Suppose we have 3 motors that need to be operated for (x) number of hours the present worth is already calculated in terms of (x): PWI= 2800 • 0.53X PW2= 4000+ 0.41X PW3= 2500 + 0.66X 12000 10000 8000 6000 PW1-2800 +0.534X 4000 -PW2-4000 +0.411IX 2000 -PW3-2500 + 0.66Xx hours What will be the range over which motor 3 is preferred over motor 12 0000t 0008 0009 000 0002

Q: The population, P, of the city of Hazelton has grown according to the mathematical model P =…

A:

Q: 20. In "x" years from now, one investment plan will be generating profit at the rate of R₁ (x) = 50+…

A: Given: R1x=50+x2R2x=200+5x

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A:

Q: The volume of fluid in an IV (intravenous) drop decreases according to the mathematical model…

A: The  given model of the volume of fluid in IV drop versus time is:   V=-0.110t+1   Where, V is the…

Q: It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in…

A:

Q: A tank initially holds 245 liters of brine solution containing 25 Ibm (pound mass) of salt. At t =…

A: Initial amount in tank = 245 liters, in which 25lb Fresh water is poured into @ 7g/m. Well stirred…

Q: Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20 grams…

A:

Q: At what rate in cubic centimeters per minute is the volume increasing at this instant?

A:

Q: A population of mosquitoes increases at a daily rate of 1/2 times the current population. You can…

A: Given that A population of mosquitoes increases at a daily rate of 1/2 times the current population.…

Q: A 50 – gallon tank of pure water has a brine mixture with concentration of 2 pounds per gallon…

A: Form the first order differential equation then find its solution to get amount of salt at any time…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: The population of a bacteria culture grows at a rate of P = 100(2)n, where P is the population and n…

A:

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A: Using the similarity of triangles.

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

Q: e company wishes to produce both products, but not at equal portions. 60% X’s and 40% Y’s is desired…

A: Given that the company wishes to produce both products, but not in equal portions. 60% X’s and 40%…

Q: Suppose, the scientists working in the north pole want to grow vegetables to meet their own demand.…

A: MatLab Code: %Open-Loop systems = tf('s');Gs = 0.39s+1.5; %Open-Loop system responsedisp('Open-loop…

Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres…

A:

Q: The half-life of polonium is 139 days, but your sample will not be useful to you after 95% of the…

A:

Q: nitially, there were 100 milligrams of a radioactive substance. After six hours, the mass decreased…

A: initially there are 100 milligrams of a radioactive substance. P=100 mg after 6 hour the mass…

Q: Lake Taal has a volume of 458 cubic km, and its rate of inflow and outflov are both 175 cubic…

A:

Q: A lake has a water volume of 450 km³ and a flow rate (in and out) of 175 km³ per year. If at some…

A: The rate of change in pollution equals the product of the flow rate and pollution change. Therefore…

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A:

Q: When it comes to bacteria growing by binary fission, its generation time will be the time interval…

A: Given,              G=t3.3 logbB; G= generation time  t=  time interval in hours or minutes b=…

Q: In an extraction unit operating with continuous and counter current, 100 kg of kerosene-nicotine…

A:

Q: Element X is a radioactive isotope such that every 4 years, its mass decreases by half. Given that…

A:

Q: Here is a new twist on the question. Suppose we want to cool our hot coffee to 100 °F as quickly as…

A: Given:T(t) = A + (To-A)e-ktA = 72°Fk = 0.125To=170°F HenceT(t) = 72 + 170-72e-0.125tT(t) = 72 +…

Q: The total cost in pesos of producing x pools of low voltage cable is given by C = 0.002 x - 05 x2 50…

A:

Q: Tank A contains 499 litres of brine holding 192 N of dissolved salt, and tank B contains 499 litres…

A:

Q: Suppose that a healthy population of some species is growing in a limited environment and that the…

A: Given, M0 is initial carrying capacity P0 is initial population M1 is carrying capacity after…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: Provide the exact solution of the initial value problemx''  = -x; x(0) = 0,  x'(0) = 1

A:

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: Given that  C = 0.001x3 + 3x + 432  To Find the number of units x that produces the minimum average…

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A:

Q: 3. Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20…

A:

Q: 2. It takes a car salesman 2.5 hours to drive from one city to another if he drives at a constant…

A: We know that , distance = velocity×Time

Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

A:

Q: The​ half-life of polonium is 139​ days, but your sample will not be useful to you after 91​%of the…

A:

Q: It is estimated that t months from now, the population of a certain town will be changing at the…

A: This question is related to population growth, We will solve it using integration.

Q: A bacterial colony is rapidly expanding. It has 10 bacteria at time t=0 and 2000 bacteria at time…

A: As per our guidelines we only solve first question and rest of the question will be reposted.

Q: Two tanks are connected as in Figure Q2b. Tank 1 initially contains 20 kilograms of salt dissolved…

A: Here we will use differential equation to solve this problem

Q: The population of a bacteria increases at a rate proportional to the present number of bacteria ‘P0’…

A: Given problem is : The population of a bacteria increases at a rate proportional to the present…

Q: 4. One bucket starts at noon with two liters of water, and water is gradually leaking out at a rate…

A: As per our guidelines I am solving only first problem please repost other question.     For first…

Q: Some initial value problems do not have unique solutions صواب ihi

A: Yes statement is true: y(t)=0 for t∈[0,1] and y(t)=(t−1)^2 for t≥1.

Q: A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

Q: 2) Solve the following initial value problem using the method of variation of parameters Yo = 2.

A:

Q: During the Covid-19 pandemic, the number of people that are infected at any time increases at a rate…

A: Solved below

Q: 2. Solve x3 + x² – 1 = 0, correct to three decimal places by using fixed point | iteration method.

A: Given: x3+x2-1=0

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.