Chapter 7, Problem 9CA

(a)

To determine

To Find: The estimation and the interpretation of $D\left(2\right)$ .

Answer to Problem 9CA

The distance travelled by the traveller is 500 units.

Given:

The given diagram is shown in Figure 1

  

Figure 1

The function for the distance travelled by the traveller is $y=D\left(x\right)$ .

Calculation:

Consider the function $D\left(2\right)$ .

From the graph the function $D\left(2\right)$ shows that the distance and the time have a liner relation at $D\left(2\right)$ and at $D\left(2\right)$ the distance travelled by the traveller is 500 units.

(b)

To Find: The solution to determine the solution of the equation $D\left(x\right)=3500$ and explain its relevance.

The solution is $D\left(15\right)=3500$ .

Consider the given function $D\left(x\right)=3500$ .

Consider the given function is $y=D\left(x\right)$ .

Then at $y=35000$ the time is $x=15$ and the required solution is,

  $D\left(15\right)=3500$

(c)

To Find: The time for which the traveller has to wait for the shuttle bus.

The wait time of the traveller is $15\min$ .

The graph shows that the time taken by the traveller to reach the shuttle is of $x=15$ minute.

(d)

To Find: The distance travelled by the traveller on the shuttle bus.

The distance travelled by the traveller on the shuttle bus is not determined from the graph.

From the graph the distance travelled by the rider on the shuttle bus is not determined as the graph shows the distance travelled by the traveller to reach the bus in feet.

(e)

To Find: The total distance that the traveller walks before and after riding the shuttle bus.

The total distance travelled is $5508$ .

Consider the distance from the origin to the first point $\left(4,1000\right)$ is,

  $\begin{array}{c}{d}_1=\sqrt{{\left(4-0\right)}^2+{\left(1000-0\right)}^2}\\ =1000\end{array}$

Consider the distance from $\left(4,1000\right)$ to the first point $\left(12,1000\right)$ is,

  $\begin{array}{c}{d}_2=\sqrt{{\left(12-4\right)}^2+{\left(1000-1000\right)}^2}\\ =8\end{array}$

Consider the distance from $\left(12,1000\right)$ to the first point $\left(13,3000\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(3000-1000\right)}^2+{\left(13-12\right)}^2}\\ =2000\end{array}$

Consider the distance from $\left(13,3000\right)$ to the first point $\left(13,3500\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(15-12\right)}^2+{\left(3500-1000\right)}^2}\\ =2500\end{array}$

Thus, the total distance travelled by the traveller is,

  $\begin{array}{c}d=1000+8+2000+2500\\ =5508\end{array}$

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The function for the distance travelled by the traveller is $y=D\left(x\right)$ .

Calculation:

Consider the function $D\left(2\right)$ .

From the graph the function $D\left(2\right)$ shows that the distance and the time have a liner relation at $D\left(2\right)$ and at $D\left(2\right)$ the distance travelled by the traveller is 500 units.

(b)

To determine

To Find: The solution to determine the solution of the equation $D\left(x\right)=3500$ and explain its relevance.

Answer to Problem 9CA

The solution is $D\left(15\right)=3500$ .

Consider the given function $D\left(x\right)=3500$ .

Consider the given function is $y=D\left(x\right)$ .

Then at $y=35000$ the time is $x=15$ and the required solution is,

  $D\left(15\right)=3500$

(c)

To Find: The time for which the traveller has to wait for the shuttle bus.

The wait time of the traveller is $15\min$ .

The graph shows that the time taken by the traveller to reach the shuttle is of $x=15$ minute.

(d)

To Find: The distance travelled by the traveller on the shuttle bus.

The distance travelled by the traveller on the shuttle bus is not determined from the graph.

From the graph the distance travelled by the rider on the shuttle bus is not determined as the graph shows the distance travelled by the traveller to reach the bus in feet.

(e)

To Find: The total distance that the traveller walks before and after riding the shuttle bus.

The total distance travelled is $5508$ .

Consider the distance from the origin to the first point $\left(4,1000\right)$ is,

  $\begin{array}{c}{d}_1=\sqrt{{\left(4-0\right)}^2+{\left(1000-0\right)}^2}\\ =1000\end{array}$

Consider the distance from $\left(4,1000\right)$ to the first point $\left(12,1000\right)$ is,

  $\begin{array}{c}{d}_2=\sqrt{{\left(12-4\right)}^2+{\left(1000-1000\right)}^2}\\ =8\end{array}$

Consider the distance from $\left(12,1000\right)$ to the first point $\left(13,3000\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(3000-1000\right)}^2+{\left(13-12\right)}^2}\\ =2000\end{array}$

Consider the distance from $\left(13,3000\right)$ to the first point $\left(13,3500\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(15-12\right)}^2+{\left(3500-1000\right)}^2}\\ =2500\end{array}$

Thus, the total distance travelled by the traveller is,

  $\begin{array}{c}d=1000+8+2000+2500\\ =5508\end{array}$

Explanation of Solution

Consider the given function $D\left(x\right)=3500$ .

Consider the given function is $y=D\left(x\right)$ .

Then at $y=35000$ the time is $x=15$ and the required solution is,

  $D\left(15\right)=3500$

(c)

To determine

To Find: The time for which the traveller has to wait for the shuttle bus.

Answer to Problem 9CA

The wait time of the traveller is $15\min$ .

The graph shows that the time taken by the traveller to reach the shuttle is of $x=15$ minute.

(d)

To Find: The distance travelled by the traveller on the shuttle bus.

The distance travelled by the traveller on the shuttle bus is not determined from the graph.

From the graph the distance travelled by the rider on the shuttle bus is not determined as the graph shows the distance travelled by the traveller to reach the bus in feet.

(e)

To Find: The total distance that the traveller walks before and after riding the shuttle bus.

The total distance travelled is $5508$ .

Consider the distance from the origin to the first point $\left(4,1000\right)$ is,

  $\begin{array}{c}{d}_1=\sqrt{{\left(4-0\right)}^2+{\left(1000-0\right)}^2}\\ =1000\end{array}$

Consider the distance from $\left(4,1000\right)$ to the first point $\left(12,1000\right)$ is,

  $\begin{array}{c}{d}_2=\sqrt{{\left(12-4\right)}^2+{\left(1000-1000\right)}^2}\\ =8\end{array}$

Consider the distance from $\left(12,1000\right)$ to the first point $\left(13,3000\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(3000-1000\right)}^2+{\left(13-12\right)}^2}\\ =2000\end{array}$

Consider the distance from $\left(13,3000\right)$ to the first point $\left(13,3500\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(15-12\right)}^2+{\left(3500-1000\right)}^2}\\ =2500\end{array}$

Thus, the total distance travelled by the traveller is,

  $\begin{array}{c}d=1000+8+2000+2500\\ =5508\end{array}$

Explanation of Solution

The graph shows that the time taken by the traveller to reach the shuttle is of $x=15$ minute.

(d)

To determine

To Find: The distance travelled by the traveller on the shuttle bus.

Answer to Problem 9CA

The distance travelled by the traveller on the shuttle bus is not determined from the graph.

From the graph the distance travelled by the rider on the shuttle bus is not determined as the graph shows the distance travelled by the traveller to reach the bus in feet.

(e)

To Find: The total distance that the traveller walks before and after riding the shuttle bus.

The total distance travelled is $5508$ .

Consider the distance from the origin to the first point $\left(4,1000\right)$ is,

  $\begin{array}{c}{d}_1=\sqrt{{\left(4-0\right)}^2+{\left(1000-0\right)}^2}\\ =1000\end{array}$

Consider the distance from $\left(4,1000\right)$ to the first point $\left(12,1000\right)$ is,

  $\begin{array}{c}{d}_2=\sqrt{{\left(12-4\right)}^2+{\left(1000-1000\right)}^2}\\ =8\end{array}$

Consider the distance from $\left(12,1000\right)$ to the first point $\left(13,3000\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(3000-1000\right)}^2+{\left(13-12\right)}^2}\\ =2000\end{array}$

Consider the distance from $\left(13,3000\right)$ to the first point $\left(13,3500\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(15-12\right)}^2+{\left(3500-1000\right)}^2}\\ =2500\end{array}$

Thus, the total distance travelled by the traveller is,

  $\begin{array}{c}d=1000+8+2000+2500\\ =5508\end{array}$

Explanation of Solution

From the graph the distance travelled by the rider on the shuttle bus is not determined as the graph shows the distance travelled by the traveller to reach the bus in feet.

(e)

To determine

To Find: The total distance that the traveller walks before and after riding the shuttle bus.

Answer to Problem 9CA

The total distance travelled is $5508$ .

Consider the distance from the origin to the first point $\left(4,1000\right)$ is,

  $\begin{array}{c}{d}_1=\sqrt{{\left(4-0\right)}^2+{\left(1000-0\right)}^2}\\ =1000\end{array}$

Consider the distance from $\left(4,1000\right)$ to the first point $\left(12,1000\right)$ is,

  $\begin{array}{c}{d}_2=\sqrt{{\left(12-4\right)}^2+{\left(1000-1000\right)}^2}\\ =8\end{array}$

Consider the distance from $\left(12,1000\right)$ to the first point $\left(13,3000\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(3000-1000\right)}^2+{\left(13-12\right)}^2}\\ =2000\end{array}$

Consider the distance from $\left(13,3000\right)$ to the first point $\left(13,3500\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(15-12\right)}^2+{\left(3500-1000\right)}^2}\\ =2500\end{array}$

Thus, the total distance travelled by the traveller is,

  $\begin{array}{c}d=1000+8+2000+2500\\ =5508\end{array}$

Explanation of Solution

Consider the distance from the origin to the first point $\left(4,1000\right)$ is,

  $\begin{array}{c}{d}_1=\sqrt{{\left(4-0\right)}^2+{\left(1000-0\right)}^2}\\ =1000\end{array}$

Consider the distance from $\left(4,1000\right)$ to the first point $\left(12,1000\right)$ is,

  $\begin{array}{c}{d}_2=\sqrt{{\left(12-4\right)}^2+{\left(1000-1000\right)}^2}\\ =8\end{array}$

Consider the distance from $\left(12,1000\right)$ to the first point $\left(13,3000\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(3000-1000\right)}^2+{\left(13-12\right)}^2}\\ =2000\end{array}$

Consider the distance from $\left(13,3000\right)$ to the first point $\left(13,3500\right)$ is,

  $\begin{array}{c}{d}_3=\sqrt{{\left(15-12\right)}^2+{\left(3500-1000\right)}^2}\\ =2500\end{array}$

Thus, the total distance travelled by the traveller is,

  $\begin{array}{c}d=1000+8+2000+2500\\ =5508\end{array}$