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2 years ago

Divide. 2/5÷5/6 Express your answer in simplest form. will give brainliest who answers it and rate 5 star

1 answer:

5 0

Dividing a fraction by another fraction is to multiply the first fraction by the reciprocal of the second fraction.
2/5<span>÷5/6= 2/5 x 6/5 2 x 6=12 and 5 x 5=25
=12/25
and 12/25 is the simplest form because you can't divide 12 and 25 by the same number. 12 is an even number and 25 is an odd number.</span>

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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

2 years ago

)) Matt's bill for breakfast at a restaurant was $91. He left an 18% tip. What was the total

gladu [14]

Answer:

$107.38

Step-by-step explanation:

$91 (the price) multiplied by the percentage 18% (91 x 18 = 1630) (1638/100=16.38 [the tip})

$91 (th original price) + 15.38 (the tip) = $108.38 (final price)

4 0

2 years ago

Read 2 more answers

Seth goes to the farmers' market every month to buy some of Ms. Wells's homemade jam. The jam costs $5 per jar. Last weekend, Ms

ELEN [110]

Answer:

add

Step-by-step explanation:

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2 years ago

Cual es la sustitución de x/2+3=7

Maslowich

Answer:

conio

Step-by-step explanation:

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2 years ago

A basketball team played six games. In those games, the team won by 8 points, lost by 25,won by 9, won by 10,lost by 1, and won

Aneli [31]

Answer:

about 10 without a remainder of 4

Step-by-step explanation:

So, add up the number and divide by how many number you have (definition of mean). 8 + 25 + 9 + 10 + 11 + 1 all divide by 6 (since there are 6 numbers)

8 + 25 + 9 + 10 + 11 + 1 is 64.

64/6 is about 10 without a remainder of 4

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2 years ago

Divide. ​ 2/5÷5/6 ​ Express your answer in simplest form. will give brainliest who answers it and rate 5 star

Divide. 2/5÷5/6 Express your answer in simplest form. will give brainliest who answers it and rate 5 star