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
Darina [25.2K]
3 years ago
15

Evaluate the given integral by changing to polar coordinates. 8xy dA D , where D is the disk with center the origin and radius 9

.
Mathematics
1 answer:
BabaBlast [244]3 years ago
5 0

Answer:

0

Step-by-step explanation:

∫∫8xydA

converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.

So,

∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ

So we integrate r from 0 to 9 and θ from 0 to 2π.

∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ

= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ

= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ

= 8[6561/4]∫(cosθsinθ)dθ

= 13122∫(cosθsinθ)dθ

Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2

Substituting this we have

13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ

= 13122/2[-cos2θ]/2 from 0 to 2π

13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]

= -13122/4[cos4π - cos(0)]

= -13122/4[1 - 1]

= -13122/4 × 0

= 0

You might be interested in
Over the three evenings,Karen received a total of 137 phone calls at the call center. The third evening, she received 4 times as
marin [14]

Answer:

1st: 22, 2nd: 27, 3rd: 88

Step-by-step explanation:

Make an equation

If she recieved x calls the 1st evening, then the 2nd evening she recieved x+5, and the 3rd evening she recieved 4x.

x+x+5+4x=137

Combine like terms

6x+5=137

Subtract 5 from both sides

6x=132

Divide by 6 on both sides

x=22

First:

22 calls

Second:

x+5

22+5

27 calls

Third:

4x

4*22

88 calls

Hope this helps!

3 0
2 years ago
Tom is sorting cookies with his little sister Betty. He notices that when he takes a cookie she takes three cookies, when he tak
telo118 [61]
T   1     2    3     4
B   3     6    9   12
This is linear relationships B=3*T (it can be also called directly proportional)
3 0
3 years ago
1. My number has two digits.
lana [24]

\implies {\blue {\boxed {\boxed {\purple {\sf {Your\:answer\:is\:59.}}}}}}

\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}

1. My number has two digits.

  • 59 is a two-digit number. ✔

2. Double my number is less than 150.

  • Double of 59 is 118, which is less than 150. ✔

3. I am not divisible by 12.

  • Since 59 is an odd number, hence it is not divisible by 12. ✔

4. My digits are different from each other.

  • The digits 5 and 9 are different. ✔

5. The second digit in my number is divisible by an odd number.

  • 9 is divisible by an odd number, i.e. 3. ✔

6. My first digit is less than my second digit.

  • 5 is less than 9. ✔

7. My digits add up to 14.

  • 5 + 9 gives us 14. ✔

Therefore, the required number is \sf\pink{59}.

\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}

7 0
2 years ago
Read 2 more answers
if a tourist walked all 3 trails in a day,how many kilometers would he or she have walked? km, (2.39, 1.28, 2.542)
natita [175]
He or she would have walked a total of all three numbers for example 2.39 + 1.28 would be 3.67, add 2.542 to that to get the total of 6.202 km that he/she walked.


   hope this helps  :)
4 0
3 years ago
Which is an algebraic expression for 5 more than z? <br> 5z<br> Z+5<br> 5z+5<br> 5-z
svetoff [14.1K]
"5 more than z"  means 5+z, or z+5.


what the other mean is as follows:

<span>5z   "5 times z"
Z+5  
5z+5  " 5 more 5 times z"
5-z    "z less than 5 "


Answer: </span>z+5
5 0
3 years ago
Read 2 more answers
Other questions:
  • One third of the square root of which number is 0.001
    7·1 answer
  • Can someone explain how to solve this?
    13·1 answer
  • WHAT IS THIS ANSWER ASAP!!!
    13·2 answers
  • Which expression is equivalent to 2x - 17?
    15·2 answers
  • please help, answer will get brainliest!!! The formula for the area of a triangle is A = one-half b h. Hiro is solving the equat
    6·2 answers
  • What is the value of the expression 6z2+2z+10 when z=3?
    10·1 answer
  • Answer this for me please?
    14·2 answers
  • (-5,7) and (2,5) <br> find the slope of the line passing through the given points
    12·1 answer
  • Factorise pls explain me i will make u brainlinst​
    9·1 answer
  • Need help 7 th grade math from 5 to 7
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!