Chapter 1.7, Problem 34E

To determine

To find: The reproduced image with the help of graphing calculator.

Answer to Problem 34E

The required diagram is shown in Figure 2

Explanation of Solution

Given:

The given image is shown in Figure 1

Figure 1

Calculation:

The wheels of the trolley are in the first quadrant and represents the circle with the centre at $\left(3,1\right)$ and with the radius 1 and the other circle with centre $\left(8,1\right)$ with the radius 1

The parametric equation of the circle of radius $r=1$ and the centre at $\left(h,k\right)=\left(3,1\right)$

  $\begin{array}{l}x=h+r\cos t\\ y=k+\sin t\end{array}$

Then

  $\begin{array}{l}x=3+\cos t\\ y=1+\sin t\end{array}$

The range for the $t$ is,

  $-3.65\le t\le 0.5$

The parametric equation of the circle of radius $r=1$ and the centre at $\left(h,k\right)=\left(8,1\right)$ ,

  $\begin{array}{l}x=8+\cos t\\ y=1+\sin t\end{array}$

The range for the $t$ is,

  $-3.65\le t\le 0.5$

Consider the parametric equation of the line that joins the two wheels is,

  $\begin{array}{l}x=t\\ y=1.5\end{array}$

The range for the $t$ is,

  $1\le t\le 10$

Consider the parametric equation of the left vertical line is,

  $\begin{array}{l}x=1\\ y=t\end{array}$

The range for the $t$ is,

  $1.5\le t\le 4$

Consider the parametric equation of the right vertical line is,

  $\begin{array}{l}x=10\\ y=t\end{array}$

The range for the $t$ is,

  $1.5\le t\le 4$

Consider the parametric equation of the slant line is,

  $\begin{array}{l}x=t\\ y=t-6\end{array}$

The range for the $t$ is,

  $10\le t\le 13$

The maple code for the picture is,

plot([[3+cos(t), l+sin(t), t = -3.65.. .5], [8+cos(t), 1+sin(t), t = -3.65.. .5], [t, 1.5, t = 1 .. 101, [1, t, t= 1.5 .. 4], [10, t, t = 1.5 .. 4], [t, t-6, t = 10.. 13]], color = [red, green, orange, blue, purple, black],thickness = 2);

The output for the graph is shown in Figure 2

Figure 2