Math Answers

A and B are equally good tennis players. Which of the following two events is more probable? (i) A beats B exactly in 3 games out of 4. (ii) A beats B exactly in 5 games out of 8

Find the area of an equilateral triangle inscribed in the circle x2+y2 - 6x + 2y – 15 = 0.

A person standing at the crossing at two straight paths represented by the equations 2x-3y-4 = 0 and 3x-4y-5 = 0, wants to reach a path represented by 6x-7y+8 = 0 in least time. Find the equations of path he should follow.

Two cyclists start together in the same direction from the same place. The first goes with uniform speed of 10km per hour. The second goes at a speed of 8 km per hour in the first hour and increases the speed ½ km each succeeding hour. After how many hours the second cyclist overtake the first if both go non-stop?

Two boats leave the same bank of sea at the same time. One goes 12km per hour in the direction N550E and other goes 16km per hour in the direction S650E. Find the distance between the boats at the end of two hours.

true/false?justify.
If lim n→∞ (u)subscript n =0, then the series (∞)∑(n=1) (u)subscipt n is convergent.

true/false? justify.
The function f defined by f(x) =|x −(5/2)| ,x∈R has a local maxima of x=5/2

Show that the function f defined on R by
f(x)={3x^(2) cos(1)/(2x), when x≠0 ; 0, when x=0
is derivable on R but f ′ is not continuous at x=0

true/false? prove.
1/2 is a limit of the interval ]− 2.5,1.5[