Chapter 7.4, Problem 64E

To determine

To graph: the inequality $-\frac{1}{6}{x}^2-\frac{2}{7}y<-\frac{1}{3}$

Answer to Problem 64E

The graph of $-\frac{1}{6}{x}^2-\frac{2}{7}y<-\frac{1}{3}$

  $-\frac{1}{6}{x}^2-\frac{2}{7}y<-\frac{1}{3}$

Explanation of Solution

Given information:

The given inequality is $-\frac{1}{6}{x}^2-\frac{2}{7}y<-\frac{1}{3}$

Calculation:

Given:

The inequalty is $-\frac{1}{6}{x}^2-\frac{2}{7}y<-\frac{1}{3}$

Calculation:

  $\begin{array}{l}-\frac{1}{6}{x}^2-\frac{2}{7}y<-\frac{1}{3}\\ \frac{-7x^2-12y}{42}<-\frac{1}{3}\\ -\left(\frac{7x^2+12y}{42}\right)<-\frac{1}{3}\\ 7x^2+12y>14\end{array}$

The above equation is smilar to the equation of parabola and the region will be above the parabola or the region that does not include point (0,0) because it does not satisfy the equation.

Using graphing utility the graph looks like