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2 years ago

Find the slope of the line that passes through each pair of points.

Mathematics

1 answer:

Leno4ka [110]2 years ago

3 0

Answer:

The equation of the line is y = 6/7x + 2/7

Step-by-step explanation:

In order to find this, we first need to find the slope. For that we use slope intercept form.

m(slope) = (y2 - y1)/(x2 - x1)

m = (2 + 4)/(2 + 5)

m = 6/7

Now that we have this, we can use the slope and either point in slope-intercept form to get the equation.

y - y1 = m(x - x1)

y - 2 = 6/7(x - 2)

y - 2 = 6/7x - 12/7

y = 6/7x + 2/7

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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

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

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 $z$ :

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

5 0

2 years ago

Multiply. Do not round your answer.<br><br> 3.5 × 7.1

rosijanka [135]

Answer:

24.85

multiply 3.5 to 7.1 then move the decimal to the left two times

3 0

2 years ago

What is the value of x?

Andrew [12]

Answer:

45??

Step-by-step explanation:

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2 years ago

Read 2 more answers

A room is 20 feet long, 12 feet wide, and 10 feet high. What is the maximum distance from one corner to another

exis [7]

Answer:

25.38

Step-by-step explanation:

Its a 3-D block, so you have to find the distance from on corner to the opposite corner of the roof, but first find the distance from corner to corner on the floor.

20^2+12^2=c^2

400+144=544=c^2

c= $\sqrt{544}$