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
Georgia [21]
2 years ago
14

I

Mathematics
1 answer:
amid [387]2 years ago
7 0

Answer:

21.56

Step-by-step explanation:

You might be interested in
Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t
pashok25 [27]

Direct computation:

Parameterize the top part of the circle x^2+y^2=1 by

\vec r(t)=(x(t),y(t))=(\cos t,\sin t)

with 0\le t\le\pi, and the line segment by

\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)

with 0\le t\le1. Then

\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)

=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt

=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}

Using the fundamental theorem of calculus:

The integral can be written as

\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}

If there happens to be a scalar function f such that \vec F=\nabla f, then \vec F is conservative and the integral is path-independent, so we only need to worry about the value of f at the path's endpoints.

This requires

\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)

\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C

So we have

f(x,y)=-\cos x+\sin y+C

which means \vec F is indeed conservative. By the fundamental theorem, we have

\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}

3 0
3 years ago
A shoe box in the shape of a right rectangular prism has a base that measures 7 inches by 12 inches and is 5 inches high. What i
AlekseyPX

Answer:

The volume of the shoe box is 420 cubic inch

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a righ rectangular prism

Given data

Length of prism l= 12inches

Width of prism w= 7 inches

Height of prism h= 5 inches

We know that the volume of a rectangular prism is expressed as

Volume =l*w*h

Volume = 12*7*5= 420in³

6 0
3 years ago
Read 2 more answers
What is the circumference of a circle with a diameter 9cm
xz_007 [3.2K]
The circumference follows the formula
C= 2 (pi)R
R is the radius which is half the diameter when we put this into the equation we get
C = 2 (pi)(4.5)
C=28.274334
5 0
3 years ago
Read 2 more answers
Question 4 (1 point)<br> (-7x + 5) - (-82 – 6) =
Keith_Richards [23]

no ye puedo ayudar amigo o amiga

8 0
3 years ago
When Jasper won the jackpot prize of
denpristay [2]

Answer:m

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • Find the "i" in here for brainlyest and 50 points! (Underline it) NOT IN THE QUESTION IN THE GROUP OF l's
    5·2 answers
  • 9) Endpoint: (-10,10), midpoint: (4,8)<br> what is the other endpoint?
    7·1 answer
  • An airplane covers 94 miles in 1/6 of an hour.<br> The plane can cover <br> miles in 6 hours
    11·2 answers
  • Help me solve,Brainlist for first to answer
    11·1 answer
  • What is the slope of the function, represented by the table of values below?
    14·1 answer
  • Liam has bought 48 feet of fencing that he will use to build a pig pen. List 6 different dimensions he could create for his pen
    15·1 answer
  • The product of two fractions that are each between 0 and 1 is also between 0 and 1.Is this true or false?
    13·2 answers
  • - 3x = 18 answer = m = - 6 answer = 3 4 + y = 0 answer = 2x = - 6 answer = h=2 answer = 5 d = 1 answer = - 8 6 + x = 2 answer =
    9·1 answer
  • Help plz thank you so much
    6·2 answers
  • Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the tab
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!