A fisherman sets out upstream on a river. His small boat, powered by an outboard motor, travels at a constant speed v in still water. The water flows at a lower constant speed vw. The fisherman has traveled upstream for 2.00 km when his ice chest falls out of the boat. He notices that the chest is missing only after he has gone upstream for another15.0 min. At that point, he turns around and heads back downstream, all the time traveling at the same speed relative to the water. He catches up with the floating ice chest just as he returns to his starting point. How fast is the river flowing? Solve this problem in two ways. (a) First, use the Earth as a reference frame. With respect to the Earth, the boat travels upstream at speed v - vw and downstream at

v + vw. (b) A second much simpler and more elegant solution is obtained by using the water as the reference frame. This approach has important applications in many more complicated problems; examples are calculating the motion of rockets and satellites and analyzing the scattering of subatomic particles from massive targets.

In a galvanic cell, one half-cell consists of a lead strip dipped into a 1.00 M solution of Pb(NO₃)₂. In the second half-cell, solid neodymium is in contact with a 1.00 M solution of Nd(NO₃)₃. Pb is observed to plate out as the galvanic cell operates, and the initial cell voltage is measured to be 2.197 V at 25°C.


(a) Write balanced equations for the half-reactions at the anode and the cathode. Show electrons as e^-. Use the smallest integer coefficients possible and the pull-down boxes to indicate states. If a box is not needed, leave it blank.

Half-reaction at anode (do not multiply by factor):

Half-reaction at cathode (do not multiply by factor):

(b) Calculate the standard reduction potential of a Nd³⁺|Nd half-cell. The standard reduction potential of the Pb²⁺|Pb electrode is -0.126 V.

---------- V

Consider a simple electrical circuit where you charge a capacitor through a resistor by connecting a battery (closing the switch) at time t=0.

The charge Q on the capacitor is related to the current I by dQ/dt=I. Furthermore, by Kirchhoff’s law, V – RI – Vc =0, and the charge Q on the capacitor is Q=CVc, where C is the capacitance. That can be combined to give the differential equation

dQ/dt = V/R - Q/RC

The analytic solution is Q(t)=CV(1 – exp(-t/(RC)). Write a MATLAB code that solves the differentia equation with the Euler forward method, Predictor-Corrector method, and Runge Kutta 4th Order. Use values of 1F for the capacitor, 10 Ohm for the resistor, and 10 V for the battery. Run the code from 0 to 10 seconds. Use values for dt of 1.0, 0.1, and 0.01. For each of the runs calculate the percentage error at the end, and make a table of the errors. Discuss and submit the table and only the first plot for Euler/dt=1. Which dt and how many step do you need with each of the methods to achieve an accuracy of better than 0.01%?

V. S. Yogurt is considering two possible expansion plans. Proposal A involves opening 10 stores in northern California at a total cost of $3,150,000. Under another strategy, Proposal B, V. S. Yogurt would focus on southern California and open six stores for a total cost of $2,500,000. Selected data regarding the two proposals have been assembled by the controller of V. S. Yogurt as follows.

Required:
a. For each proposal, compute the following. Assume discounted at management's required rate of return of 15 percent. Use Exhibits 26-3 and 26-4 where necessary.

(1) Payback period
(2) Return on average investment
(3) Net present value
b. On the basis of your analysis in part a, state which proposal you would recommend.

1. How do apparent (ostensible) authority and actual authority differ? What effect does this have on a corporation’s liability?

See 7.18.  

In Freeman v Lockyer [1964] 2 QB 480 (upheld by the Australian High Court in Crabtree-Vickers Pty Ltd v Australian Direct Advertising & Addressing Co Pty Ltd (1975) 133 CLR 72), the difference between actual and ostensible authority was discussed:

• Actual authority is a legal relationship between the principal and an agent, created by an agreement between themselves, of which the contractor may be ignorant, although contractual rights and liabilities will be created between the principal and the contractor.

• Apparent or ostensible authority is a legal relationship between the principal and the contractor created by a representation made by the principal to the contractor, which is intended to be and is in fact acted on by the contractor, that the agent has the authority to enter into contracts on behalf of the principal. This then will render the principal liable to perform the obligations arising under the contract.

The company is liable in case of actual authority. It may also be liable in case of ostensible authority when three elements discussed in Freeman v Lockyer [1964] 2 QB 480 are present.

Consider the following capital budgeting and cash flow estimation problem. You have developed a new energy drink that uses various vegetables. The drink is called V-DRINK. You have an existing building that you are using to produce V-DRINK. The building is fully depreciated. You determine a need to buy $400,000 in equipment. Shipping and installation is an additional $50,000. Additionally you determine you will need to have $16,995 in inventory. What is the total initial outlay associated with the project?

The equipment cost (equipment plus shipping and installation) can be depreciated at the rate of 32% the first year. The remaining 5 years (years 2-6) the depreciation will be equal to $30,000 per year. What is the amount of depreciation in year 1?

Based on some market research you expect to sell around 200,000 bottles of V-Drink a year at wholesale price of $1.9. Operating costs (excluding depreciation) are expected to be 50% of revenue. The firms tax rate is 40%. What is the annual operating cash flow associated with this project in year 2. (Note you will need to factor in $30,000 in depreciation in year 2 from the prior question).

Suppose the straight-line distance between New York and San Francisco is 4.1 × 106 m (neglecting the curvature of the earth). A UFO is flying between these two cities at a speed of 0.68c relative to the earth. What do the voyagers aboard the UFO measure for this distance?

The total energy of an object is 7.86 × 10¹² J, and its kinetic energy is 6.00 × 10¹² J. What is the mass m of the object?

A radar antenna is rotating and makes one revolution every 25 s, as measured on earth. However, instruments on a spaceship moving with respect to the earth at a speed v measure that the antenna makes one revolution every 45 s. What is the ratio v/c of the speed v to the speed c of light in a vacuum?

As observed on earth, a certain type of bacteria is known to double in number every 24 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.932c relative to the earth. At a time when the earthbound culture has grown to 16 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer?

A transformer with rated power of 250 kVA and a secondary voltage of 230/400 V, 50 Hz, delivers energy to the following loads:
- 1 three-phase engine of nominal power 30 kW, 93% efficiency and power factor 0.9
- 90 lightning systems of 250 W each, rated voltage 230 V, and cos(phi)=0.6 (i), connected in a balanced manner
Consider a direct sequence and a reference of voltages V1=V∠0º
Find:
a) The true, reactive and apparent power provided by the transformer
b) The effective value of the current in each load
c) The phasors of the line currents provided by the transformer
d) The equivalent single phase circuit of the load
e) The reactive power and capacity (in wye and delta configurations) of a battery of capacitors so that we obtain a global power factor of 0.95 (i)
f) The new apparent power provided by the transformer after correcting the power factor
g) The effective value of the line currents if the transformer works at a power factor of 0.7 (i) in a balanced manner
h) The effective value of the line currents if the transformer works at a power factor of 1 in a balanced manner

A marketing survey looked at the preferences of hot drink size among 1275 random
customers of a coffee shop chain. The survey was also interested in whether the customer’s gender
affects their preference. The results of the survey were used to estimate the probabilities in this joint
probability distribution:
Tall (T) Grande (G) Venti (V)
Female (F) 0.12 0.24 0.06
Male (M)    0.08 0.38    0.12

a) What is p (M, T), the joint probability that a customer in the survey was both male and prefers tall
drinks?
b) What is p (F), the marginal probability that a customer in the survey was female?
c) What is p(G), the marginal probability that a customer in the survey prefers Grande drinks?
d) What is p (V | M), the conditional probability, given a customer in the survey was male, that he prefers
venti drinks?
e) What is p (F | V), the conditional probability, given a customer in the survey prefers venti drinks, that the customer was female?
f) There are two random variables in this situation, drink size and gender. Are they independent or dependent? Explain how you arrived at the answer and show your calculations.

In the same file, complete the following exercises in the author’s pseudocode as presented in the
text book and material on Blackboard in this chapter, and following all requirements for good
program design that were shown in Chapter 2 and all examples since then.

At the Summer Olympic Games every four years, for historical reasons, athletes represent
National Olympic Committees (NOCs) rather than strictly countries. For the sake of convenience
in our program, let us refer to them simply as “nations”. As of the 2016 Rio Olympics, then,
there were 206 nations eligible to participate in the Olympics. Write a program that could be
used to represent the medal table for the next Olympics that will be held in Tokyo in 2020. Since
we do not know how many nations will actually participate, our program will have to plan on
there being a maximum of 225 nations (in case some more NOCs are recognized before the 2020
Olympics), but must adapt to fewer nations actually being present. So, write a program that

1. Allows a user to enter
a. The names of the nations that are participating
b. The number of gold medals that nation has won
c. The number of silver medals it has won
d. The number of bronze medals it has won
e. “ZZZ” as the nation’s name to indicate that they have finished entering input

2. Outputs a list of sentences that describe each nation’s performance, e.g., for the 2016
Olympics, to describe the performance of the United States, this program would have
output “United States won 46 gold, 37 silver, and 38 bronze
medals, for a total of 121 medals” . Below this list, the program must
output the total number of gold medals awarded, silver medals awarded and bronze
medals awarded, and total of all medals awarded.

3. Scans for and outputs
a. The names of the nations with the most and least gold medals, along with their
gold medal counts, e.g., “United States won the most gold
medals: 46”
b. Similarly, the names of the nations with the most and least silver and bronze
medals respectively

4. Allows the user to enter the name of a nation that they want to search for, and if it finds
that nation, outputs a sentence in the format shown in #2 above.

All of the above must be done by applying the concepts and algorithms shown in Chapter 6, both
in the text book and in the material provided on Blackboard, and building on what we have
learned in all the chapters before this one.

The only data that this program stores is the names of the nations, and the matching counts of
gold, silver and bronze medals. All calculations and scanning for highest and lowest, etc., must
be done by the program after the user has entered the sentinel to indicate the end of their input.
All output sentences described above must be generated when they are required.

Book this is from is "Programming Logic and Design 8th Edition" by: Joyce Farrell. Must be written in pseudocode that resembles that in the book.

this is what I have so far. It probably isn't right, but it will at least give you some structure to follow. Any help is appreciated.

Start
   Declarations
       string EXIT = ZZZ
       NATION_CAPACITY = 225
       string NATION_NAME[NATION_CAPACITY]
       num goldMedals
       num silverMedals
       num bronzeMedals
       num totalMedals
       num count
       num nextNation
       num mostGold
       num leastGold
       num mostSilver
       num leastSilver
       num mostBronze
       num leastBronze

   output "Welcome to our Medal Tracker Program."
   output "This program will allow the user to enter the name of nations participating in the olympics, allow
       the user to enter the number of gold, silver, and bronze medals that nation has won."

   output "Please enter the name of the first nation (type ", ZZZ, " to stop): "
   input nextNation

   count = 0
  
   while nextNation <> ZZZ AND count < NATION_CAPACITY
       NATION_NAME[NATION_CAPACITY] = nextNation

       output "Please enter the amount of gold medals this nation has won: "
       input goldMedals[count]

       output "Please enter the amount of silver medals this nation has won: "
       input silverMedals[count]

       output "Please enter the amount of bronze medals this nation has won: "
       input bronzeMedals[count]

       count = count + 1

       output "Please enter the next nation or ", ZZZ, " to stop: "
       input nextCustomerID
   endwhile

   output "You entered data for ", count, " nations."

   totalMedals = goldMedals + silverMedals + bronzeMedals

   output "The nation ", nextNation, " won ", goldMedals, " gold medals, ", silverMedals, " silver medals, and ", bronzeMedals, "
       bronze medals, for a total of ", totalMedals, " medals.

   mostGold =