Problem 70 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed a nonlinear system that modeled the orbits of Earth and Mars, and the graphs indicated the system had a solution with a real ordered pair.

Step-by-Step Solution

Answer

The statement does not make sense because it suggests that there is a common point in the orbits of Earth and Mars, which is not possible as each planet moves in its own distinct path around the Sun.

Step 1: Determine the situation

The situation describes that a nonlinear system has been graphed to represent the orbits of Earth and Mars. The term 'nonlinear system' is used to describe equations or systems of equations that are not considered linear. These could include equations representing orbits of planets, which are often elliptical and hence, are nonlinear.

Step 2: Understand the statement

The statement talks about a real ordered pair solution. In a graph, an ordered pair is used to represent a point on the plane. In this case, an ordered pair would likely represent a coordinate point where the two orbits intersect. This would mean, theoretically, that there is a point in space where the orbits of Earth and Mars intersect.

Step 3: Analyze the sense of the statement

It is known that orbits of different planets do not intersect in the real world. Because each planet has its own path around the sun and these paths do not coincide with one another. So, it doesn't make sense when we say that there exists an ordered pair (a point) where the orbits of Earth and Mars intersect.