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3 years ago

Which of the following is a function?

Mathematics

1 answer:

seropon [69]3 years ago

7 0

Answer:

Step-by-step explanation:

For any of the functions described above, the only way any of those could be functions is that there has to be a difference value for each x, unless it is the same x-value. If the x is mentioned twice, that is fine, as long as the y point is also the same. If it is different, it is not a function.

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N over three point N over four<br> Write without exponents.י

Sever21 [200]

Answer:

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3.N

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Step-by-step explanation:

7 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

Please help with hair question- it’s in the photo

Levart [38]

Salutations!

Growth meters per second = 4.8 × $10^{-9}$

First, you need to convert standard form into a normal number.

4.8 × $10^{-9}$ = 4.800000000

a) In one day there are 24 hours, therefore you will multiplying 4.800000000 and 24

4.800000000 × 24 = 115.2 = 115.2 × $10^{-9}$ (standard form)

b) 365 days in a year, so multiply 4.800000000 and 365

4.800000000 × 365 = 1752 = 1.7 × $10^{3}$ (standard form)

Hope I helped (:

have a great day!

3 0

3 years ago

What’s the answer to this

Fed [463]

Answer:

This is the wrong subject. and please provide a passage.

Step-by-step explanation:

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3 years ago

Last year there were 205 ducks living on the pond. This year there are 20% more ducks living on the pond. How many ducks are liv

Rus_ich [418]

Answer:

246

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers