** Using Calculus**

We have a client asking for our recommendations on which storage containers are better for shipping and storing hazardous waste. Their requirements are as follows: The container should hold 50,000 cm3 (which is 50 liters); The sides of the container will be made from aluminum sheets with a thickness of 2 mm; The two bases of the container need to be thicker (for greater support) and will be made from aluminum sheets with a thickness of 6 mm; There are two options to consider for the shape of the containers: Option 1: closed cylinders; Option 2: closed boxes with a square base (note the top and bottom are squares, but the sides could be rectangles). Some considerations to take into account: The fixed cost of production of a cylinder container is $10 per cylinder; The fixed cost of production of a box container is $4 per box; The current price for 2mm aluminum sheets is $0.011 per square centimeter. The current price for 6mm aluminum sheets is $0.045 per square centimeter; You need to advise the client on the dimensions of the containers that will both meet the size requirement and minimize cost. Based on the cost, you should make a recommendation to the client on whether square or cylinder containers should be used.

CHAPTER 7 Problem 4  Programmable Logic Controllers

Study the ladder logic program in Figure 7-41 and answer the questions that follow:

a. What type of timer has been programmed?

b. What is the length of the time-delay period?

c. What is the value of the accumulated time when power is first applied?

d. When does the timer start timing?

e. When does the timer stop timing and reset itself?

f. When input LS1 is first closed, which rungs are true and which are false?

g. When input LS1 is first closed, state the status (on or off) of each output.

h. When the timer’s accumulated value equals the preset value, which rungs are true and which are false?

i. When the timer’s accumulated value equals the preset value, state the status (on or off) of each output.

j. Suppose that rung 1 is true for 5 s and then power is lost. What will the accumulated value of the counter be when power is restored?

Figure 7-41 Ladder logic program for Problem.

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Experiment 3: Measure the Mass of Air

Took a 150 mL Erlenmeyer flask & a balance & placed them on the workbench.

Moved the flask onto the balance; the mass = 88.000 g

Closed the flask & attached a pressure gauge to the Erlenmeyer flask.

Weight of the closed Erlenmeyer flask = 88.179 g

Added 1.50 atm to the Erlenmeyer flask.

The pressure = 1.50 atm

The mass = 88.269 g

Added air to the Erlenmeyer flask to a pressure of 2.00 atm.

The pressure = 2.00 atm

The mass = 88.358 g

Added air to the Erlenmeyer flask to a pressure of 2.50 atm.

The pressure = 2.50 atm

The mass = 88.448 g

Added air to the Erlenmeyer flask to a pressure of 3.00 atm.

The pressure = 3.00 atm

The mass = 88.538   

How many moles of air were in the Erlenmeyer flask when the total air pressure was 2.00 atm?

A. 0.179 mol

B. 0.0124 mol

C. 0.00620 mol

D. 0.0155 mol

How many moles of air were in the Erlenmeyer flask when the total air pressure was 2.00 atm?

A. 0.179 mol

B. 0.0124 mol

C. 0.00620 mol

D. 0.0155 mol

Consider a vapor power cycle as shown below. Steam enters the first turbine stage at 12 MP a, 480 oC, and expands to 2 MP a. Some steam is extracted at 2 MP a and fed to the closed heater. The remainder expands through the second-stage turbine to 0.3 MP a, where an additional amount is extracted and fed into the open heater operating at 0.3 MP a. The steam expanding through the third-stage turbine enters the condenser at a pressure of 6 kP a and leaves the condenser as saturated liquid at 6 kP a. Liquid water leaves the closed heater at 210 oC, 12 MP a, and condensate exiting as saturated liquid at 2 MP a is trapped into the open heater. Saturated liquid at 0.3 MP a leaves the open heater. Assume all pumps and turbine stages operate isentropically. Determine for the cycle: (a) the heat transfer to the working fluid passing through the steam generator, in MW, (b) the heat transfer from the working fluid passing through the condenser, in MW, (c) the thermal efficiency (%), and (d) sketch a T ?s diagram for the entire cycle with labeled states, isobars, and process directions

Consider the following sum (which is in expanded form): 1−4 + 7−10 + 13−16 + 19−22 +···±(3n−2).

Note that this is slightly different from the previous sum in that every other term is negative.

(a) Write it as a summation (∑).

(b) Evaluate the sum for every integer n from 1 to 9. (Be careful - if you get this wrong, you will likely get the rest of this question wrong!)

(c) Write a closed-form formula for the value of the sum as a function of n. As in problem 1, do not use a "by cases" or piecewise definition (will need to write a single closed-form expression to receive full credit).(Hint 1: floor and ceiling functions may be useful here.)(Hint 2: try splitting up the sequence of partial sums into two subsequences, finding formulas foreach of the subsequences, then combining the formulas.)

(d) Prove that your formula from part (c) is correct using Mathematical Induction. (You may separateout the cases wherenis even/odd if you wish, but if so please do it as late as possible.)

i. State and prove the Base Case.

ii. State the Inductive Hypothesis.

iii. Show the Inductive Step

Please select all that are correct.

Select one or more:

a. If two trucks (same model) are driving with the same velocity, the empty truck has less momentum than the truck fully loaded with rubber ducks

b. Law of conservation of momentum only works in 1D and 2D, but no higher

c. A snowball is thrown on a wall. It bounces off, but leaves a white mark behind. This is neither a perfect elastic collision, nor a perfect inelastic collision

d. Halving the time the force is applied on an object doubles the impulse

e. When the law of conservation of momentum is concerned, a pile of sand cannot be used as a closed system because the grains of sand do not stick together and there are too many of them

f. If a cup of hot coffee is defined as a closed system, then the steam coming off the surface has to be accounted for as part of the system

g. Having a pie thrown on one's face is an example of an inelastic collision

h. Velocity, momentum, and impulse can all be expressed in terms of their x-, y-, and z- components

i. When two figure skaters (one going SouthEast, the other going NorthEast) clasp hands, they begin moving West before

The Down Towner is considering a project with a life of 4 years that will require $164,800 for fixed assets and $42,400 for net working capital. The fixed assets will be depreciated using the Year 2018 bonus depreciation method. At the end of the project, the fixed assets can be sold for $37,500 cash and the net working capital will return to its original level. The project is expected to generate annual sales of $195,000 and costs of $117,500. The tax rate is 24 percent and the required rate of return is 13 percent. What is the project's net present value? Multiple Choice $46,482.43 $42,316.67 $56,500.00 $59,488.87 $48,909.09

Water is flowing down through the pipe shown in the drawing. Point A is at the higher elevation, while B and C are at the same elevation. The cross-sectional areas are the same at A and B. Rank the pressures at the three points, largest first. C has a larger diameter than the other two.

Whether or not it is moral for the government to force businesses to shut down during the pandemic using utilitarianism.