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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.
Perpendicular to the line given by 10 y + 3x= -2 For this part we desire the line to be perpendicular to 10 y + 3x= -2 & so we know we can determine the new slope as follows,
find the number of ways 17 employees can b chosen from 327
Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ± tS x¯ x¯ = Sample mean S x¯ = s/√n S = standard deviation
The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these
cos^2(A)x sin(A)
The average age of a woman and her daughter is 16 years. The ratio of their ages is 7: 1. Then the woman''s age is
How would you solve this question? 4/5 = 8/x+2
how can i round decimals
FIND PRODUCT (-41)*(102)
Urn A contains 1 white,2 black and 3 red balls;Urn B contains 2 white,1 black and 1 red balls;and Urn C contains 4 white,5 black and 3 red balls.One urn is chosen at random and two
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