urgent!! Please help me out with the calculus questions. Thank you so much!

You do not have a graph of C(t). Instead, you have the following pieces of information: . Because of the Nevada heat, cleanup crews are most active in the AM shift, which runs from midnight to noon. The PM shift runs from noon to midnight. . There are 30 workers on-site during each of the first two AM shifts, and 60 workers on site during the last two AM shifts. Every AM shift worker removes waste at a constant rate of 0.05 thousands of gallons per hour. . There are 5 workers on-site during the first PM shift. Each subsequent day adds 5 more workers (with 20 total in the last PM shift). Every PM shift worker removes waste at a constant rate of 0.1 thousands of gallons per hour. Answer each of the following. (a) Sketch a graph of C(t) on the same axes as W (t). *48 (b) Give a practical interpretation of the integral J24 C(t) dt in the context of the problem. (c) Over the course of the first two days of the cleanup effort, what was the average rate at which new waste was being dumped into the site? Over the same interval of time, what was the average rate at which waste was being removed by the workers? (d) At what time t 2 0 was the amount of radioactive waste at the work site the greatest? How much waste was present at this time? Be sure to fully justify your answer. (e) At time t = 96 hours, the workers found and managed to shut off the hidden pipeline. How much radioactive waste did the pig slop manufacturer dump in total? (f) How much waste was left at the end of the 4 day cleanup effort?4. Save the aliens! A pig slop manufacturing giant has (allegedly) been dumping thousands of gallons of extremely dangerous radioactive waste into a local alien wildlife park in Rachel, NV (near Area 51). The city declared a public health emergency and immediately started intense cleanup efforts over the next four days. Unfortunately, even as they were cleaning up, new waste was still spewing out from an illegal hidden pig slop pipeline. . Let W(t) be the rate, in thousands of gallons per hour, at which new radioactive waste was being dumped into the site at time t hours since the cleanup began. . Let C(t) be the rate, in thousands of gallons per hour, at which radioactive waste was being removed from the site by cleanup crews at time t hours after the cleanup began. Time t = 0 is exactly midnight. A graph of W(t) is shown below. At the time when Rachel city officials discovered the illegal dumping site, there were already 40 thousand gallons of waste present. y = W(t) CT 3 2 12 24 36 48 60 72 84 96 You do not have a graph of C(t). Instead, you have the following pieces of information: . Because of the Nevada heat, cleanup crews are most active in the AM shift, which runs from midnight to noon. The PM shift runs from noon to midnight. . There are 30 workers on-site during each of the first two AM shifts, and 60 workers on site during the last two AM shifts. Every AM shift worker removes waste at a constant rate of 0.05 thousands of gallons per hour. . There are 5 workers on-site during the first PM shift. Each subsequent day adds 5 more workers (with 20 total in the last PM shift). Every PM shift worker removes waste at a constant rate of 0.1 thousands of gallons per hour.*11 CAPE = 9800 P(h) - A(h) 3 A(h) + 273 dh J/kg. The atmosphere is said to have strong instability if 2500 4000. (a) Estimate the CAPE value using left-hand and right-hand Riemann sums with 4 equal subdivisions. Does either of these estimates reach the threshold of strong instability? Do either reach the threshold of extreme instability? (b) Consider the function appearing in the integrand, B(h) = P(h) - A(h) A(h) + 273 You must use derivatives to justify your answer to the following two questions. i. Is B(h) increasing or decreasing on the interval 3 4000. If you cannot rule out the possibility of extreme instability, you will issue a severe thunderstorm watch. Hint: You will need your answer to part (b). i. Using left or right Riemann sums (as appropriate) with 4 equal subdivisions, give an overestimate and an underestimate of the integral 7 P(h) - A(h) 9800 dh. A(h) + 273 ii. Using left or right Riemann sums (as appropriate) with 4 equal subdivisions, give an overestimate and an underestimate of the integral 11 P(h) - A(h) 9800 dh. A(h) + 273 iii. Use your answers to (i) and (ii) to give an overestimate and an underestimate of the CAPE value. iv. Can you be certain whether or not the CAPE value reaches the level of strong instability? v. Should you issue the severe thunderstorm watch?5. It actually is just a weather balloon. You are a meteorologist working for the National Weather Service (NWS), collecting data from a weather balloon. An important piece of information is the Convectione Available Potential Energy (CAPE) value, measured in units of Joules per kilogram (J/kg). A large CAPE value indicates a high risk of severe thunderstorms, tornadoes, and other catastrophic weather events. . Let A(h) be the ambient temperature, in degrees Celsius (C), measured by the weather balloon at a height of h km above the surface. . Let P(h) be the internal temperature, in C, that a cloud of surface air (called a parcel) would be if it rose to a height of h km. This is a function that meteorologists can model using other pieces of data collected by the weather balloon. After launching your weather balloon earlier today, you obtained the following graph of the functions T = A(h) (solid and red) and T = P(h) (dashed and blue). T 30 20 10 P(h) h 1 -09 5 11 -10 -20 A(h) -30 Meteorologists call the atmosphere unstable if air rising up from the surface can become warmer than the ambient air high up in the atmosphere, that is, if P(h) > A(h). The CAPE value is an integral taken over the heights h where P(h) > A(h). For this data, the CAPE value is therefore defined as follows