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3 years ago

The relation {(-1, 4), (2, 7), (3, 7)} is a function.

Mathematics

1 answer:

natita [175]3 years ago

6 0

Answer:

Yes this is correct. Each x value is put with only one y value.

Step-by-step explanation:

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7/30+9/20 what is the answer pls hurry im so confused

Svetradugi [14.3K]

Here is your answer:

$\frac{7}{30} + \frac{9}{20}$
Find common denominator:
$30 \times 20 = 60 /20 \times 30 = 60$
Common denominator is 60:
$\frac{7}{30} + \frac{9}{20} = \frac{140}{60} + \frac{270}{60}$
$140 + 270 = 410$
$= \frac{410}{60}$
$\frac{410}{60} \div 2 = \frac{205}{30} \div 5 = \frac{41}{6}$
= $\frac{41}{6} or 6\frac{5}{6}$

Hope this helps!

8 0

3 years ago

Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

6 0

4 years ago

Given f(x)=x^2-2x find f(6)

-BARSIC- [3]

Step-by-step explanation:

In the picture, I hope that it's a clear solution.

7 0

3 years ago

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I didn’t learn to do this please help

Naddika [18.5K]

Find the area of the blue square including the white square then find the area of the white square and subtract that from the area of the blue square.

Hope that helps if you need more help just comment and I’ll try to explain it better!

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3 years ago

Sarah paid a food bill of 13.74 with a $20 bill how many change was she owed

slamgirl [31]

6.26 because 20 subtract 13.74= 6.26

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3 years ago

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