Chapter 4

Solve each problem involving rate of work. It takes an inlet pipe of a small swimming pool 20 minutes less to fill the pool than it takes an outlet pipe of the same pool to empty it. Through an error, starting with an empty pool, both pipes are left open, and the pool is filled after 4 hours. How long does it take the inlet pipe to fill the pool, and how long does it take the outlet pipe to empty it?

In Exercises \(97-108,\) graph by hand the equation of the circle or the parabola with a horizontal axis. $$x=-(y+1)^{2}+2$$

Solve each problem involving rate of work. A sink can be filled by the hot-water tap alone in \(4 \mathrm{min}\) utes more than it takes the cold-water tap alone. If both taps are open, it takes 4 minutes, 48 seconds to fill an empty sink. How long does it take each tap individually to fill the sink?

In Exercises \(97-108,\) graph by hand the equation of the circle or the parabola with a horizontal axis. $$x=(y-2)^{2}-1$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &x^{2}+y^{2}=100\\\ &[-15,15] \text { by }[-10,10] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &x^{2}+y^{2}=81\\\ &[-15,15] \text { by }[-10,10] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window.$$\begin{aligned} &(x-2)^{2}+y^{2}=9\\\ &[-9.4,9.4] \text { by }[-6.2,6.2] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &(x+3)^{2}+y^{2}=16\\\ &[-9.4,9.4] \text { by }[-6.2,6.2] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &x=y^{2}+6 y+9\\\ &[-10,10] \text { by }[-10,10] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &x=y^{2}-8 y+16\\\ &[-10,10] \text { by }[-10,10] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &x=2 y^{2}+8 y+1\\\ &[-10,10] \text { by }[-10,10] \end{aligned}$$

In Exercises \(109-116\), describe the graph of the equation as either a circle or a parabola with a horizontal axis of symmetry. Then, determine two functions, designated by \(y_{1}\) and \(y_{2},\) such that their union will give the graph of the given equation. Finally, graph \(y_{1}\) and \(y_{2}\) in the given viewing window. $$\begin{aligned} &x=-3 y^{2}-6 y+2\\\ &[-9.4,9.4] \text { by }[-6.2,6.2] \end{aligned}$$