All categories

3 years ago

Please help if you know

Mathematics

1 answer:

denis23 [38]3 years ago

4 0

Henry made a mistake.

4z² - z² = 3z² not 4.

You might be interested in

5×10 to the ninth power

nikklg [1K]

Answer:

5,000,000,000 or 1,953,125,000,000,000

Depends on what you mean

Step-by-step explanation:

If (5*10)^9

(50)^9

1,953,125,000,000,000

Or if 5 * (10)^9

5 * 1,000,000,000 = 5,000,000,000

4 0

4 years ago

Read 2 more answers

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

Alenkasestr [34]

$\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1$

Converting to spherical coordinates, we have

$\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi$

On the other hand, we can parameterize the boundary of $E$ by

$\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\pi$ . Now, consider the surface element

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv$

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

$\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv$
$=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi$

as required.

3 0

4 years ago

Which ratio is not equivalent to 84:20?

cupoosta [38]

You didn't put any options but any ratio that 4.2:1 doesn't go into is not equivalent.

Hope this helps :)

8 0

3 years ago

Mary spent a total of $293.37 for a party. She spent $200.67 on food, plus an additional $30.90 for each hour of the party. How

Elina [12.6K]

Answer:

3 hours i think

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Express and simplest radical form.

strojnjashka [21]

Answer:

4 square root 5 is the answer

root(20*4)

2 × root(5×4)

4×root(5)

4 0

3 years ago