What is the volume of a shoe box with length 13 inches, width 7 inches, and height 5 inches?

Write a an equation to represent the following statement. 24 is 4 times as great as k solve for k

Naddik [55]

Answer:

4k = 24, k = 6

Step-by-step explanation:

4k = 24

4k / 4 = 24 / 4

k = 6

brainliest pls xd

4 0

3 years ago

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

3 years ago

BRAINLIEST PLUS 100 POINTS

nexus9112 [7]

See the attached picture for the answers:

4 0

3 years ago

Which equation should be used to graph y=sec^-1(x) on a calculator ?

erastova [34]

Arcsecant or arcsec or sec⁻¹ is an inverse trigonometric function. And many calculators don't have a key for them because they can be calculated with basic trigonometric functions like so:

sec⁻¹(x)=cos⁻¹(1/x).

So the correct answer is the fourth one: y=cos⁻¹(1/x).

4 0

3 years ago

The moon has a radius of 1736 1736 kilometers. The earth has a radius of 6371 6371 kilometers. How many times as large is the vo

Vlad1618 [11]

Answer:

The volume of the Earth is 49 times as large as that of the moon

Step-by-step explanation:

Firstly, we consider that both entities are spherical in shape.

Mathematically, the volume of a sphere = 4/3 * pi * r^3

The volume of the moon with radius 1736 kilometers will be ;

4/3 * pi * 1736^3 = (20,927,105,024 π)/3 km^3

The volume of the earth with radius 6371 kilometers will be;

4/3 * pi * 6371^3 =( 1,034,386,411,244 π)/3 km^3

Now to get the number of times the earth is as big as the moon, we simply divide the volume of the earth by that of the moon.

= ( 1,034,386,411,244 π)/3 divided by (20,927,105,024 π)/3

= 1,034,386,411,244/20,927,105,024 = 49.43 which is approximately 49 times

3 0

3 years ago