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3 years ago

How do I establish this identity??

Mathematics

1 answer:

Aloiza [94]3 years ago

8 0

$\frac{cosec\theta+cotan\theta} {sec\theta+tan\theta}=\frac{cosec\theta+cotan\theta} {sec\theta+tan\theta}\times\frac{cosec\theta-cotan\theta}{cosec\theta-cotan\theta}\times\frac{sec\theta-tan\theta} {sec\theta-tan\theta}$

And use that,

$\sec^2\theta-\tan^2\theta=1$

$cosec^2\theta-cotan^2\theta=1$

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Express the integral as an iterated integral in six different ways, where E is the solid bounded by y=4-x^2-4z^2 and y=0

zmey [24]

Assuming you need the integral expressing the volume of $E$ , the easiest setup is to integrate with respect to $y$ first.

This is done with either

$\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_{-2}^2\int_0^{4-x^2-z^2}\mathrm dy\,\mathrm dx\,\mathrm dz$
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Thanks to symmetry, integrating with respect to either $x$ or $z$ first will be nearly identical.

First, with respect to $x$ :

$\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_0^4\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-z^2}}\mathrm dx\,\mathrm dy\,\mathrm dz$
$\displaystyle\iiint_E\mathrm dV=\int_0^4\int_{-2}^2\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-z^2}}\mathrm dx\,\mathrm dz\,\mathrm dy$

Next, with respec to $z$ :

$\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_0^4\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-x^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$
$\displaystyle\iiint_E\mathrm dV=\int_0^4\int_{-2}^2\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-x^2}}\mathrm dz\,\mathrm dx\,\mathrm dy$

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3 years ago

Kaitlyn was asked to find which expression below is equivalent to -3x + 5(x + 2)?

NISA [10]

The correct answer is c (2x+10)
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FromTheMoon [43]

Answer:

Mean: For this case would be not useful since in the stem leaf plot is difficult to find this measure with this chart

Step-by-step explanation:

We want construct a stem and leaf plot and we want to find the measure least useful.

And for this case if we analyze the option we have:

Range: That very useful and it can be extracted from the stem and leaf plot

Median: It could be easy to find it with the stem leaf plot

Mode: With a stem leaf plot we can find easily the most repeated value

Mean: For this case would be not useful since in the stem leaf plot is difficult to find this measure with this chart

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