Using exploration data the management of an oil company estimates that over a period of 20 years oil can be pumped from a west texas oil field at a rate given by r(t) = 8t 4t 2 + 7 stone (ins278) – hw32 – clark – (52400) 2 where r(t) is the production rate (measured in hundreds of barrels per year) t years after pumping begins. determine the number of barrels that will be produced during the first 5 years of production.

what is the question

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft