Simplify the following expression:
1/(1 + loga (bc)) + 1/(1 + logb (ac)) + 1/(1 + logc (ac))
Note that a, b, c are greater than 0 but none is equal to 1.
Suppose the binary operation ☆ is defined so that
x ☆ y = (x + y) / (1 + xy).
Simplify the expression
{ … [(2 ☆ 3) ☆ 4] ☆ … } ☆ 2021
If in the following image AC is the diameter of the circle where AB = 4cm and BC = 1cm. Find the x?
Triangle ABC has AB = BC = 10 and AC = 10√2. The triangle is folded so that point A falls on the midpoint M of BC. The crease endpoints P, Q are along sides AB and AC, respectively. What is the length of the crease PQ?
Triangle ABC has a right angle at B. Let Q be along BC and P be along AB such that AQ bisects angle A and CP bisects angle C. If AQ = 9 and CP = 8√2, what is the length of the hypotenuse AC?
