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3 years ago

Verify that the divergence theorem is true for the vector field f on the region

1 answer:

5 0

$\nabla\cdot\mathbf f(x,y,z)=\dfrac{\partial(2x)}{\partial x}+\dfrac{\partial(xy)}{\partial y}+\dfrac{\partial(3xz)}{\partial z}=2+x+3x=4x+2$

The flux across $\partial\mathcal E$ (boundary of $\mathcal E$ ) is

$\displaystyle\iint_{\partial\mathcal E}\mathbf f(x,y,z)\cdot\mathrm d\mathbf S=\iiint_{\mathcal E}(4x+2)\,\mathrm dV$
$=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(4x+2)\,\mathrm dx\,\mathrm dy\,\mathrm dz=48$

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What is the 8th term of the geometric sequence with this explicit formula? an = 6.(-2)(n-1)

Kaylis [27]

Answer:

-768

….......

Substitute n = 8 into the explicit formula

$a_{8} = 6$ × $(-2)^{7}$ = $6$ × $-128$

= -768

6 0

2 years ago

A bamboo shoot is 20 inches tall at the zero and gross 24 inches each day which functions show below can be used to determine he

ale4655 [162]

It is definitely D because on part 1 n=24n+20 and if n equals 0 than 24 (0) +20= 20 and that is true. on part 2 if n =0 than 24 (0)+ 20 (0-1)=20 than 20 (-1)=20 -20= 20. that statement is false because-20 does not equal 20. AND for part 3 n=1 and f (1-1) + 24= 44 so f (0) + 24 =44 and keep in mind f (0) equals 20 so 44=44 because 24+20 is 44. so that is a true statement too

8 0

3 years ago

Read 2 more answers

Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.20.2, 0.30.3, and 0.50.5, res

PIT_PIT [208]

Answer:

0.78

Step-by-step explanation:

We have the next probability distribution:

X P(X)

0 0.2

1 0.3

2 0.5

As we can see when we add all the probabilites the result is 1. Now calculating the mean we have:

$mean=\mu=(0\times0.2)+(1\times 0.3)+(2\times 0.5)=0+0.3+1=1.3$

The standard deviation is:

$\sigma=\sqrt{\sum(x-\mu)^{2}(P(x))}$

Then using the data that we have:

$\sigma=\sqrt{\sum(x-\mu)^{2}(P(x))}\\\sigma=\sqrt{(0-1.3)^{2}(0.2)+(1-1.3)^{2}(0.3)+(2-1.3)^{2}(0.5)}\\\\\sigma=\sqrt{(-1.3)^{2}(0.2)+(-0.3)^{2}(0.3)+(0.7)^{2}(0.5)}\\\\\sigma=\sqrt{(1.69)(0.2)+(0.09)(0.3)+(0.49)(0.5)}\\\\\sigma=\sqrt{0.338+0.027+0.245}\\\\\sigma=\sqrt{0.61}\\\\\sigma=0.78\\$

Then the standard deviation is 0.78

6 0

3 years ago

forty percent of 25 students in the class are boys. write 40% as a reduced fraction. then find the ratio of girls to boys in the

Dafna11 [192]

25/10x4=10 boys

100%-40%=60%

25/10x6= 15

boys:girls
10:15

5 0

4 years ago

Read 2 more answers

For all values of x, f(x) = x^2 + 1 and g(x) = x-5

Elena-2011 [213]

Answer:

a) f g(x) = x³ - 5 x² + x -5

b) g(f(x) = x³ - 5 x² + x -5

Step-by-step explanation:

Step(i):-

Given that f(x) = x² + 1 and g(x) = x-5

f(g(x)) = f(x-5) = (x-5)²+1 = x² - 10x +25 +1 = x² - 10 x +26

Step(ii):-

a) f g(x) = f(x) g(x) = (x² + 1 )(x-5) = x³ - 5 x² + x -5

b) g(f(x) = g(x) f(x) = (x-5) (x²+1) = x³ - 5 x² + x -5

6 0

3 years ago