Water flows in a little tank, which has a leak. At the moment t=0 the tank is empty. The volume of the tank is Vcm3 at the moment (t) minutes. Water flows in the tank at a flow of 80m3 per minute. Due to the leak water leak out of the tank with a flow of kV cm3 per minute where k is a positive constant. (i) By using a differential equation show that: V=1/k (A-Ae-kt) where A is a real positive a to be determinate. (ii) Determinate the value of k when t=15 and V=500

Q: According to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is…

A: Given , The current pollutants is Po=25 pu Quadruple for every 9.5 years so, Q=9.5 Using the formula…

Q: dy Solve for the value of C in the equation: (1-2x)dx when y(0) - 1 3y3 3

A:

Q: The human population of a small island satisfies the logistic law with k = 0.04, λ = 2(10)^-7, and…

A: Given that k=0.04 which is the growth rate and λ=2×10-7 which is same as 1M where M is the carrying…

Q: 1. The fuel efficiency of vehicles depends on engine revolutions per minute (rpm = x)) and usually…

A:

Q: A biologist noticed that a small forest has a population of deer that naturally grows according to…

A: For part-1: The biologist noticed the logistic model to be y'=0.0005y300-y where y is the number of…

Q: dt' Population growth is commonly modeled upon the simple statement that the popu- lation growth…

A:

Q: nce. For this model we will take the tion due to gravity to be -9.81 is is given by mass times e…

A:

Q: dy/dt + 2y = e^(4t). Using the guessing method because 2 is constant. I need help solving this…

A: Solution of the first order differential equations

Q: A 120-gallon tank initially contains 90 lbs of salt dissolved in 90 gallons of water. Brine…

A:

Q: y' = y*.x* Find a general solution. find the custom solution so that y(2) = 1.

A: We have to find General and Custom solution of given differential equation.

Q: A body was found at 10 a.m. in a warehouse where the temperature was 40 degrees * F . The medical…

A:

Q: Please Solve Using Differential Equation Thank you!

A: Answer:The rate at which the radius of the raindrop is changing when it has a radius of 10 mm and is…

Q: Solve the differential equation: f"(x) =x', f(0) = 3, f'(0)=6

A:

Q: Please use Differential equation or intergral equation to solve thanks

A: written solution provided.Explanation:Step 1:Step 2: Step 3: Step 4:

Q: The population of a virus in a host can be modeled by the function W that satisfies the differential…

A: Note:-Since you asked multiple questions which are not interlinked, according to our policy we can…

Q: Consider the function y=4e^rx+7 where r is some real number. If y satisfies the differential…

A: In this question we have to find the value of r.

Q: The population of a town grows at a rate of r(t)=300.e^0.3t people per year, (where t is time in…

A:

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.