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3 years ago

What is 2 and 3/4 divided by 1/4

Mathematics

1 answer:

Tanya [424]3 years ago

3 0

2 3/4 divided by 1/4
is
2 3/4 multiplied by 4/1

which is (2+3/4)*4 = 2*4 + 3/4*4 = 8+3 =<em>11</em>

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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

3 years ago

3×10+2×1+6×1/100+4×1/1000 is the expanded form of which decimal?

motikmotik

The answer would be 32.064

5 0

3 years ago

Please help me find X

Zanzabum

Answer:

x = 2

Step-by-step explanation:

The product of distances from the intersection of secants to the near and far intersections with the circle are the same. For a tangent, the near and far points of intersection with the circle are the same. This relation tells us ...

(2√3)(2√3) = x(x +4)

12 = x² +4x

16 = x² +4x +4 . . . . . add the square of half the x-coefficient to complete the square

4² = (x +2)² . . . . . . . . write as squares

4 = x +2 . . . . . . . . . . positive square root

2 = x . . . . . . . . . . . . . subtract 2

_____

<em>Alternate solution</em>

If you believe x to be an integer, you can look for factors of 12 that differ by 4.

12 = 1×12 = 2×6 = 3×4

The factors 2 and 6 differ by 4, so x=2 and x+4=6.

6 0

3 years ago

4×<img src="https://tex.z-dn.net/?f=10%5E%7B3%7D" id="TexFormula1" title="10^{3}" alt="10^{3}" align="absmiddle" class="latex-fo

Anettt [7]

4000 (4x10^3) times 400 (4x10^2) is equal to 16x10^5 ( 1,600,000)

5 0

3 years ago

What is the distance between points (4,7) and (-3,6) using the Pythagorean theorem

uysha [10]

A² + b² = c².
Make a triangle with the points on a grid.
One leg is 7 units and the other is 1 unit.
7² is 49 and 1² is 1.
49 + 1 = 50
√50 ≈ 7.071.
Hope this helps!

6 0

3 years ago