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2 years ago

Find the distance between the two points 5,6 and 0,-6. Show your work

Mathematics

1 answer:

valkas [14]2 years ago

3 0

Answer:

The distance between two points is √169 or 13.

Step-by-step explanation:

In the question we need to find the distance between two points 5,6 and 0,-6 given.

Distance between two points can be found using the formula:

$d(P1,P2) = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$

Putting the given points in the formula we get,

x₂ = 0, x₁ = 5, y₂= -6, y₁= 6

$=\sqrt{(0-(5))^2 + (-6-(6))^2} \\=\sqrt{(0-5)^2 + (-6-6)^2}\\=\sqrt{(-5)^2 + (-12)^2}\\=\sqrt{25 + 144}\\=\sqrt{169}\\=13$

So, the distance between two points is √169 or 13.

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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

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1 year ago

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trapecia [35]

Answer:

Step-by-step explanation:

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2 years ago

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DaniilM [7]

The correct answer is : of those planning to not to go on vacation, more of them are women.

The correct answer is (C)

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Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event

Given: total people asked =145

The first option is not correct because plan to go on vacation women are more than men.

The second option is also incorrect because more women were asked than men.

The third option is correct because out of planning who were not going any vacation, women are more than of men.

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Learn more about probability here:

brainly.com/question/11234923

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1 year ago

A and b are positive integers. Find <img src="https://tex.z-dn.net/?f=-2a%2B3b" id="TexFormula1" title="-2a+3b" alt="-2a+3b" ali

lord [1]

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From what I know you can't really solve a a single equation with two-variables so it's just a matter of trial and error.

Just try plugging in a small number like 2 for a just to try it and you get 8b^2=72.

Divide everything by 8 to isolate b and you get that b^2=9.

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Now that we know that a=2 and b=3 just plug them into the equation.

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Sorry about having to use this ^ symbol, the equation maker is not working.

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2 years ago

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ss7ja [257]

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3 years ago

Find the distance between the two points 5,6 and 0,-6. Show your work​

Find the distance between the two points 5,6 and 0,-6. Show your work