Brine containing 1.5lb/gal of salt enters a tank at the rate of 2gal/min and the mixture well stirred leaves at the same rate. The tank initially contains 100 gal of brine with10 lbs of dissolved salt. When will the amount of salt in the tank be 20 lbs?

Brine containing 1.5lb/gal of salt enters a tank at the rate of 2gal/min and the mixture well stirred leaves at the same rate. The tank initially contains 100 gal of brine with10 lbs of dissolved salt. When will the amount of salt in the tank be 20 lbs?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: The differential equation y2(1+(y')2)=x+yy' is given.Find the general solution and Singular solution…

A: Solve, as follows:

Q: 8. A tank initially contains 500 L of pure water. Two streams of brine enter the tank: one with a…

Q: The indicated function y1(x) is a solution of the given differential equation. Use reduction of…

Q: 4. General solutions of differential equations (x² + y² +x)dx + xy dy = 0 is..

Q: 5. In previous problems dealing with two species, one of the animals was the predator and the other…

A: (b) we have given the system A dxdt =-5x+2xydydt =-4y+3xy we have to determine all the equilibrium…

Q: (b) Consider the second-order differential equation: x" + 3x² + 4x = t² +3e¹ Using the method of…

A: The given second-order differential equation is- x''+3x'+4x=t2+3et To rewrite this equation as a…

Q: Find the differential equation whose solutions correspond to the following equation a. cx2 + x+ y2 =…

Q: (a) Which system of differential equations describes a situation where the two species compete and…

A: please comment if you need any clarification. If you find my answer useful please put thumbs…

Q: 2. A climbing vine is taking over the side of a building. At first the vine only covered 10% of the…

A: Introduction: A differential equation has one or more equilibrium points. The equilibrium points are…

Q: A. y"- 3y' + 2y = 0 B. y" + 2y' + 2y = 0 C. y" + 4y = 0 D. y" + 2y' + y = 0 Table 1: A-D are…

A: A y''-3y'+2y=0 its C.F m2-3m+2=0m2-2m-m+2=0(m-1)(m-2)=0m=1,2then solution is y(x)=aex+be2xthe graph…

Q: Find the general solution of the differential equation x2y'-2lnx-e2y+4(l

A: Given: x2y'-2lnx-e2y+4(lnx)x=0 ⇒y'-2lnxx2-e2y+4(lnx)xx2=0⇒y'=2lnxx2+e2y+4(lnx)xx2 .....(i) Let…

Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

Q: How do I prove the answer algebraicly?

A: Given the differential equation:

Q: 1) Match each differential equation with a solution. You must use each solution once and only once.…

A: Given, the differential equations, we have to match these DE with solutions.

Q: 5- in the differential equation a) Normal point Then x = 0 is x*(x − 3) ý + (3x +2)ỷ+x*y=0 b) single…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Solve differential equations 1. y - xy = 0; M(1,1). - 2. y4y² = 1; M(1,0). 3. y 4. yy ry³ = 0;…

Q: Solve the differential equation: (1-x)y'=y^2 * O y Inlc(1-x)|=1 O y^2 In/c(1-x)|+1 O Inlc(1-x)|=y^2…

A: To solve the given differential equation

Q: Determine the solution of the following differential equations: 2. ((D^2) − 2D − 3)y = 0; when x =…

A: The given differential equation is (D2-2D-3)y = 0 with y(0) = 4 and y'(0) = -4

Q: 3) Find the solutions to the Differential Equation. Determine if the solutions are Linearly…

A: SEE BELOW THE SOLUTION

Q: 4. Consider the differential equation: y'+y+x 0 (a) Is the differential equation separable? If yes,…

A: As you asked more than one Question, only first question is solved. For other solution please…

Q: general solution of the differential equation y^2 y' = 2e^x b ) particular solution (if it exists)…

Q: Problem 4. Consider the autonomous differential equation x' = sin x. a. Does the differential…

A: '

Q: 1) Find the general solution to the differential equation. (6 + x)y' = (x + 7)(y − 6) y =

Q: 2. Single-Tank Mixing a) Write an initial value problem to model the following situation: A tank…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: 4 Given the differential equation xy" +3y' –-y=0. a) First convert the equation to a Cauchy-Euler…

A: Given differential equation xy''+3y'−4xy=0 (a) we have to convert the equation to a Cauchy Euler…

Q: 2. A climbing vine is taking over the side of a building. At first the vine only covered 10% of the…

A: Proportionality is the comparison between two numbers. Two numbers can be directly or inversely…

Q: Given the differential equation y''-y=x and using variation of parameters: a. What is the…

A: Use differential equation rules

Q: (a) What can you say about a solution of the equation y' = -y2 just by looking at the differential…

Q: find serious solution of differential equation (x+3)^2y''-9(x+3)y'+25y=0

Q: one solution of the differential equation is given. Find the general solution. 3y3 -2y"+12y'-8y = 0;…

A: 3y3 -2y"+12y'-8y = 0; Auxiliary equation will be: 3m3 - 2m2 + 12m - 8 = 0 The general solution will…

Q: Determine the solution of the following differential equations: 1. ((4D^4) − (8D^3) − (7D^2) + 11D…

Q: Find the General/ Particular Solution of the Given differential Equation. y '−(4 x− y+1)²=0

A: we have to find general /particular solution of given differential equation.

Q: 2. xydx + (y/x² + y² – x²)dy = 0

Q: If we use the method of variation of parameters, the particular solution of the following…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: Solution :∴ y''-y =0 , y(o)= 0, y'(0)=1given family of solution is y = C1ex+C2e-x

Q: Solve the elementary applications of Differential equation: 1. Suppose that the quantity of a…

A: 1. Suppose that the quantity of a radioactive substance originally weighing Xo grams decomposes at a…

Q: A solution containing 2lb of salt per gal starts to flow into a tank of 50 gal of pure water at a…

A: Given that, A solution containing 2lb of salt per gal starts to flow into a tank of 50 gal of pure…

Q: 2. Solve the simultaneous systems of differential equations: x', = 3e" y', = x +y

A: Given: A system of differential equations, x'=3e-ty'=x+y To find: Solution of given system of…

Q: Find the general solution to the differential equation. (4 + x)y' = (x + 5)(y − 4) y =

Q: One solution of the differential equation is given. Find the general solution. 4x y(3). + 2y" + 10y'…

Q: Module 4 Obtain the solution of the following differential equation. 1. y((x^2)+(y^2) - 1)dx +…

A: By inspection, solve by making exact form.

Q: 8. A vibrating string without damping can be modelled by the differential equation my" + ky = 0. a.…

Q: 12. Given the differential equation x dx = 0 and one solution y₁ = A (constant), use reduction of…

Q: Which system of differential equations describes a situation where the two species compete and which…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (a). If you…

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

Q: the 3rd-order differential equation y'''-3y''+2y'=3cos^2 2x using the Method of variation of…

Q: Two different concentrations of a solution are separated by a membrane through which the solute can…

A: Note:- In given problem, some signs are missing in given equation. So, please check equation i'm…

Q: 9. It turns out that finding explicit solutions for H(t) and L(t) for a system of equations like…

Question

4. )Applications of Differential Equations

4. Brine containing 1.5lb/gal of salt enters a tank at the rate of 2gal/min and the mixture well stirred leaves at the same rate. The tank initially contains 100 gal of brine with10 lbs of dissolved salt. When will the amount of salt in the tank be 20 lbs?

Expert Solution