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jarptica [38.1K]
3 years ago
14

If c is the curve given by \mathbf{r} \left( t \right = \left( 1 5 \sin t \right \mathbf{i} \left( 1 3 \sin^{2} t \right \mathbf

{j} \left( 1 2 \sin^{3} t \right \mathbf{k}, 0 \leq t \leq \frac{\pi}{2} and f is the radial vector field \mathbf{f} \left( x, y, z \right = x \mathbf{i} y \mathbf{j} z \mathbf{k}, compute the work done by f on a particle moving along c
Mathematics
1 answer:
jonny [76]3 years ago
6 0
With the curve C parameterized by

C:\mathbf r(t)=\underbrace{15\sin t}_{x(t)}\,\mathbf i+\underbrace{13\sin^2t}_{y(t)}\,\mathbf j+\underbrace{12\sin^3t}_{z(t)}\,\mathbf k

with 0\le t\le\dfrac\pi2, and given the vector field

\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+z\,\mathbf k

the work done by \mathbf f on a particle moving on along C is given by the line integral

\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int\limits_{t=0}^{t=\pi/2}\mathbf f(x(t),y(t),z(t))\cdot\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\,\mathrm dt

where

\mathrm d\mathbf r=(15\cos t\,\mathbf i+26\sin t\cos t\,\mathbf j+36\sin^2t\cos t\,\mathbf k)\,\mathrm dt

The integral is then

\displaystyle\int_0^{\pi/2}(15\sin t\,\mathbf i+13\sin^2t\,\mathbf j+12\sin^3t\,\mathbf k)\cdot(15\cos t\,\mathbf i+13\sin2t\,\mathbf j+18\sin t\sin2t\,\mathbf k)\,\mathrm dt
=\displaystyle\int_0^{\pi/2}(432\sin^5t\cos t+338\sin^3t\cos t+225\sin t\cos t
=269
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Answer:

0.5 + 0.5, 0 + 1, 0.6 + 0.4, etc etc

Step-by-step explanation:

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What is the solution of the equation. find the value of y when x equals -10. 2x - 9y = -38
cestrela7 [59]

Answer:

y =2

Step-by-step explanation:

Substitute -10 for x:

2(-10)-9y = -38

-20-9y = -38

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9y = 18

y = 2

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One person can do a certain job in fifteen minutes and another person can do the same job in thirty minutes how many minutes wil
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here is an equation that is true for all values of x:5(x+2)=5x+10. Elena saw this equation and says she can tell 20(x+2)=4(5x+10
Trava [24]

Elena is wrong, because the two sides of equation are not equal for all values of x

Step-by-step explanation:

An equation of x is true for all values of x when the left hand side

is equal to the right hand side

To prove that an equation is true for all values of x do that

  • Simplify the left hand side and the right hand side
  • Solve the equation to find x, you will find the x in the left hand side is equal to x in the right hand side, so they canceled each other, and the numerical terms in the two sides equal each other, that means the equation is true for any values of x

Lets check that with given equation 5(x + 2) = 5x + 10

∵ 5(x + 2) = 5x + 10

- Simplify the left hand side

∵ 5(x) + 5(2) = 5x + 10

∴ 5x + 10 = 5x + 10

- Subtract 5x from both sides

∴ 10 = 10

∵ L.H.S = R.H.S

∴ The equation is true for all values of x

Lets do that with Elena's equation

∵ 20(x + 2) = 4(5x + 10) + 31

- Simplify the two sides of the equation

∵ 20(x) + 20(2) = 4(5x) + 4(10) + 31

∴ 20x + 40 = 20x + 40 + 31

- Add like terms in the right hand side

∴ 20x + 40 = 20x + 71

- Subtract 20x from both sides

∴ 40 = 71 ⇒ and that not true

∵ L.H.S ≠ R.H.S

∴ The equation is not true for all values of x

Elena is wrong, because the two sides of equation are not equal for all values of x

Learn more:

You can learn more about the equations in brainly.com/question/11306893

#LearnwithBrainly

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