If (a + b + c) = 14, and (a³ + b³ + c³ - 3abc) = 98, find the value of (ab + bc + ca)

If A = 22.5°, what is the value of (10√2 sin 2A - 7√2 cos 2A + 9 tan 2A)?

The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32 . What is the product of the two given numbers?

The force (in pound-force) needed to keep a car from skidding on a curve varies directly with the weight of the car (in pounds) and the square of its speed (in miles per hour [mph]) and inversely with the radius (in feet) of the curve. Suppose 6125 pound force is required to keep a 2750 pound car, travelling at a speed of 35 mph, from skidding on a curve of radius 550 feet. How much pound-force is then required to keep a 3600 pound car, travelling at a speed of 50 mph, from skidding on a curve of radius 750 feet?