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coordinate geometry

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coordinate geometry
The line joining the points A(-2,3) and B(a,5) is parallel
to the line joining C(0,5) and D(-2,1). Find the value of a.
Slope of AB = [y2-y1]/[x2-x1] = [5-3]/[a-(-2)] = 2 / [a+2]
slope of BC = [1-5]/[-2-0]=(-4)/(-2)=2
for parallel lines m1=m2 [slopes are equal]
therefore 2/[a+2]=2
therefore a+2 = 1
a= -1


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problem 2
 
Show that 
the standard deviation of the
first n natural numbers is sqrt{[(n^2)-1]/12}
The values are 1,2,3,...,n
use the formula for standard deviation
Then use the formula for the sum of the
first n natural numbers and
the sum of the squares of the first n natural
numbers formula
simplify and finally use the identity
 for (a+b)(a-b)


standard deviation of the first n
                      natural numbers

other questions and problems:


*integral calculus integration formula





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trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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