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Three quantities a, b and c are said to be in harmonic progression if,
In this case we observe that we have to consider three terms in order to conclude whether they are in harmonic progression or not.
An important proposition in this case is that the reciprocal of quantities in harmonical progression are in arithmetical progression. Let us understand this by considering three quantities a, b and c. By definition, if a, b and c are in harmonic progression then they satisfy the condition that
By cross multiplying, we obtain
a(b - c) = c(a - b)
That is, ab - ac = ac - bc
Dividing each of these terms by abc, we have
This can be written as
Canceling the common terms, we have
This gives us the common difference between the reciprocal terms of a, b and c. This also proves our proposition.
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Learning geometric progression vis-á-vis arithmetic progression should make it easier. In geometric progression also we denote the first t
If α, β are the zeros of the polynomial x 2 +8x +6 frame a Quadratic polynomial whose zeros are a) 1/α and 1/β b) 1+ β/α , 1+ α/β. Ans. P(x) = x 2 +8x +6 α + β = -8
what are these all about and could i have some examples of them please
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Example of Log Rules: Y = ½ gt 2 where g = 32 Solution: y = 16 t 2 Find y for t = 10 using logs. log y = log 10 (16 t 2 ) log 10 y = log 10 16 + log 10
Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi
In the earlier section we modeled a population depends on the assumption that the growth rate would be a constant. Though, in reality it doesn't make much sense. Obviously a popula
If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro
write 107 in expanded form.
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