Jim began a 174-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of 3 miles per hour and rides at 37 miles per hour, find the amount of time he spent on the bicycle. Jim rode for ___ hours.

Si la base de un triángulo isósceles mide 70 m y el ángulo opuesto a ésta mide 58°; entonces ¿cuánto mide la altura de dicho triángulo? a) 21.87 m. b) 40.01 m. c) 43.74 m. d) 63.14 m.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25