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
ElenaW [278]
3 years ago
6

What is the area of a sector with a central angle of 131 degrees and a radius of 7.2 ft?

Mathematics
1 answer:
svetoff [14.1K]3 years ago
5 0

Answer:

162.78

Step-by-step explanation:

Use your π =3.14

3.14 times 7.2 times 7.2

You might be interested in
The angle θ lies in Quadrant II. sinθ=3/4 What is cosθ ?
Elden [556K]

Hello from MrBillDoesMath

Answer:

[email protected] = - sqrt(7)/ 4    

which is choice B

Discussion:

This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:

([email protected])^2 + (sin2)^2 = 1

If [email protected] = 3/4 , the

([email protected])^2 + (3/4)^2 = 1 =>              (subtract (3/4)^2 from both sides)

([email protected])^2 = 1 - (3/4)^2  = 1 - 9/16   = 7/16

So...... taking the square root of both sides gives

[email protected] =  +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4

But is [email protected] positive or negative?  We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative

[email protected] = - sqrt(7)/ 4    

which is choice B


Thank you,

Mr. B


4 0
3 years ago
Calculus 3 help please.​
Reptile [31]

I assume each path C is oriented positively/counterclockwise.

(a) Parameterize C by

\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}

with -\frac\pi2\le t\le\frac\pi2. Then the line element is

ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt

and the integral reduces to

\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt

The integrand is symmetric about t=0, so

\displaystyle 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \,dt

Substitute u=\sin(t) and du=\cos(t)\,dt. Then we get

\displaystyle 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^1 u^4 \, du = \frac{2^{13}}5 (1^5 - 0^5) = \boxed{\frac{8192}5}

(b) Parameterize C by

\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}

with 0\le t\le1. Then

ds = \sqrt{3^2+4^2} \, dt = 5\,dt

and

\displaystyle \int_C x e^y \, ds = \int_0^1 (3t-2) e^{4t} (5\,dt) = 5 \int_0^1 (3t - 2) e^{4t} \, dt

Integrate by parts with

u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}

\displaystyle \int u\,dv = uv - \int v\,du

\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}

(c) Parameterize C by

\begin{cases} x(t) = 3(1-t)+t = -2t+3 \\ y(t) = (1-t)+2t = t+1 \\ z(t) = 2(1-t)+5t = 3t+2 \end{cases} \implies \begin{cases} x'(t) = -2 \\ y'(t) = 1 \\ z'(t) = 3 \end{cases}

with 0\le t\le1. Then

ds = \sqrt{(-2)^2 + 1^2 + 3^2} \, dt = \sqrt{14} \, dt

and

\displaystyle \int_C y^2 z \, ds = \int_0^1 (t+1)^2 (3t+2) \left(\sqrt{14}\,ds\right) \\\\ ~~~~~~~~ = \sqrt{14} \int_0^1 \left(3t^3 + 8t^2 + 7t + 2\right) \, dt \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 t^4 + \frac83 t^3 + \frac72 t^2 + 2t\right) \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 + \frac83 + \frac72 + 2\right) = \boxed{\frac{107\sqrt{14}}{12}}

8 0
1 year ago
What is the unit rate of five and 15?
-BARSIC- [3]
For miles... 0.333333 Miles per Mile
6 0
2 years ago
Which is greater 8.2 or 8.23
faust18 [17]
I believe 8.23 is greater because 8.2 can be 8.20 so that’s why my answer is 8.23
8 0
3 years ago
Read 2 more answers
Evaluate the expectations for the given value of x <br> 3x-2forx=2
vova2212 [387]
3x - 2 when X = 2
= 3(2) - 2
= 6 - 2
= 4
So, in conclusion, the answer to this question is 4.
7 0
3 years ago
Other questions:
  • What is the 3rd quadrant of 10,20,30,40,50,60​
    5·2 answers
  • the distance between Cincinnati,Ohio and Charlotte, north Carolina, is about 366 miles. the distance between Cincinnati and Chic
    10·1 answer
  • 1. twice the square of the sum of a number and 3 is 98.find the number​
    13·1 answer
  • 7. You have invested $2500 in a 30-day savings certificate paying 4.15% per annum. Find the
    12·1 answer
  • In the right triangle above, a =2.7 and b =4.3. find the value of c round to the nearest tenth
    11·1 answer
  • lily has $18. matt has twice as much of a third of the amount lily has, and carolyn has $23 more than matt has. how much money d
    8·2 answers
  • In simplest form 3n-13-5n+6n​
    12·1 answer
  • Plzzzzz help !.!.!.!.!.!.!!..!!.!.!.!.!.!.?
    6·2 answers
  • A) draw the image of PQR after a 180 about the origin. Label the image P'Q'R
    14·1 answer
  • Gina rented shoes for 2.75 dollars she then bowled three games (2.50 dollars) and then brought nachos for 1.75.she used a coupon
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!