A pole is broken such that top of the pole touches the ground. If pole is broken at a height of 119 feet from the ground and top of broken pole touches the ground at a distance of 120 feet from its base, find the length of pole.

An arithmetic sequence is a sequence of numbers a_{1}, a_{2}, a_{3},... where a_{n} - a_{n-1} is the same value for all n. For example 2, 4, 6, 8, 10,....is such a sequence where the difference between adjoining numbers is 2. Given a, b, c, d and e are consecutive members of such a sequence, and that a + b + c + d + e = 90, what is the value of c?

A gymnasium weighs all the people that come in to exercise. On one morning, it notes down the weights of 5 people in kgs as follows 62 kgs, 69.9 kgs, 65 kgs, 69 kgs, 84.1 kgs The average of their weights is calculated. If a new person now comes in to exercise, and the new average is calculated to be 70.9, then what was the weight of the new person in kgs?

A poultry farm produced 16b^{2} - 5b - 4 eggs in a year. It packaged 4b^{2} - b - 6 eggs and sent them to market while 9b^{2} - 6b - 7 eggs got destroyed. How many eggs are left with the poultry farm?