Q1:

Oil is being pumped into a tank at a rate of r'(t) liters per minute, where t is in minutes. Selected values of r(t) are given in the table below. EEIZEEI Use the information given in the table to answer the following questions. (a) Use the right hand sum with n = 3 to estimate 12 _ f rum =|:| 0 Enter our calculation here. 12 mlm E . Enter your calculation here. | 4| (c) Estimate r'(12) s: |:| ---Select--- 3' Enter our calculation here. The following graphs show the position of four objects moving along the x-axis as a function of time, 0 s t s 6. The questions below refer only to this time interval. Time is measured in seconds. Object A colact a (a) Which object ends up farthest from its starting point? | --Select- * (b) Which object, if any, has an average velocity of zero over the first 6 seconds? ( ---Select- * (c) Which object, if any, has zero acceleration throughout the first 6 seconds? | ---Select- * (d) Which object, if any, has a decreasing velocity throughout the first 6 seconds? ---Select-You are constructing a closed box whose length, I, is three times its width, w, as indicated in the labels on the figure below. The material costs 55 per square inch for the top and bottom and $3 per square inch for the sides. The box must hold 60 cubic inches. 3W (a) Write an equation for the cost of the box In terms of w and h. c = 12w: + 10w2 c = 4m: + 2w2 c = 24m: + 30w," 6 = 12wh + sow2 C = Bwh + 61.1.2 C = 35w: + 30w2 (b) Write an equation for the cost in terms of w only. Use lower case w. CIW) = I (c) Find C'(w) = E (d) Find the exact width that minimizes the cost of the box. w = |:| inches