Suppose the binary operation ☆ is defined so that
x ☆ y = (x + y) / (1 + xy).
Simplify the expression
{ … [(2 ☆ 3) ☆ 4] ☆ … } ☆ 2021
What is the shortest distance between circle A defined by (x − 5)2 + (y − 4)2 = 4 and circle B defined by (x − 1)2 + (y − 1)2 = 1? There is some point P on circle A closest to B, and there is another point Q on circle B closest to A. What are the coordinates of P and Q?
The temperature on a unit sphere x^2 + y^2 + z^2 = 1, is given by a temperature distribution
T(x,y,z) = 50.(xy + yz)
What is the temperature difference between the coldest and warmest point on the sphere?
Find the angle in which these two curves intersect each other: 1) xy=1 2) x^2-y^2=1
If x and y are the lengths of two sides of a triangle such that the product xy = 18, where x and y are integers, then how many such triangles are possible?
