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
wolverine [178]
3 years ago
15

Find the area of the region that lies inside the first curve and outside the second curve. r = 6 − 6 sin θ, r = 6

Mathematics
1 answer:
yan [13]3 years ago
8 0
Each curve completes one loop over the interval 0\le t\le2\pi. Find the intersections of the curves within this interval.

6-6\sin\theta=6\implies 1-\sin\theta=1\implies \sin\theta=0\implies \theta=0,\theta=\pi

The region of interest has an area given by the double integral

\displaystyle\int_\pi^{2\pi}\int_6^{6-6\sin\theta}r\,\mathrm dr\,\mathrm d\theta

equivalent to the single integral

\displaystyle\frac12\int_\pi^{2\pi}\bigg((6-6\sin\theta)^2-6^2\bigg)\,\mathrm d\theta

which evaluates to 9\pi+72.

You might be interested in
Choose the expression that could be used to solve this problem.davin spent $8.40 for gasoline. he saw gas priced at $1.40/gal an
alex41 [277]
$1.40 • y = $8.40 I hope that helps
6 0
3 years ago
If angle 1= 105°, angle 12= (3x + 15)°, and angle 7 = (8y-5)°, determine the values<br> of x and y.
Darina [25.2K]

The value of the variable x is 30° and the value of the variable y is 10°.

The missing diagram is attached below.

<h3>What is an angle?</h3>

The angle is the distance between the intersecting lines or surfaces.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Vertically opposite angle – When two lines intersect, then their opposite angles are equal.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

∠1 = ∠5 = ∠9 = 105° (corresponding angles)

∠1 = ∠4 = 105° (Vertical opposite angles)

∠1 + ∠2 = 180° (linear angle)

       ∠2 = 75°

∠2 = ∠3 = 75° (Vertical opposite angles)

∠3 = ∠8 = ∠12 = 75° (corresponding angles)

If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.

Then the value of x and y will be

   ∠9 = ∠12

   ∠1 = ∠12

105° = (3x + 15)°

  3x = 90°

    x = 30°

∠6 = ∠7

75° = (8y – 5)°

8y = 80°

  y = 10°

More about the angled link is given below.

brainly.com/question/15767203

#SPJ1

7 0
2 years ago
Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers w
kirza4 [7]

\bf (b^4)^2\implies b^{4\cdot 2}\implies b^8

8 0
3 years ago
Calculate the diameter of a circle if it's circumference is 25.1
Dmitrij [34]
The answer would be 7.99.
5 0
3 years ago
Doug says that this clock shows 8:43.is he correct? Explain why or why not
Lena [83]
Depending on what the clock says yes and no.
4 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP PICTURE SHOWN
    6·2 answers
  • Describe the possible locations, in terms of quadrants or axes, for point A(x,y) if x and y satisfy the following condition
    14·1 answer
  • Please help aleks sucks will give brainliest PLEASE HELP ME! :(
    10·1 answer
  • Plot the x intercepts,maxima and minima of y=cos(x) from 0 to 2pi
    15·1 answer
  • Sarah and Gavyn win some money and share it in the ratio 5:2. Sarah gets £33 more than Gavyn. How much did they get altogether?
    15·1 answer
  • What is the surface area of 10cm 15cm and 10
    5·1 answer
  • Use similar triangles to find the value of x and y​
    8·2 answers
  • Y = x^2+ 2x + 3<br> 2y - 2x = 10<br><br><br> (Solving the following system of equations)
    14·1 answer
  • ∠3 and ∠4 are supplementary angles. Given m∠3=56°, find m∠4
    13·1 answer
  • 1) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 i
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!