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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.
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f
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Here is not too much to this section. We're here going to work an illustration to exemplify how Laplace transforms can be used to solve systems of differential equations. Illus
Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t
two numbers differ by 7 and have a product of 120.what are they ?
Evaluate following. (a) 625 3/4 Solution (a) 625 3/4 Again, let's employ both forms to calculate this one. 625 3/4 =( 625 1/4 ) 3 =(5) 3 = 12
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The Central Limit Theorem The theories was introduced by De Moivre and according to it; if we choose a large number of simple random samples, says from any population and find
Test Of Hypothesis On Proportions It follows a similar method to the one for means except that the standard error utilized in this case: Sp = √(pq/n) Z score is computed
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