Question 2. A truck mounted tank 2.5 m wide, 8 m length and 2.1 m high is 2/3 full of water. a. What greatest horizontal acceleration can be applied on the truck without any amount spilled? b. Compute the force on the rear and front wall of the tank when acceleration is 1.5 m/s2. c. How much volume of water will spill if acceleration is 2.0 m/s2?

Please do parts 2(d) and 2(e) 2. (36 pts.) A road has a triangular fundamental diagram. It has critical density is 40.0 veh/km, free-flow speed of 100.0 km/hr and jam density of 440.0 veh/km. The flow coming from upstream on the road is initially 3000.0 veh/hr. It travels at the free-flow speed. At 9:00 AM, a bottleneck forms on the road, but the upstream flow continues to be 3000 veh/hr. The bottleneck has a capacity of 2270 veh/hr. A queue begins to form at the bottleneck. 2(a) (10 pts.) Calculate the speed of the shockwave at the back of the queue and indicate what direction it's moving. 2(a) 2(b) (3 pts.) What is the length of the queue at 9:45 AM? 2(b) At 9:45 AM, the flow from upstream drops from 3000.0 veh/hr to 1880.0 veh/hr. 2(c) (10 pts.) What is the new speed and direction of the shockwave at the back of the queue after 9:45 AM? 2(c) At 10:00 AM, the bottleneck is removed. Cars leave the bottleneck at the road's capacity. 2(d) (3 pts.) What is the length of the queue at 10:00 AM? 2d) 2(d) 2(e) (10 pts.) At what time, and at what distance from the bottleneck, does the queue dissipate?

Moments and shear stress 2. The following figure shows all the stresses on a small volume element (of volume dxdydz) in equilibrium. By calculating the moments about the centre of the element and understanding that in equilibrium the total sum of moments around the x, y and z axes are zero, prove that: Txy Tyx Txz = T7x and Tyz Tzy dx буг бу dz Ох бу Оух xy Moments and shear stress 2. The following figure shows all the stresses on a small volume element (of volume dxdydz) in equilibrium. By calculating the moments about the centre of the element and understanding that in equilibrium the total sum of moments around the x, y and z axes are zero, prove that: Txy Tyx Txz = T7x and Tyz Tzy dx буг бу dz Ох бу Оух xy бх dy (Hint: calculate the moments about the centre of the element in the x, y and z axes separately.) 60

7–26. Lagrange multipliers Each function ƒ has an absolute maximum value and absolute minimum value subject to the given constraint. Use Lagrange multipliers to find these values. ƒ(x,y) = x2 subject to x2 + xy + y2 = 3

The Gourmand Cooking School runs short cooking courses at its small campus. Management has identified two cost drivers it uses in its budgeting and performance reports—the number of courses and the total number of students. For example, the school might run two courses in a month and have a total of 65 students enrolled in those two courses. Data concerning the company's cost formulas appear below: Instructor wages Classroom supplies Utilities Campus rent Insurance Administrative expenses Fixed Cost per Cost per Cost per Month Course Student $ 2,960 $280 $1,240 S 80 $4,600 $2,400 $3,600 44 S 5 $ For example, administrative expenses should be $3,600 per month plus $44 per course plus $5 per student. The company's sales should average $890 per student. The company planned to run four courses with a total of 65 students; however, it actually ran four courses with a total of only 57 students. The actual operating results for September appear below: Revenue Instructor wages Classroom supplies Utilities Campus rent Insurance Administrative expenses Actual $ 54,950 $11,120 $ 18,050 $ 1,970 $ 4,600 $ 2,540 $ 3,527 Required: Prepare a flexible budget performance report that shows both revenue and spending variances and activity variances for September. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.) Required: Prepare a flexible budget performance report that shows both revenue and spending variances and activity variances for September. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.) Gourmand Cooking School Flexible Budget Performance Report For the Month Ended September 30 Flexible Actual Results Budget Planning Budget Courses 4 Students 57 $ 54,950 Revenue Expenses: Instructor wages Classroom supplies Utilities Campus rent Insurance Administrative expenses Total expense Net operating income 11,120 18,050 1,970 4,600 2,540 3,527 41,807 13,143 $

13) The emf and the internal resistance of a battery are as shown in the figure. If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery, what is the power dissipated by the resistor R? - 95.0 V 5.0 92 - - - - - A) 620 W B) 530 W C) 440 W D) 790 W E) 700 W

Find the linearization of y=sin(x) at x=π/4, and use your result to approximate sin(11π36). Enter exact values only and don't leave trigonometric functions unevaluated. (a) What is dxdx? (b) Using your linearization, approximate sin(11π36)sin(11π36). sin(11π36)