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
Amanda needs to cut a board to use for a project. The board is 10 feet long. She first has to cut off 1 3/4 feet from one end of
masya89 [10]

Answer : 4x + 1 3/4 = 10

Step - by - step explanation : The reason 4 has an " x " at the end of it is because we don't know its exact number

8 0
2 years ago
Read 2 more answers
REMOVE the outlier from the data, and then do the following: Round answers to the nearest
tresset_1 [31]

Answer:

outliar is23

Step-by-step explanation:

7 0
3 years ago
Solve the system by substitution.<br> y = –2x + 18<br> y = -4x<br> HURRY PLEASE
Irina-Kira [14]

Answer:

x = -9

Step-by-step explanation:

x = -y/4

y = -2(-y/4) + 18

y = y/2 + 18

y/2 = 18

y = 36

x = -36/4

x = -9

5 0
2 years ago
A jar of peanut butter contains 454 g with a standard deviation of 10.2 g. Find the probability that a jar contains more than 46
Fofino [41]

Answer:

The probability that a jar contains more than 466 g is 0.119.

Step-by-step explanation:

We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.

Let X = <u><em>Amount of peanut butter in a jar</em></u>

The z-score probability distribution for the normal distribution is given by;

                                Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean = 454 g

           \sigma = standard deviation = 10.2 g

So, X ~ Normal(\mu=454 , \sigma^{2} = 10.2^{2})

Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)

            P(X > 466 g) = P( \frac{X-\mu}{\sigma} > \frac{466-454}{10.2} ) = P(Z > 1.18) = 1 - P(Z \leq 1.18)

                                                                  = 1 - 0.881 = <u>0.119</u>

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

4 0
3 years ago
Josie buys a necklace for $24 which is 80% off. How much was the full price of the necklace
Sedbober [7]

Answer:

4.8

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is 95.833 (three repeating) as a fraction?
    9·2 answers
  • What is 0.312 in expanded notation
    7·1 answer
  • What is the y-intercept of 2x+5y=−20 ?<br><br> (0,−4)<br><br> (10,4)<br><br> (0,10)<br><br> (−4,0)
    9·2 answers
  • Describe the difference between solving |x| ≤ 5 and solving |x| ≥ 5.
    14·1 answer
  • The chord BC is a diameter of o​
    11·1 answer
  • OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPOR
    11·2 answers
  • There is a elephant shaped weather vane at the top of a corn dryer tower that is 45 m high. If the weather vane weighs 190 N, wh
    13·1 answer
  • Your Assignment
    13·1 answer
  • ethan is saving money in his piggery bank for his upcoming trip to disney world. on the first day me put 10$ and plans to add 5
    10·1 answer
  • -1/4 (24ab + 8c) please help
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!