All categories

3 years ago

I need help with 3-5

Mathematics

1 answer:

Brums [2.3K]3 years ago

5 0

Number 3 is 8 inches. number 4 is 16. number 5 is 135 ft.

You might be interested in

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

The square root 2..25 is _____.

nata0808 [166]

Answer:

Hi there!

Your answer is:

B. 1.5

Step-by-step explanation:

The square root of 2.25 = 1.5

Check your work!

1.5×1.5 = 2.25!!✓

Hope this helps!

7 0

3 years ago

Find each product.

kvasek [131]

Answer: The answer is -2

Step-by-step explanation: positive and a positive is a positive, but, a positive and a negative is a negative.

3 0

4 years ago

In countries that use the metric system of measurement, corn yields are sometimes expressed in quintals per hectare (q/ha) inste

Fittoniya [83]

Answer:

The answer is below

Step-by-step explanation:

Different countries have different metric system of measurement, but the metric system of measurement accepted all over the world is the international system of unit (SI unit)

1 quintal = 220.462 lbs and 1 bushel of corn = 56 lbs.

151 q/ha = (151 × 220.462) lbs/ha = 33289.762 lbs/ha

But 1 hectare = 2.471 acre, hence:

33289.762 lbs/ha = $\frac{33289.762\ lbs}{1\ ha*\frac{2.471\ acre}{1 \ ha} } =13472.182\ lbs/acre$

Since 1 bushel of corn = 56 lbs, hence:

$13472.182\ lbs/acre=\frac{13472.182\ lbs*\frac{1\ bushels}{56\ lbs} }{acre}=240.6\ bushels/acre$ = 240.6 bu/ac

For a Margin of Error: +/- 1 bu/ac, the bushels per acre = (239.6 bu/ac, 241.6 bu/ac)

5 0

3 years ago

I need help pls on this problem

blsea [12.9K]

No because her tax would cost $76.
76+950= 1026, which is out of her budget.

6 0

3 years ago