Let a, b,c be 3 positive real numbers satisfying a. b.c=1. Prove that (a+b)(b+c)(c+a) >= 4(a+b+c-1)

Acar started driving from city a to city b, distance between which is 620 miles, at a rate of 60 mph. two hours later a truck left city b and started moving towards city a at a rate of 40 mph. what distance from city a is the point where the truck and the car will meet?

Marquise has 200 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w w (in meters) is modeled by: a ( w ) = − w 2 + 1 0 0 w a(w)=−w 2 +100w what side width will produce the maximum garden area? meters

Two years ago a man was six times as old as his daughter. in 18 years he will be twice as old as his daughter. determine their present ages.