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3 years ago

How to solve -6r(4r-5)-2(r-2) plz...

Mathematics

1 answer:

wlad13 [49]3 years ago

6 0

-6r(4r - 5) - 2(r - 2)

(-6r).4r - 5.(-6r) - 2.r - 2.(-2)

-24r² + 30r - 2r + 4

-24r² + 28r + 4

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g Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 7yi + xzj + (

Sati [7]

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

where $S$ is any oriented surface with boundary $C$ . We have

$\vec F(x,y,z)=7y\,\vec\imath+xz\,\vec\jmath+(x+y)\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-7)\,\vec k$

Take $S$ to be the ellipse that lies in the plane $z=y+9$ with boundary on the cylinder $x^2+y^2=1$ . Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+9)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

Then we have

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\big((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+2)\,\vec k\big)\cdot\big(-u\,\vec\jmath+u\,\vec k\big)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(3u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{3\pi}$

5 0

3 years ago

Which pair of figures has the same number of faces as vertices

ira [324]

Answer:

1.triangular prism and triangular pyramid

2. triangular prism and rectangular prism

3. rectangular pyramid and triangular pyramid

4. rectangular pyramid and rectangular prism

3 0

2 years ago

Consider the sequence {4,6,8,10,...} find the 130th term of the sequence

Olin [163]

262

Step-by-step explanation:

Step 1:

To find the nth term of a sequence the basic formula is

Sn = (n*d) + (a-d)

Whereas

Sn= nth Term

n= Term to be found

d= Difference between the terms in the sequence

a= First term in the sequence

Step 2:

Sn = (130*2) +(4-2)

= 260+2

Sn= 262

The nth term for the given problem is 262

3 0

3 years ago

Geraldine has 200 feet of fencing. She wants to fence in a rectangular area. Which function A(w) represents the area of land tha

Brut [27]

Answer:

A(w) = - $w^{2}$ + 100w

Step-by-step explanation:

First, we need to find down the length (l) of the rectangular area in term of w

We have 200 feet of fencing is the perimeter of the rectangular area, which mean:

2 (w + l) = 200

<=> l = 100-w

But the area of land: w*l

= w (100-w)

=- $w^{2}$ + 100w

So, A(w) = - $w^{2}$ + 100w

5 0

3 years ago

X - 3/5 =10 give your answer as an improper fraction

elixir [45]

Answer:

53/5

Step-by-step explanation:

Multiply both sides by 5: 5x - 3 = 50

Add 3 to both sides: 5x = 53

Divide both sides by 5: x = 53/5

8 0

1 year ago

Read 2 more answers