Consider a curve with which passes through four points .
All these points are taken in given order for constructing a convex quadrilateral, which has maximum possible area.
Find minimum possible value of
A rectangle's bottom is at
while its top corners are on the curve between and . The maximum area of this rectangle can be expressed as
where and are prime numbers. What is the sum
(Don't count twice)
Let
Then can be written as
where is square free & . Find the value of .
A cow is tied to a silo with radius by a rope just long enough to reach the opposite end of the silo.
Find the area available for grazing by the cow.
Enter the answer for , rounded to the nearest hundredth.
For positive integer , the limit evaluates to for coprime positive integers . What is the value of ?