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
iogann1982 [59]
3 years ago
13

Let C = C1 + C2 where C1 is the quarter circle x^2+y^2=4, z=0,from (0,2,0) to (2,0,0), and where C2 is the line segment from (2,

0,0) to (3,3,3). Compute the work done by the force F(x,y,z) =
Mathematics
1 answer:
trapecia [35]3 years ago
5 0
Not much can be done without knowing what \mathbf F(x,y,z) is, but at the least we can set up the integral.

First parameterize the pieces of the contour:

C_1:\mathbf r_1(t_1)=(2\sin t_1,2\cos t_1,0)
C_2:\mathbf r_2(t_2)=(1-t_2)(2,0,0)+t_2(3,3,3)=(2+t_2, 3t_2, 3t_2)

where 0\le t_1\le\dfrac\pi2 and 0\le t_2\le1. You have

\mathrm d\mathbf r_1=(2\cos t_1,-2\sin t_1,0)\,\mathrm dt_1
\mathrm d\mathbf r_2=(1,3,3)\,\mathrm dt_2

and so the work is given by the integral

\displaystyle\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r
=\displaystyle\int_0^{\pi/2}\mathbf F(2\sin t_1,2\cos t_1,0)\cdot(2\cos t_1,-2\sin t_1,0)\,\mathrm dt_1
{}\displaystyle\,\,\,\,\,\,\,\,+\int_0^1\mathbf F(2+t_2,3t_2,3t_2)\cdot(1,3,3)\,\mathrm dt_2
You might be interested in
For his job at the hardware store, Michael distributes 2,345 packages of screws into 5 equal groups for shipping. How many packa
drek231 [11]

\\
\text{Michael distrinutes  2345 packages of screws into 5 equal groups for shipping.}\\
\\
\text{we need to find the number of packages of screws in each group.}\\
\\
\text{so for this we use the unitary method.}\\
\\
\text{The number of packages of screws in 5 groups}=2345\\
\\
\text{so the number of packages of screws in 1 group}=\frac{2345}{5}\\
\\
=469

Hence the number of packages of screws in each shipping box is: 469

Hence option (B) is correct.

6 0
3 years ago
a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the
nlexa [21]

Answer:

The standard equation of the parabola is:

y=-\frac{3}{2}x^2+12x-18

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}

Then the equation of the parabola becomes:

y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18

7 0
3 years ago
Please help me as fast as you can PLEASE
e-lub [12.9K]

Answer:

C

Step-by-step explanation:

6 0
3 years ago
Simplify the following;<br><br> 8v + w + 7 - 8v + 2w<br> 4c² + 6c - 3c² - 2c - 3<br><br> Thanks!
Dominik [7]

Answer:

3w+7

c^2 + 4c - 3

Step-by-step explanation:

8v+w+7-8v+2w

8v-8v +w+2w +7

0+3w+7

3w+7

4c^2+6c-3c^2-2c-3

4c^2-3c^2 + 6c-2c -3

c^2+4c-3

3 0
3 years ago
4294 divided by 68
Nataly_w [17]

Answer:

1. 63.1. 2.22.5 3. 74.3 4. 56.1

8 0
3 years ago
Other questions:
  • You invest $350 in an account with an interest rate of 1.2% compounded continuously. How much money would be in the account afte
    11·2 answers
  • Hey need help figuring out the correct mathematical sentence for this: Sam created some artwork to sell at a craft fair. She use
    15·1 answer
  • 4x + 5y=159 what is x and y together
    14·1 answer
  • What is the solution of the equation 9^2x=6? Round your answer to the nearest ten-thousandth.
    12·1 answer
  • What does x equal?<br> 21 x=177
    12·1 answer
  • Please help me solve this short problem guys
    5·1 answer
  • I really need help, please​
    13·1 answer
  • Write an equation for a line with a slope of (-2) and the point (5,9)
    12·1 answer
  • Help<br><br>Activity:<br>2x²2+2x-312=0​
    13·1 answer
  • Solve this for me please
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!