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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.
Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price? The original price of the bike
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Get the Delta H (Enthalpy) and Delta V (Volume) of the both components below and compare by ratio. You need to use clapeyron equation and also need to draw the graphs. S A LG
Suppose that the probability of your favorite baseball player getting a hit at bat is 0.45. Assume that each at bat is independent. What is the probability that he bats eight times
It is the simplest case which we can consider. Unforced or free vibrations sense that F(t) = 0 and undamped vibrations implies that g = 0. Under this case the differential equation
One of the more significant ideas that we'll be discussing in this section is slope. The slope of a line is a measure of the steepness of any particular line and it can also be uti
Derive the probability distribution of the completion times: a. The following probability distributions relate to the completion times, in weeks, T A and T B of two independ
Example of Word problem: There is a man who is 21 years older than his son. 5 years ago he was four times as old as his son. How older are both now? Solution: Step 1
the operations of cyclic permutations
Find the 20 th term from the end of the AP 3, 8, 13........253. Ans: 3, 8, 13 .............. 253 Last term = 253 a20 from end = l - (n-1)d 253 - ( 20-1) 5 253
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