Problem 5. Group of students from GGC and Kamphaeng Phet Rajabat University collected data for a scientific experiment. The data collection was based on the following set up: "5 sets of bowls (Yellow, Blue and White) were set up 10 meters apart in a straight line. starting at a flower patch and extending for 40 meters." The picture below gives a visual representation of the problem: O 0 20 30 40 After several weeks of collecting, the data was compiled and stored in excel tables, A function P(m) was created where P is the number of insects caught, and m is the distance from the flower patch. Unfortunately, one of the GGC students fell asleep over the computer and erased most of the data pressing the keyboard with his nose. Fortunately, enough information survived to (approximately) recover some of the lost data points. Use calculus as needed to answer the following questions: The following table represented the number of Spiders caught per bowl sets and the rate of change as we move from a set to a set. (For example -2.1 is the rate of change in spiders per meter as we move from Setl to Set2: 1.2 is the rate of change from Set2 to Set3 and so on) Number of Rate of change of the Spiders per SPIDERS meter (Set to Set) Bowl Set 1 -2.1 Bowl Set 2 1.2 Bowl Set 3 3.7 Bowl Set 4 -0.9 Bowl Set 5 TOTAL a) Based on the information above at what bowl set do you expect to have the maximal number of Spiders? Why? b) Can we approximate the number of spiders in each bowl set by using the information in the table? Why or why not? c) At some point one of the students who worked on the data remembered that there were 69 spiders in Bowl Set 4. Compute the number of Spiders in each set and the total number of spiders for all sets. Fill the information in the original table above.Problem 2. Find a9 if Q(t) =- 2 -5e Vt Problem 3. Evaluate the following: [Hint: Use implicit differentiation] dy = ? dx if xy + y' =1-sin(2x) Problem 4. Evaluate [4x3 sin(x* - 1)dx [Hint: Use the substitution u = x4 - 1]Problem 6. Find the net area and the area of the region bounded by the function y = 2cos x and the x-axis between x = -T/2 and x = 2xt. Shade the areas on the graph. [Hint: Recall that the net area is the integral of the function on the given boundaries, while the area is the sum of the positive area regions and the absolute value of the negative area regions in the boundaries] Problem 7. A rectangular flower garden with an area of 238 m2 is surrounded by a grass border 1 m wide on two sides and a 2 m wide on the other two sides as shown in the figure. What dimensions of the garden minimize the combined area of the garden and borders? 2 m Flower garden I m