{11 + 8 + 7 + a + 16 + 10}{6}\\\\\dfrac{52 + a}{6}& = & 11\\52 + a & = & 66\\a & = & 66 - 52\\& = & \mathbf{14}\\\end{array}

4 0
3 years ago
What consists of one endpoint and all the points on one side of the endpoint extends infinitely in one direction?
GREYUIT [131]
A ray, is a line that has one endpoint on one side and on the other side is an infinity amount of numbers

6 0
3 years ago
Evaluate the following algebraic expression, if (x = 5, y = 3)<br> x² +9y - 5
gladu [14]

Answer: 47

Step-by-step explanation:

simply substitute the constants with 5 and 3.

(5)^2 + 9(3) - 5 = 47

3 0
3 years ago
Read 2 more answers
Other questions:
  • △MNO ~△DEF. Identify the perimeter and area of △MNO to the nearest tenth. PLEASE HELP!!!
    5·1 answer
  • Can someone please tell me what the formula to find area and volume for this would be?
    7·1 answer
  • Is 30 and 138 relatively prime
    10·2 answers
  • A circle has center (5. --4) and radius 8. Which gives the equation for the circle?
    10·1 answer
  • Add the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers o
    7·1 answer
  • If f(x) = 3x + 7, find:<br> f(-2) = [ ? ]
    13·1 answer
  • Work out the value of (6.31×10⁵)+(2.6×10⁴) give your answer in standard form​
    12·2 answers
  • Let f,g,Andy be functions such that f(x) A) f(2)=h(2)=g(2)=4<br> B) h(x) C) h(x) D) f(x), g(x), and h(x) are all continuous on t
    15·1 answer
  • A money box contains only 10-cent and 20-cent coins. There are 40 coins with a total value of $6.50. How many coins of each?
    15·2 answers
  • Last week, Caden's Ice Creamery sold 14 sundaes with nuts and 36 sundaes without nuts. What is the ratio of the number of sundae
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!