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MakcuM [25]
3 years ago
6

Evaluate the surface integral s f · ds for the given vector field f and the oriented surface s. in other words, find the flux of

f across s. for closed surfaces, use the positive (outward) orientation. f(x, y, z) = x i + y j + 6 k s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2
Mathematics
1 answer:
charle [14.2K]3 years ago
3 0
Since \mathcal S is closed, use the divergence theorem:

\displaystyle\iint_{\mathcal S}\mathbf f(x,y,z)\cdot\,\mathrm d\mathbf S=\iiint_{\mathcal V}\nabla\times\mathbf f(x,y,z)\,\mathrm dV

where \mathcal V is the solid with boundary \mathcal S. Now,

\nabla\times\mathbf f=\dfrac{\partial x}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial6}{\partial z}=1+1+0=2

so the volume integral, converting to cylindrical coordinates via

\begin{cases}x(r,u,v)=r\cos u\\y(r,u,v)=v\\z(r,u,v)=r\sin u\end{cases}

is

\displaystyle2\iiint_{\mathcal V}\,\mathrm dV=2\int_{u=0}^{u=2\pi}\int_{r=0}^{r=1}\int_{v=0}^{v=2-r\cos u}r\,\mathrm dv\,\mathrm dr\,\mathrm du=4\pi
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If ∠A and ∠B are complementary, find the value of x given that ∠A=3x-2 and ∠B=x+12
xxMikexx [17]

Answer:

x=20 degrees

Step-by-step explanation:

complementary means the angles equal 90 degrees

so ∠A+∠B=90 degrees

∠A=3x-2 and ∠B=x+12

so subsitute

(3x-2)+(x+12)=90

then solve for x

4x+10=90

4x=80

x=20 degrees is your answer

6 0
3 years ago
Albert receives $0.30 per pound for 1 to 49 pounds of glass bottles he recycles. He receives $0.40
Marina86 [1]

Answer:

Yes

Step-by-step explanation:

The amount of money Albert receives is described by the expression

y = \begin{cases}0.30x  & \quad \text{if } 0 \leq x \leq 49 \\0.40x & \quad \text{if } x > 50\\\end{cases}

The graph is shown below.

To determine if the relation is a function,  we can use the vertical line test:  

If a vertical line crosses the graph more than once in any location, the relation is not a function.

We see that at no place will a vertical line intersect the graph more than once.

The relation is a function.

3 0
4 years ago
I get paid $40 a month. If i want 5 less each month, how much should i get paid every week?
agasfer [191]

Answer:

$5 each week

Step-by-step explanation:

$40 a month

$10 a week

$10-$5 is $5 each week

4 0
3 years ago
Read 2 more answers
901334 x 2368 = ? I WILL GIVE BRAINLIEST TO A CORRECT ANSWER PLEASE HURRY
aliya0001 [1]

Answer:

901334 x 2368 = 2134358912 is the correct answer

Step-by-step explanation:

I hope this helps you :)

5 0
3 years ago
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The population of a town is 14,000 and is decreasing at a rate of 1.5% each year. Write an exponential decay equation to find th
sergejj [24]

Answer: the population after 10 years is 12036

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

A = P(1 - r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 14000

r = 1.5% = 1.5/100 = 0.015

t = 10 years

Therefore, the exponential decay equation to find the population of the town after 10 years is

A = 14000(1 - 0.015)^10

A = 14000(0.985)^10

A = 12036

8 0
3 years ago
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