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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.
X-intercept If an intercept crosses the x-axis we will call it as x-intercept . Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter
The subsequent topic that we require to take a look at is the determinant of a matrix. The determinant is in fact a function that gets a square matrix and converts this in a number
Multiplication Rule: Dependent Events The joint probability of two events A and B which are dependent is equal to the probability of A multiplied by the probability of B given
degree of a diffrential equation
Determine y′′ for x 2 + y 4 = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w
Interpretations of derivatives. Example: Find out the equation of the tangent line to x 2 + y 2 =9 at the point (2, √5 ) .
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. H v (~T > R) 2. Hv (E > F) 3. ~T v E 4. ~H & D / R v F INSTRUCTIONS: Con
i don''t understand how
draw a line OX=10CM and construct an angle xoy = 60. (b)bisect the angle xoy and mark a point A on the bisector so that OA = 7cm
compute the monthly payment on a 30 year level payment mortagagesasuming an annual mortgages principal of $400000
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