We will compare the rigorous method results with the values from the short cut methods. The rigorous method is based on an equation of state like the Soave-Redlich-Kwong SRK for calculating the required enthalpies and entropies. The enthalpies and entropies are used to determine the power requirement and the discharge temperatures. The results indicate that the accuracy of the shortcut method is sensitive to the value of heat capacity ratio, k.

Questions Eliciting Thinking Can you reread the first sentence of the second problem? A difference is described between two values. What are these two values?

What is the difference? Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?

Instructional Implications Model using absolute value to represent differences between two numbers. For example, represent the difference between x and 12 as x — 12 or 12 — x.

Emphasize that each expression simply means the difference between x and Evaluate the expression x — 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and Guide the student to write an equation to represent the relationship described in the second problem.

Ask the student to solve the equation and provide feedback. Then explain why the equation the student originally wrote does not model the relationship described in the problem.

Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i. Provide additional opportunities for the student to write and solve absolute value equations.

Examples of Student Work at this Level The student: Finds only one of the solutions of the first equation. Writes the solutions of the first equation using absolute value symbols.

Questions Eliciting Thinking How many solutions can an absolute value equation have? Do you think you found all of the solutions of the first equation? What are the solutions of the first equation? Should you use absolute value symbols to show the solutions?In this section we solve linear first order differential equations, i.e.

differential equations in the form y' + p(t) y = g(t). We give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process.

Free absolute value equation calculator - solve absolute value equations with all the steps. Type in any equation to get the solution, steps and graph Absolute Value Equation Calculator Solve absolute value equations step-by-step.

Equations. Basic (Linear) High School Math Solutions – Absolute Value Equation Calculator. (We will discuss projectile motion using parametric equations here in the Parametric Equations section.). Note that the independent variable represents time, not distance; sometimes parabolas represent the distance on the \(x\)-axis and the height on the \(y\)-axis, and the shapes are ph-vs.com versus distance would be the path or trajectory of the bouquet, as in the following problem.

How to Write an Absolute-Value Equation That Has Given Solutions By Chris Deziel; Updated April 25, You can denote absolute value by a pair of vertical lines bracketing the number in question. What's New at MMM Calculus Acrostic Our subscription fo r the year is an acrostic game.

In /, we did a crossword puzzle game that gave students typical AP free response questions. Section The Heat Equation. Before we get into actually solving partial differential equations and before we even start discussing the method of separation of variables we want to spend a little bit of time talking about the two main partial differential equations that we’ll be solving later on in the chapter.

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How to write an absolute value equation with given solutions