A jawbreaker is a ball of hard candy filled with multiple colored layers (or rings) of hardened sugar. Mirra sells jawbreakers of three layers. The yellow core (r-3 cm) is surrounded by a 1 cm layer of pink sugar, which in turn, is coated with 2 cm of white sugar. If each layer is 1 cm thicker than it is supposed to be, use partial differentials to approximate how much larger (in cm³) the cross sectional area will be. Divide your final answer by n before inputting

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…

A tank initially holding 80 gals of fuid with 40 lbs of salt has two sources of fluid being pumped in. One source is pumping pure water in at 8 gal/min and the second source is pumping in a salt solution of 0.5 Ibs/gal at 2 gal/min. The tank is emptying at 10 gal/min. Find the amount of salt in the tank after 30 minutes?

Use linearization to estimate the change in volume of a sphere when its radius changes from r to r+ Δr. Then calculates the exact value of the volume change and calculates the difference of both results