In reaction engineering, the average residence time 7 is the amount of time an element of fluid spends in a reactor and is related to the amount of substance present in the system. The easiest method to determine 7 is via a pulse stimulus, where a small amount of a tracer is put into a reactor operating under steady state and the effluent concentration is measured over time. The average residence time is calculated as: Ĵt-C dt 7 = jc dt 0 ; where C is the concentration. 0 100 200 300 400 500 600 700 800 900 C (ppm) 0 20 20 16 10 7 5 3 1 0 Given the data in the table, use Excel to numerically integrate this equation (note there are two integrals to evaluate) to solve for 7 using the Trapezoidal Rule.

A pasta company with a blue box produces 1,400 tons of semolina pasta per day. The pasta is fed into a machine as a large, loose dough and then squeezed through a bronze die to form a desired shape. As the pasta is squeezed through the die, the volume of space it takes up decreases while the mass remains constant, and thus the resulting shape is more dense. If m is the constant mass of the pasta in grams and V is the volume of the pasta in mL, then the density p is given by p= - m (a) If the mass remains constant while the volume changes with time, find dp dt (b) Suppose the mass of the pasta is 80g, the density is 0.8 g/mL, and the volume is decreasing at a rate of 400 mL/sec. How fast is the density of the pasta changing at that moment? mL · sec

A student is concerned with the amount of air pollution students are exposed to in the school's parking lot after school. The student conducts an investigation to compare the quantity of particulate matter released from the diesel-powered buses, natural gas-powered buses, and the large and small cars as they idle waiting to pick up students. To make measurements, a small piece of white fabric is used to collect particulate matter from the tailpipe of each vehicle as it idles for five minutes. Each piece of fabric is then analyzed to measure the amount of particulate matter it collected. (i) Identify the independent variable in the investigation. (j) Identify one variable that was not mentioned in the description that could affect the results of the investigation. (k) Describe a realistic alternate sampling method to collect particulate matter from the vehicles in the investigation. (1) The student wants to ensure that the results are reliable. Explain how the student could modify the…