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muminat
3 years ago
7

Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) = z, y, x , E is the solid ball x2

+ y2 + z2 ≤ 64 For your answer, put in the flux across the boundary of E with respect to the outward normal.
Mathematics
1 answer:
Setler [38]3 years ago
8 0

\vec F(x,y,z)=\langle z,y,x\rangle

has divergence 1, so by the divergence theorem, the flux of \vec F across the boundary of E is exactly the volume of E,

\displaystyle\iiint_E\mathrm dV=\int_0^\pi\int_0^{2\pi}\int_0^8\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

or simply \dfrac43\pi8^3=\boxed{\frac{2048\pi}3}.

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What is the solution to the system of equations y=-1/3x+9 and y=2/3x+12
amm1812

Answer:

{x = -3 , y = 10

Step-by-step explanation:

Solve the following system:

{y = 9 - x/3 | (equation 1)

{y = (2 x)/3 + 12 | (equation 2)

Express the system in standard form:

{x/3 + y = 9 | (equation 1)

{-(2 x)/3 + y = 12 | (equation 2)

Swap equation 1 with equation 2:

{-(2 x)/3 + y = 12 | (equation 1)

{x/3 + y = 9 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{-(2 x)/3 + y = 12 | (equation 1)

{0 x+(3 y)/2 = 15 | (equation 2)

Multiply equation 1 by 3:

{-(2 x) + 3 y = 36 | (equation 1)

{0 x+(3 y)/2 = 15 | (equation 2)

Multiply equation 2 by 2/3:

{-(2 x) + 3 y = 36 | (equation 1)

{0 x+y = 10 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{-(2 x)+0 y = 6 | (equation 1)

{0 x+y = 10 | (equation 2)

Divide equation 1 by -2:

{x+0 y = -3 | (equation 1)

{0 x+y = 10 | (equation 2)

Collect results:

Answer:  {x = -3 , y = 10

3 0
3 years ago
There is a square with a perimeter of<br> 412<br> what is the length of the diagonal?
Llana [10]

Answer:

hhjbvft

Step-by-step explanation:

jojo giving kbjvuvuvvuvugubibbibiogg

7 0
3 years ago
A florist prepares an order of daisies and roses. For every 5 daisies she orders 2 roes. What 2 equations show the relationship
Vsevolod [243]

Answer:

d = 2.5r and r = \frac{d}{2.5}

Step-by-step explanation:

Given

5 daises to 2 roses

Required

Determine the relationship between them

The question shows a direct proportion between number of daises and roses.

i.e.

d\ \alpha\ r

Where d = daises and r = roses

Convert the above expression to an equation

d = kr

Make k the subject

k = \frac{d}{r}

When d = 5 and r = 2;

k = \frac{5}{2}

k = 2.5

So, the first relationship between d and r can be gotten by substituting 2.5 for k in d = kr

So:

d = 2.5 * r

d = 2.5r ----------- (1)

Make r the subject in (1)

r = \frac{d}{2.5} ------------------------(2)

Hence, the relationships between d and r are:

d = 2.5r and r = \frac{d}{2.5}

6 0
3 years ago
Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____.
Bogdan [553]

Answer:  The correct option is (B) less than 2.

Step-by-step explanation:  Given that Y varies directly with X and has a constant rate of change of 6.

We are to find the possible value of X when the value of Y is 11.

Since Y varies directly with X, so we can write

Y\propto X\\\\\Rightarrow Y=kx~~~~~~~~~~~~~~~(i),~~~~~~~~~\textup{[where 'k' is the constant of variation]}

Since the rate of change is constant and is equal to 6, so we must have

k=6.

So, from equation (i), we have

Y=kX\\\\\Rightarrow Y=6X~~~~~~~~~~~~~~~~~~~~~~(ii)

Now, when Y = 11, then from equation (ii), we get

Y=6X\\\\\Rightarrow 11=6X\\\\\Rightarrow X=\dfrac{11}{6}

Thus, the value of X is less than 2 when Y = 11.

Option (B) is CORRECT.

8 0
3 years ago
20 POINTS <br> WILL GIVE BRAINLIEST<br> plz help me
Anvisha [2.4K]

Answer:

16m

Step-by-step explanation:

solve it out: 16*(9+3)

6 0
4 years ago
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