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3 years ago

Please help me with this problem I don't understand how to solve it 1.) Simplify. √18

Mathematics

2 answers:

sp2606 [1]3 years ago

7 0

4.24 :)
This is simplified and not the full answer btw
hope this helps

Citrus2011 [14]3 years ago

6 0

Answer:
3√2 or 4.2426

Explanation:
18 can be written as 9*2
This means that:
√18 can be written as √9 * √2
Now, √9 is equal to 3
So, the simplified form of √18 is 3√2 which is equal to 4.2426 in decimal form.

Hope this helps :)

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What expression is equal to 5/8?<br> pls help!

ehidna [41]

Answer:

10/16; 15/24; etc

Step-by-step explanation:

if u multiply any fraction, both parts of it by the same number, ull get an equal expression. so, for example, 5*2/8*2=10/16=5/8

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3 years ago

F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 3)j + zk. find the flux of f across s, the part of the paraboloid x2 + y2 + z = 18 that l

Cerrena [4.2K]

$\mathbf F(x,y,z)=z\tan^{-1}(y^2)\,\mathbf i+z^3\ln(x^2+3)\,\mathbf j+z\,\mathbf k$
$\implies\mathrm{div}\mathbf F(x,y,z)=0+0+1=1$

By the divergence theorem, the flux of $\mathbf F$ across the *closed* surface $\mathcal S$ combined with the plane $z=2$ is given by a volume integral over the closed region:

$\displaystyle\iint_{\mathcal S}\mathbf F\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}\nabla\cdot\mathbf F\,\mathrm dV$

So in fact, to find the flux over $\mathcal S$ alone, we'll need to subtract the flux of $\mathbf F$ over the planar portion, oriented outward. First, compute the volume integral by converting to cylindrical coordinates:

$x^2+y^2+z=18$
$z=2\implies x^2+y^2=16\implies r^2=16\implies r=4$

$\displaystyle\iiint_{\mathcal R}\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}\int_{z=2}^{z=18-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=128\pi$

If the surface does actually contain $z=2$ , then you can stop here; otherwise, continue.

Now, parameterize the part of the *closed* surface in $z=2$ by

$\mathbf s(r,\theta)=r\cos\theta\,\mathbf i+r\sin\theta\,\mathbf j+2\,\mathbf k$

where $0\le r\le4$ and $0\le\theta\le2\pi$ . We get a surface element

$\mathrm d\mathbf S=(\mathbf s_r\times\mathbf s_\theta)\,\mathrm dr\,\mathrm d\theta=(r\,\mathbf k)\,\mathrm dr\,\mathrm d\theta$

We don't need to worry about the first two components of

and so the surface integral over this region is

$\displaystyle\iint_{z=2\,\land\,x^2+y^2\le16}\mathbf F\cdot\mathrm d\mathbf S=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}2r\,\mathrm dr\,\mathrm d\theta=32\pi$

Then the total flux over $\mathcal S$ alone is $(128-32)\pi=96\pi$ .

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3 years ago

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Answer:

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3 years ago

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Answer:

total population after a year ≅ 452525

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4 years ago

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We have a garden that measures 17 feet by 20 feet. We want to pour concrete for a 3‐foot‐wide sidewalk around the garden. To mak

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The inside perimeter would be the perimeter of the garden: 17 + 17 + 20 + 20 = 74 feet.

The outside dimensions would be 6 feet longer on each side ( 3 feet wide on both sides for the sidewalk)

Outside perimeter: 23 + 23 + 26 + 26 = 98 feet.

Total = 74 + 98 = 172 feet.

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3 years ago