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Ivanshal [37]
3 years ago
14

I need help! Find the equation of a line parallel to 3x-3y=5 that contains the point (-1,-5). Write the equation in slope Interc

ept form.

Mathematics
1 answer:
Readme [11.4K]3 years ago
6 0

the equation of the line is y= x-4

Step-by-step explanation:

so so the first thing that you're going to do is get y alone

-x-5=y

next you're going to find your slope which in this case is negative one.

after that in order to find the equation of a parallel line you're going to find the reciprocal of the slope.

so in this case the reciprocal is one.

next you're going to substitute in the cordinates to find the y intercept

x+b=y. (-1)+b= -5. (. b is the y intercept)

b= -4

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The unit disk can be parameterized by the function

\mathbf p(r,\theta)=(r\cos\theta,r\sin\theta)

where 0\le r\le 1 and 0\le\theta\le2\pi. The squared distance between any point in this region (x,y)=(r\cos\theta,r\sin\theta) and the point (1, 1) is

(x-1)^2+(y-1)^2=(r\cos\theta-1)^2+(r\sin\theta-1)^2
=(r^2\cos^2\theta-2r\cos\theta+1)+(r^2\sin^2\theta-2r\sin\theta+1)
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=r^2-2r(\cos\theta-\sin\theta)+2

The average squared distance is then going to be the ratio of [the sum of all squared distances between every point in the disk and the point (1, 1)] to [the area of the disk], i.e.

\dfrac{\displaystyle\iint_{x^2+y^2
=\dfrac{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}[r^2-2r(\cos\theta-\sin\theta)+2]r\,\mathrm dr\,\mathrm d\theta}{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r\,\mathrm dr\,\mathrm d\theta}
=\dfrac{\frac{5\pi}2}\pi=\dfrac52
5 0
2 years ago
There are 10 balls in an urn, numbered from 1 to 10. If 5 balls are selected at random and their numbers are added, what is the
Kisachek [45]

Let B_i denote the value on the i-th drawn ball. We want to find the expectation of S=B_1+B_2+B_3+B_4+B_5, which by linearity of expectation is

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(which is true regardless of whether the X_i are independent!)

At any point, the value on any drawn ball is uniformly distributed between the integers from 1 to 10, so that each value has a 1/10 probability of getting drawn, i.e.

P(X_i=x)=\begin{cases}\frac1{10}&\text{for }x\in\{1,2,\ldots,10\}\\0&\text{otherwise}\end{cases}

and so

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Then the expected value of the total is

E[S]=5(5.5)=\boxed{27.5}

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2 years ago
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