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3 years ago

Write each rational number in the form, where a and b are integers. -29 , 8 1/3 , 0.7

Mathematics

1 answer:

Vinil7 [7]3 years ago

3 0

a.) 0.3 = 3/10 b.)5 1/3 = 16/3 c.)0 = 0/1 d.)73 = 73/1 e.)-0.21 = -21/100 Cheers, Stan H.

0.3

2 7/8

-5

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The pair of points is on the graph of an inverse variation. Find the missing value.

Ann [662]

Answer:

x = 16/3

Step-by-step explanation:

y varies inversely with x if ...

y = k/x

The constant k can be found from ...

xy = k

For the given point, ...

2·8 = k = 16

The relation is symmetrical, so we also have ...

x = k/y = 16/3 . . . . substituting the value at the second given point

The missing value is 16/3.

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2 years ago

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2 years ago

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3 years ago

During second period,Emma completed a grammar worksheet.Of the 60 questions Emma got 90% right how many questions did Emma get r

Alona [7]

She got 54 questions rights.
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2 years ago

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x

Lady_Fox [76]

By Stokes' theorem, the line integral of $\vec F$ over $C$ is given by the surface integral of the curl of $\vec F$ over $S$ , where $S$ is the region of intersection of the plane $z=y+6$ and the cylinder $x^2+y^2=1$ with $S$ having positive/upward orientation.

Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+6)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

The curl of $\vec F$ is

$\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-2)\,\vec k$

Then the line integral is equivalent to

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\bigg((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+4)\,\vec k\bigg)\cdot\bigg(-u\,\vec\jmath+u\,\vec k\bigg)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(5u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{5\pi}$

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2 years ago