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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.
Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section
Arc Length with Polar Coordinates Here we need to move into the applications of integrals and how we do them in terms of polar coordinates. In this part we will look at the a
Terry earns $680 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.
how to calculate the npv
Use Newton's Method to find out an approximation to the solution to cos x = x which lies in the interval [0,2]. Determine the approximation to six decimal places. Solution
if two circles O and O''intersect in two points, A and B, the the line segment OO is what?
Dividing Whole Numbers: Example: Divide 347 by 5. Solution: Beginning from the left of the dividend, the divisor is divided into the
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4/(x+7)(x+4)
Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
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