Now that we have learned to graph nonlinear inequalities, we can learn how to graph systems of nonlinear inequalities. A
system of nonlinear inequalities is a system of two or more inequalities in two or more variables containing at least one inequality that is not linear. Graphing a system of nonlinear inequalities is similar to graphing a system of linear inequalities. The difference is that our graph may result in more shaded regions that represent a solution than we find in a system of linear inequalities. The solution to a nonlinear system of inequalities is the region of the graph where the shaded regions of the graph of each inequality overlap, or where the regions intersect, called the
feasible region .
Given a system of nonlinear inequalities, sketch a graph.
Find the intersection points by solving the corresponding system of nonlinear equations.
Graph the nonlinear equations.
Find the shaded regions of each inequality.
Identify the feasible region as the intersection of the shaded regions of each inequality or the set of points common to each inequality.
Graphing a system of inequalities
Graph the given system of inequalities.
These two equations are clearly parabolas. We can find the points of intersection by the elimination process: Add both equations and the variable
will be eliminated. Then we solve for
Substitute the
x -values into one of the equations and solve for
The two points of intersection are
and
Notice that the equations can be rewritten as follows.
Graph each inequality. See
[link] . The feasible region is the region between the two equations bounded by
on the top and
on the bottom.
There are three possible types of solutions to a system of equations representing a line and a parabola: (1) no solution, the line does not intersect the parabola; (2) one solution, the line is tangent to the parabola; and (3) two solutions, the line intersects the parabola in two points. See
[link] .
There are three possible types of solutions to a system of equations representing a circle and a line: (1) no solution, the line does not intersect the circle; (2) one solution, the line is tangent to the parabola; (3) two solutions, the line intersects the circle in two points. See
[link] .
There are five possible types of solutions to the system of nonlinear equations representing an ellipse and a circle:
(1) no solution, the circle and the ellipse do not intersect; (2) one solution, the circle and the ellipse are tangent to each other; (3) two solutions, the circle and the ellipse intersect in two points; (4) three solutions, the circle and ellipse intersect in three places; (5) four solutions, the circle and the ellipse intersect in four points. See
[link] .
An inequality is graphed in much the same way as an equation, except for>or<, we draw a dashed line and shade the region containing the solution set. See
[link] .
Inequalities are solved the same way as equalities, but solutions to systems of inequalities must satisfy both inequalities. See
[link] .
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature