Consider a conflict between two armies of x and y soldiers, respectively. During World War I, F. W. Lanchester assumed that if both armies are fighting a conventional battle within sight of one another, the rate at whichsoldiers in one army are put out of action (killed or wounded) is proportional to the amount of fire the other army can concentrate on them, which is in turn proportional to the number of soldiers in the opposing army. ThusLanchester assumed that if there are no reinforcements and t represents time since the start of the battle, then x and y obey the differential equationsdxdt-ay,dydt-bz,where a and b are positive constants.Suppose that a = 0.04 and b = 0.01, and that the armies start with x (0) = 49 and y(0)=15 thousand soldiers. (Use units of thousands of soldiers for both x and y.)(a) Rewrite the system of equations as an equation for y as a function of x:dydx(b) Solve the differential equation you obtained in (a) to show that the equation of the phase trajectory is0.04y² -0.01x2=C,for some constant C. This equation is called Lanchester's square law. Given the initial conditions x (0) = 49 and y(0) = 15, what is C'?C =

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Answered: Consider a conflict between two armies…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1) Malaria is a disease that destroys red blood cells (the parasite invades red blood cells, multiplies, and then infects more red blood cells). In a recent study (Kotepul, et al., 2015) looking at various blood counts, the authors found the following results. Results are in billion red blood cells / cubic mm. Note that I have deliberately modified these results (do not use R): n ̄y s Low infection 527 4.16 2.23 High infection 157 4.51 2.34 Is there a difference in red blood cell count?(Hint: please think about this before you just start working on the problem!)
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆy=3−5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: When amount of schooling increases by one year, the number of pregnancies tends to decrease by 3. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 5. When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. When amount of schooling increases by one year, the number of pregnancies tends to increase by 3.
QUESTION 4 Question 7. (A BUSINESS NEEDS WISE PEOPLE) A saleswoman buys the five products say, bag, sunglass, watch, makeup set, and fountain pen from a supplier. Let x = 78, x2 = 25, x3 = 22, x4 = 40 and x5 =10 be the costs respectively. A saleswoman sets a profit of $3 after selling these five products combined. If she sold one item of each product, compute her total sale as: 5 Ex; +3 i=1 QUESTION 5 Question 5.
Tim Smunt has been asked to evaluate two machines. After some investigation, he determines that they have the costs shown in the following table: Machine A Machine B Original Cost $12,000 $20,000 Labor per year $2,400 $4,400 Maintenance per year $4,000 $1,200 Salvage value $1,600 $7,500 He is told to assume that: 1. The life of each machine is 33 years. 2. The company thinks it knows how to make 88% on investments no more risky than this one. 3. Labor and maintenance are paid at the end of the year. 1. What is the NPV Value of Machine A? 2. Calculate the NPV for Machine B 3. Using the net present value as the basis of comparing the machines, Tim should recommend Machine A or B?
2. Bombardier Aerospace is the third largest airplane manufacturer in the world and has its main headquarters in Dorval, Québec. The Dash 8 series of turboprop airliners are built by Bombardier and are designed to need very short takeoff and landing strips. Suppose that a Dash 8 airplane is travelling from Edmonton to Kelowna, a trip of about 600 km (by air), at a speed of 450 km/h. Let w represent the speed of the wind, in kilometres per hour, where w is positive for a tailwind and negative for a headwind, and t represent the time, in hours, it takes to fly. The equation that represents t as a function of w is as follows: t = 500 w+ 400
I was really confused on calculating r, but if two other questions could also be answered in this problem, it would be the most help.
Table 3-4 Assume that Andrea and Paul can switch between producing wheat and producing beef at a constant rate. Minutes Needed to Make 1 Bushel of Wheat Pound of Beef 15 Andrea 30 Paul 15 5 efer to Table 3-4. Which of the following combinations of wheat and beef could Andrea produce in one 8-hour day? O a. 16 bushels of wheat and 32 pounds of beef O b. 9 bushels of wheat and 25 pounds of beef O c. 7 bushels of wheat and 15 pounds of beef O d. 10 bushels of wheat and 13 pounds of beef
In any city at any time, some of the stock of usable office space is vacant. This vacant office space is unemployed capital. How would you explain this phenomenon? In particular, which explanation regarding unemployed labor applies best to unemployed capital? Owners of office buildings seek firms to lease their available space, just like prospective employees seek firms to hire their labor. The rate of office separation would be the fraction of occupied office space that is vacated each month. The rate of office finding would be the fraction of vacant office space that is leased each month. Let u be the "natural rate of office vacancy." Use these concepts to answer the following questions. 4 a. If s is the rate of office separation, then 1/s is the average spell of b. If f is the rate of office finding, then 1/fis the average spell of c. The natural rate of office vacancy (u) will increase when
1. Two well-mixed tanks are hooked up so that water with 2 pounds of salt per gallon flows into the first tank, well - mixed water flows out of the second tank, water flows from the first tank to the second tank, and water flows from the second tank to the first tank. All flows are constant. Determine how much water is in each of the two tanks, given if x is the amount of salt in the first tank and y is the amount of salt in the second tank then 3x = -x + y + 30 and 6y' 2x - 3y. The answer should be 45 gallons in the first tank and 30 gallons in the second tank. =

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