For determining the length of the chords in Circle, Rectangular Co ordinate System is used. According the graphical representation, radius towards right side is positive and towards left is negative.

Topic : Length of Chords in a Circle of radius r

Using definite integrals we can calculate the length of chords with some constraints.

Question : In a circle of radius r, find the average length of the chords perpendicular to the diameter [-r, r].

Solution :

For more information and clarification related to the above topic you can find help at calculus help.

Topic : parabola

Question : Growth rate y (in pounds/month)of an infant is related to the present weight x(in pounds)by formula y= cx(21-x)where c is a positive constant.0<x<21.At what rate does the maximum growth occur.

Answer :

The y coordinate of the vertex is the max of a quadratic if the parabola is downward and its the minimum if its upward.

the parabola is upward if the co efficient of x^2 is positive and downward if its negative.

here we have y= c x(21-x)= 21cx -c x^2

as the co efficient of x^2 is negative, we get a maximum value

formula: for y = ax^2+bx+c , the vertex is given by ( -b/2a , f( -b/2a) )

hence the maximum y value is -b/2a

here the max growth rate = – 21c / -2c = 21/2 =10.5pounds/month.