1. Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate the definite integral from 0 to 8 of R(t)dt. Using correct units, explain the meaning of your answer in terms of water flow. Give 3 decimal places in your answer.

2. Is there some time t, 0 < t < 8, such that R′(t) = 0? Justify your answer.

3. The rate of water flow R(t) can be estimated by W(t) = ln(t^2 + 7). Use W(t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?