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Fudgin [204]
3 years ago
8

- 1)" align="absmiddle" class="latex-formula">

Mathematics
2 answers:
mestny [16]3 years ago
7 0
Hey there :)

( 5y + 9 )( 6y - 1 )

We need to use FOIL to expand, that is
First Terms
Outer Terms
Inner Terms
Last Terms

     First          Outer         Inner      Last
( 5y )( 6y ) + ( 5y )( - 1 ) + 9 ( 6y ) + 9 ( - 1 )
    30y²     -        5y      +    54y   -       9

Combine, if any, the like-terms
30y² + 49y - 9
Ostrovityanka [42]3 years ago
4 0
Hey there,

(5y + 9) (6y-1)
= 5y*6y - 5y + 6y*9 - 9
= 30y² - 5y + 54y - 9
= 30y²+ 49y - 9

Hope this helps !

Photon
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\sqrt{2} or (1/2)

Step-by-step explanation:

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We know

\boxed{\sf Surface\:area=4\pi r^2}

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\\ \sf\longmapsto r^2=\dfrac{7238\times 7}{88}

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<h3>Option b is coreect</h3>
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vitfil [10]

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-20

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Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?
cluponka [151]

Under the given transformation, the Jacobian and its determinant are

\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2

so that

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv

where D' is the region D transformed into the u-v plane. The remaining integral is the twice the area of D'.

Now, the integral over D is

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y

but through the given transformation, the boundary of D' is the set of equations,

\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}

We require that u>0, and the last equation tells us that we would also need v>0. This means 1\le v\le\sqrt2 and 0, so that the integral over D' is

\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6

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3 years ago
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Ray Of Light [21]
The width of the laptop is 6 inches long.
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