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2 years ago

Write an equation in slope-intercept form: (1,6) and (2,3) are on the line

Mathematics

1 answer:

s344n2d4d5 [400]2 years ago

5 0

Step-by-step explanation:

eqn of line : y = mx+ c

m = slope or gradient

c = y-intercept.

Lets take (1,6) = (x1,y1) and (2,3) = (x2,y2)

$m \: = \frac{y1 - y2}{x1 - x2} \\ = \frac{6 - 3}{1 - 2} \\ = \frac{3}{ - 1} \\ = - 3$

Substitute x = 1 and y = 6 into equation,

$6 = ( - 3)(1) + c \\ 6 = - 3 + c \\ c = 6 + 3 \\ = 9$

Therefore substituting m and c value, equation of line is

$y = - 3x + 9$

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Aleks04 [339]

The area of the entire sector of DEF = 60 / 360 * PI * radius^2
sector area = 1 / 6 * 3.14159265... * 20^2
sector area = 209.4395102393 

segment area = sector area - triangle DEF Area
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segment area = 36.2335102393 
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Source:
http://www.1728.org/circsect.htm

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Step-by-step explanation:

Previous concepts

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Solution to the problem

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

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