University of Phoenix Material

Critical Thinking Worksheet

In the following exercises, determine whether each statement “makes sense” or “does not make sense” and explain your reasoning in 50 to 100 words for each answer.

1. I’m using an inverse variation equation and I need to determine the value of the dependent variable when the independent variable is zero.

The rational expression is undefined at any value that produces a denominator of zero, because of this this statement does not make sense because if a variable in a rational expression is replaced by a number causing the denominator to be zero, the number should be not be a replacement.

2. The graph of this direct variation equation has a positive constant of variation and shows one variable increasing as the other variable decreases.

This makes sense to me because a positive constant remains the same so that number would not change. The continuing variation would be the result of corresponding values of the variables, or contents would multiple by which the variable multiplied. The numbers would not go up or down because it never changes. The only way for the numbers to move would be if there was a changeable variable.

3. When all is said and done, it seems to me that direct variable equations are special kinds of linear equations and inverse variation equations are special kinds of rational equations.

This makes sense because, inverse equations, rational equations, direct variable and linear equations all have the same definitions.

4. Using the language of variation, I can now state the formula for the area of a trapezoid, A = 1/2h(b1 + b2), as, “A trapezoid’s area varies jointly with its height and the sum of its bases.”

This makes sense because b1+b2+=average times the ½ height and can be used to find the trapezoid area.

5. In a hurricane, the wind pressure varies directly as the square of the wind velocity. If...