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Mathematical Formulae
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
(a + b)2 + (a - b)2 = 2(a2 + b2)
(a + b)2 - (a - b)2 = 4ab
a2 - b2 = (a + b) (a - b)
(a + b)3 = a3 + b3 + 3ab (a + b)
(a - b)3 = a3 - b3 - 3ab (a - b)
a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)
logax = y →ay = x
logaxp = p logax
logaxy = loga x + logay
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.
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The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin
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In figure, the incircle of triangle ABC touches the sides BC, CA, and AB at D, E, and F respectively. Show that AF+BD+CE=AE+BF+CD= 1/2 (perimeter of triangle ABC), Ans:
Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers
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