MATHEMATICS 2

Each year, a school allocated a sum of money for the library. The amount allocated each year increases by 2.5% of the amount allocated the previous year. In 2005, the school allocated $2000. Find the total amount allocated in the years 2005 to 2014 inclusive

Given the terms a10 = 3 / 512 and a15 = 3 / 16384 of a geometric sequence, find the exact value of the term a30 of the sequence.

The first two terms of an arithmetic proression are16 and 24. Find the least number of terms of the progression which must be taken for their sum to exceed 20000

Solve the equation exactly:  2 cos θ−3=−5, 0≤θ<2π..

Function f is defined by f(x) = - 2 x 2 + 6 x - 3 find f(- 2).

Find the area of the region enclosed between the curves y = x 2 - 2x + 2 and -x 2 + 6 .

The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what are the truck's speeds?

The distance between stations A and B is 148 km. An express train left station A towards station B with the speed of 80 km/hr. At the same time, a freight train left station B towards station A with the speed of 36 km/hr. They met at station C at 12 pm, and by that time the express train stopped at at intermediate station for 10 min and the freight train stopped for 5 min. Find The distance between stations C and B.