What is a mixing problem?

What is a mixing problem?

Mixing problems are an application of separable differential equations. They’re word problems that require us to create a separable differential equation based on the concentration of a substance in a tank. Usually we’ll have a substance like salt that’s being added to a tank of water at a specific rate.

What are mixture problems math?

Mixture problems involve combining two or more things and determining some characteristic of either the ingredients or the resulting mixture. For example, we might want to know how much water to add to dilute a saline solution, or we might want to determine the percentage of concentrate in a jug of orange juice.

What can differential equations model?

Differential equation models are used in many fields of applied physical science to describe the dynamic aspects of systems. The typical dynamic variable is time, and if it is the only dynamic variable, the analysis will be based on an ordinary differential equation (ODE) model.

What are 10 examples of mixtures?

Here are more examples of mixtures as they relate to one of American’s favorite pastimes: eating.

  • Oil and water.
  • Lemon juice and tea.
  • Honey and tea.
  • Milk and chocolate.
  • Coffee and cream.
  • Cream and sugar.
  • Flour and butter.
  • Cereal and milk.

What is mixture in algebra?

Mixture problems are ones in which two different solutions are mixed together, resulting in a new, final solution. Using a table will help to set up and solve these problems.

What is a differential equation in calculus?

Definition: differential equation. A differential equation is an equation involving an unknown function y=f(x) and one or more of its derivatives. A solution to a differential equation is a function y=f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation.

What is a mixing problem in chemistry?

Mixing Problems A typical mixing problem deals with the amount of salt in a mixing tank. Salt and water enter the tank at a certain rate, are mixed with what is already in the tank, and the mixture leaves at a certain rate. We want to write a differential equation to model the situation, and then solve it.

What is a mixing problem in aquariums?

Mixing Problems A typical mixing problem deals with the amount of salt in a mixing tank. Salt and water enter the tank at a certain rate, are mixed with what is already in the tank, and the mixture leaves at a certain rate.

How to construct a tractable mathematical model for mixing problems?

To construct a tractable mathematical model for mixing problems we assume in our examples (and most exercises) that the mixture is stirred instantly so that the salt is always uniformly distributed throughout the mixture.