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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.
using the formula sin A =under root 1+ cos2A /2 . find value of 30 degree, it is being given that cos 60 degree =1/2.
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write 107 in expanded form.
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i need help with exponents and how to add them
Example Multiply 3x 5 + 4x 3 + 2x - 1 and x 4 + 2x 2 + 4. The product is given by 3x 5 . (x 4 + 2x 2 + 4) + 4x 3 . (x 4 + 2x 2 + 4) + 2x .
Determine how many square centimeters of paper are needed to make a label on a cylindrical can 45 cm tall with a circular base having diameter of 20 cm. Leave answer in terms of π.
my daughter is having trouble with math she cant understand why please help us
Devise one activity each to help the child understand 'as many as' and 'one-to-one correspondence'. Try them out on a child/children in your neighbourhood, and record your observat
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