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Magazine Problem 32
Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 $$
Problem 32
Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=\sqrt{x} \\ x^{2}+y^{2}=20 \end{array}\right. $$
Problem 32
Graph each system. $$ \left\\{\begin{array}{r} x^{2}-y^{2} \geq 1 \\ x \geq 0 \end{array}\right. $$
Problem 33
Hint: For Exercises 33 through 38 , first divide the equation through by the coefficient of \(x^{2}\) (or \(\left.y^{2}\right)\). $$ 3 x^{2}+3 y^{2}=75 $$
Problem 33
Graph each system. $$ \left\\{\begin{array}{l} x+y \geq 1 \\ 2 x+3 y<1 \\ x>-3 \end{array}\right. $$
Problem 33
Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ \frac{y^{2}}{9}-\frac{x^{2}}{9}=1 $$
Problem 33
Graph each inequality in two variables. $$ x>-3 $$
Problem 34
Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ \frac{x^{2}}{16}-\frac{y^{2}}{4}=1 $$
Problem 34
Graph each system. $$ \left\\{\begin{array}{l} x-y<-1 \\ 4 x-3 y>0 \\ y>0 \end{array}\right. $$
Problem 34
Graph each inequality in two variables. $$ y \leq 1 $$
