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
Bogdan [553]
3 years ago
6

Find the work done by the force field F(x, y) = xi + (y + 5)j in moving an object along an arch of the cycloid r(t) = (t − sin(t

))i + (1 − cos(t))j, 0 ≤ t ≤ 2π.
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
5 0

Integrate the force field along the given path (call it <em>C</em>):

W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt

=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt

=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}

You might be interested in
A. A person's height is positively associated with their arm span (the distance between the
stiv31 [10]

Answer:

I didn't Sanderstead sorry

8 0
2 years ago
To solve 5(2^x + 4) = 15...
horrorfan [7]

I don't think you need answer for that you already did it.

5 0
2 years ago
a box of cookies contain 12 chocolate chip cookies, 6 peanut butter cookies, and 6 sugar cookies, what is the probability of sel
tatuchka [14]
24 cookies in total, probability of selecting sugar is 6/24 = 1/4 = 25%
7 0
3 years ago
Read 2 more answers
Austin is going for a walk. He takes 3 hours to walk 4.8 miles. What is his speed?
Alexxandr [17]
I hope this helps you



3 0
3 years ago
Y=7<br> Y=-2x+1<br><br> Find the intersection
stealth61 [152]
I was going to answer but she gave you the answer sooo
3 0
3 years ago
Other questions:
  • 1. The following problem ropresents a population of bacteria. P(t)=360(2)^t where toquals time in hours. How many bacteria are p
    13·2 answers
  • I don't know how to do the problem 6^4 x 10^2 over 6^2 x 2^4.<br> Do you think you could help?
    10·2 answers
  • 1/3 n=4/5 Enter the value of the n that will make the equation true.
    6·1 answer
  • Suppose that a loan of $6000 is given at an interest rate of 9% compounded each year.
    5·2 answers
  • 5) The Montgomerys borrowed $115,000 at 10% for 30 years to purchase a house. Find the monthly
    9·1 answer
  • Which expression is equivalent to 4
    5·1 answer
  • What is the equation of the circle with a radius of 4 and a center at (3, 2) ?
    7·1 answer
  • What is the minimum value of the quadratic function f(x)?
    5·1 answer
  • A recipe uses 2 cups of apple concentrate and 3.5 cups of water to make apple juice. If marcus has 6 cups of apple concentrate,
    13·2 answers
  • Please help me please!! −
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!