Question Evaluate the following integral using integration by parts. ( 3x e 5x dx Let u = 3x. Use the integration by parts formula so that the new integral is simpler than the original one. [3x e5x dx = D-SO. Зх. dx Evaluate the integral. (3xesx dx =

MSeaV has hired you to design a new prototype for an environmentally friendly plastic water bottle. The water bottle is to have a volume of 750 cm3. You are to consider a cylindrical model that is topped by a hemisphere. The design would have a puncture hole so no cap would be needed. For ergonomic purposes the radius should be at least 3 cm and at most 6 cm. Determine the dimensions and resulting surface area for a hemispherical-topped, cylindrical, plastic water bottle that minimizes the amount of plastic used.

A 181 ‑turn circular coil of radius 2.03 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 16.5 Ω resistor to create a closed circuit. During a time interval of 0.135 s, the magnetic field strength decreases uniformly from 0.627 T to zero. Find the energy 𝐸 in millijoules that is dissipated in the resistor during this time interval.

The following equations describe the variation of pressure p with veloci 0 p + A og V-2 = X (i) p + B g pv = Y (iii) p + CPV 2 = Z where, A, B, and C are dimensionless constants. X, Y, and Z are values with the same dimensions as pressure, g is the acceleration due to gravity, p is the density of the liquid, and o is the surface tension of the liquid. Which equations are dimensionally homogeneous? 2:33 PM

solve using Buckingham-pi Theorem 8-19. The force of buoyancy F is a function of the volume +of a body and the specific weight y of the fluid. Determine how F is related to ť and y.

The table below shows the monthly cost of producing vintage model cars for collectors for quantities O, 100, 200, and 500. Complete the table by filling in the average fixed cost, average variable cost, and average total cost. Instructions: Round your answers to 2 decimal places. Average Fixed Cost (dollars) Average Variable Cost (dollars) Average Total Cost (dollars) Vintage Model Car Production Costs Total Fixed Total Variable Output Cost (dollars) Cost (dollars) 0 $1,500 $0 100 1,500 600 200 1,500 1,100 500 1,500 4,150 Total Cost (dollars) $1,500 2,100 2,600 5,650

Assume that in October 2022 the Schmidt Machinery Company (Exhibit 14.1) manufactured and sold 990 units for $705 each. During this month, the company incurred $415,800 total variable costs and $180,400 total fixed costs. The master budget data for the month are as given in Exhibit 14.1. Required: 1. Prepare a flexible budget for the production and sale of 990 units. 2. Compute for October 2022: a. The sales volume variance, in terms of operating income. Indicate whether this variance was favorable or unfavorable. b. The sales volume variance, in terms of contribution margin. Indicate whether this variance was favorable or unfavorable. 3. Compute for October 2022: a. The total flexible budget variance. Indicate whether this variance was favorable or unfavorable. b. The total variable cost flexible budget variance. Indicate whether this variance was favorable or unfavorable. c. The total fixed cost flexible budget variance. Indicate whether this variance was favorable or unfavorable. d. The selling price variance. Indicate whether this variance was favorable or unfavorable. Comparison of Actual and Budgeted Operating Income SCHMIDT MACHINERY COMPANY Analysis of Operating Income For October 2022 (1) Actual Operating Income (2) Master Budget (3) Variances Units 780 1,000 220 U* Sales $ 639,600 100% $ 800,000 100% Variable costs 350,950 55 450,000 56 $ 160,400 U 99,050 F** $ 61,350 U 10,650 U Contribution margin 45% 44% $ 288,650 160,650*** $ 350,000 150,000+ Fixed costs 25 19 Operating income $ 128,000 20% $ 200,000 25% $ 72,000 U *U denotes an unfavorable effect on operating income. **F denotes a favorable effect on operating income. ***Actual fixed factory overhead cost = $130,650; actual fixed selling and administrative costs = $30,000. Budgeted fixed factory overhead cost = $120,000; budgeted fixed selling and administrative costs = $30,000. Complete this question by entering your answers in the tabs below. Required 1 Required 2 Required 3 Prepare a flexible budget for the production and sale of 990 units. Units sold ales Fixed costs Variable costs Required 1 Required 2 > Complete this question by entering your answers in the tabs below. Required 1 Required 2 Required 3 Compute for October 2022: a. The sales volume variance, in terms of operating income. Indicate whether this variance was favorable or unfavorable. b. The sales volume variance, in terms of contribution margin. Indicate whether this variance was favorable or unfavorable. Show less A Sales Volume Variance Operating income Contribution margin < Required 1 Required 3 > Complete this question by entering your answers in the tabs below. Required 1 Required 2 Required 3 Compute for October 2022: a. The total flexible budget variance. Indicate whether this variance was favorable or unfavorable. b. The total variable cost flexible budget variance. Indicate whether this variance was favorable or unfavorable. c. The total fixed cost flexible budget variance. Indicate whether this variance was favorable or unfavorable. d. The selling price variance. Indicate whether this variance was favorable or unfavorable. Show less a. The total flexible budget variance b. The total variable cost flexible budget variance c. The total fixed cost flexible budget variance d. The selling price variance < Required 2 Required 3