Answer the following as detailed as possible. 2. The tank shown below contains 80 lbs of salt dissolved in 500 gal of water. The inflow per minute is 20 Ib of salt dissolved in 20 gal of water. The outflow is 20 gal/min of the uniform mixture. Find the time when the salt content y(t) in the tank reaches 95% of its limiting value (as t → co ).

Q: Consider an initial mass M(0) of 14C at time t=0. Answer in the following order (1, 2, 3): 1. How…

A: For the solution of the problem follow the next steps.

Q: An insulated uniform metal rod, 40 cm long, has the temperature of its ends maintained at 0°C for…

A: In this,we cam find the expression for the temperature using given initial temperature distribution.

Q: Suppose a 1000 L tank contains 100 L of fresh water at time t = 0. At that time, a salt water…

A: The rate of change of a substance in a container is determined by the concentrations as well as the…

Q: Solve the following I.V.P by introducing integrating factor on the process of your calculation: xy…

A: Step to solve the linear differential equation: -  Step No. 1: Simplify the differential equation by…

Q: 2tds + s(2 + s²t)dt = 0

A:

Q: Determine whether the following equation are separable. If so, solve the initial value problem.

A: The given equation is Simplify it It implies that the given equation is separable.

Q: Assuming the most general solution, solve the one dimensional heat E. equation u, = c²u in a…

A:

Q: The number of fish, P, in a lake with an initial population of 10,00 dP = kP – r. dt satisfies, for…

A: To determine the value of r so that the population of fish remains constant.

Q: Determine whether the following equation are separable. If so, solve the initial value problem.

A:

Q: A 5-kg mass is attached to a spring with a spring constant of k = 20 N/m. The mass is set in motior…

A: A 5-kg Mass is Attached To A Spring With A Spring Constant of K From The Equilibrium Position With…

Q: Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0,…

A:

Q: 4. Calculate the concentrations of H" in the pure water solution with pH = 6.90. A. 1.10 x 10 M B.…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: a) Derive the system of differential equations and initial conditions representing this system. b)…

A: Given

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ TACHY 1. (D³ - 5D² + 3D + 9)y = 0 2 (D3 D2 1

A:

Q: A spring with spring constant k = 0.6 N/m has an equilibrium length of 1.7 m. How much work is…

A: To determine the energy stored in the spring.

Q: The temperature distribution of a long, thin aluminium rod with a length of 12 cm can be determined…

A: The heat equation k∂2u∂x2=∂u∂t---1 is given with k=0.835cm2s-1, ∆x=2cm, ∆t=0.1s, t≥0. The B.C's are…

Q: Use finite difference method to solve the heat equation with K = 1 for a 1-meter thin rod with…

A: We use the method suggested finite difference.

Q: For the following stirred tank reactions, carry out the following analysis.a. Write an initial value…

A:

Q: Consider the IVP y'= -y + t + 1 with y(0) = 1, for t e [0, 5]. What is the corresponding Lipschitz…

A:

Q: A 16-lb weight is attached to the lower end of a coil spring sus-pended from the ceiling and having…

A:

Q: 2. Analyse the following equations graphically: x = ex COS X (i) x = 1 - cos 2x (ii) Find all the…

A: 2. Given equations are: (i) x.=ex-cosx (ii) x.=1-cos2x   To Find: All equilibrium points, and…

Q: Find the temperature u(x.1) from the heat equation in a laterally insulated copper bar 80cm cm long…

A:

Q: Find the maximum possible temperature of an ideal gas undergoing the process p=p0e−βV, where β is a…

A: The given function is where p is the pressure ,β is a positive constant and V is the molar volume…

Q: A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming…

A: Given m(t)=m0-kt and the differential equation as…

Q: Solve the following initial value problem. = - 4cos(2t + x), s'(0) = 300, s(0) = 0 dt? (Type an…

A:

Q: b) Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80 cm long…

A: Given a=80 cm, c2=1.158cm2/sec Thermal conductivity N copper 1c=0.95 col…

Q: Answer parts (a) and (b) using the inhibited growth model dP = k(L-P). Let L= 5000, and assume that…

A: Given that                                  dPdt=k(L-P) where L = 5000, P passes through (19, 450)…

Q: 8. If y = xi, then the value of the differential dy as x changes from 16 to is (A) * (B) 5 (c) (D)…

A:

Q: A rocket, fired from rest at time t=0, has an initial mass of m0 (including its fuel). Assuming that…

A: Let m(t) and v(t) be the mass and velocity of the rocket at time t. If m0 is the initial mass at…

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: Q1 – Find dy / dx for the following functions : e0 -2 2.8ln2 Y= 4 6 * sinh 9x * Inxy sino log2 2 Q2-…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: A 24-lb weight is attached to the lower end of a coil spring suspended from the ceiling and having a…

A: If weight of mass m is attached to a spring with spring constant k and damping constant β then by…

Q: The position x(t) of an object of mass m that is attached to a vertical spring with constant of…

A: The main objective is to solve the IVP by using higher order linear differential equations…

Q: The velocity dx/dt of a chemical reaction is proportional to (a-x), where x is the amount…

A: Solution :-

Q: Consider the IVP y'= -y + t + 1 with y(0) = 1, for t e [0, 5]. What is the corresponding Lipschitz…

A:

Q: 4. Solve the following initial value problems. dz (a) dt cost z(0) = 1 %3D

A: Note : "As per our guidelines we will solve only first question . If you want any specific question…

Q: Solve the following initial-value problem by using integrating factors: x?y' + xy = 1, x> 0, y(1)=2

A:

Q: A spring with spring constant k = 5 N/m has an equilibrium length of 0.8 m. How much work is…

A: Given that k= 5 N/m So, F(x)=kx=5x We will have to stretch the spring (1.1-0.8)=0.3 m from its…

Q: A 5.40 mol sample of solid A was placed in a sealed 1.00 L container and allowed to decompose into…

A: Given: A 5.40 mol sample of solid A was placed in a sealed 1.00 L container and allowed to decompose…

Q: Determine whether the following equation are separable. If so, solve the initial value problem. (sec…

A: The differential equation is given as, (sec t)y '(t) = 1, y(0) = 1 Simplify the equation,…

Q: A 5,000-liter tank initially contains 1,100 liters of water with 1.2- kg of salt dissolved in it.…

A:

Q: Given the initial condition y(0) = 5, find the particular solution of the equation e'y' – 4x = 0.…

A:

Q: A 1500 gallon tank initially contains 600 gallons of water with 5 lbs of salt dissolved in it. Water…

A:

Q: Consider the initial value problem, y" + y' – 6y = 0, y(0) = 10, y'(0) = 0 Determine the value of…

A:

Q: For the following stirred tank​ reaction, carry out the following analysis.   a. Write an initial…

A: a. Given that, the volume of the tank is 400L, the concentration of copper sulfate is 25g/L and the…

Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration