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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.
I have a simple right angle triangle. All I am given is h (the hypotenuse) and that ratio of x:y is 2:3. What is the formula to find x and y in terms of h?
Class limits These are numerical values, which limits uq extended of a given class that is all the observations in a provided class are expected to fall in the interval which
1/2 + 2/8 =
shortricks of compound interest
regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
Solve the following equestions i.2x-8=8 ii.3x+2/5=4 iii.8/3x-2=2 iv.0.6x-5=7
what is rotation
which shows the rate 12 inches of rain in 6 hours as a unit rate
Universal set The term refers to the set which contains all the elements such an analyst wishes to study. The notation U or ξ is usually used to denote universal sets.
Functions of Several Variables - Three Dimensional Space In this part we want to go over a few of the basic ideas about functions of much more than one variable. Very first
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