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if f(x)+2f(1/x)=2 x find f(.25)

if f(x)+2f(1/x)=2 x find f(.25)

22/7 which is value of pie (as both number numerator and denominator are non zero) should be rational. But why is it irrational? Rational condition states that both numerator and denominator should be rational which it satisfies...

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The remainders when 4864 and 5800 are divided by a certain number, X, are the same. What is the maximum possible number of divisors of X?
In the explanation given - it says that X will be divisible by 5800-4864
Can someone explain how we can come up with this ?

Similar triangles are confusing me, specially the naming part, for instance, if it is given, triangles ABC and DEF are similar. If angle C is equal to angle E, AB is 4.2, DE is 2.1, BC is 6.4 and DF is 2.8 then find EF and AC. In the solution they have written AB/DE=BC/EF=AC/DF. But if angle C is equal to angle E then wont it be AB/DF? Since we take corresponding sides to equal angles,

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A shopkeeper marks his good at 60% above the cost price. He allows a discount of 12 1/2%. Also he cheats 14 2/7% while purchasing and 20%at selling and gives one article free on purchase of 15 articles. Find the profit/loss in whole transaction.

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