Chapter 8.3, Problem 34PPS

(a)

To determine

To calculate: To make a table to find the number of miles a whale can swim in $5,10,15,20$ minutes.

Answer to Problem 34PPS

Table is

Distance whale can swim
Time (min)	5	10	15	20
Distance (mile)	3.50	7.00	10.50	14.00

Explanation of Solution

Given information: A whale can swim half a mile per minute

Calculation:

Given that a whale can swim half a mile per minute

Let the time be $t$ and distance be $d$

Thus,

  $d=0.5t$

When $t=5$

  $\begin{array}{l}d=0.5\left(5\right)\\ d=2.5\end{array}$

When $t=10$

  $\begin{array}{l}d=0.5\left(10\right)\\ d=5\end{array}$

When $t=15$

  $\begin{array}{l}d=0.5\left(30\right)\\ d=1.5\end{array}$

When $t=20$

  $\begin{array}{l}d=0.5\left(20\right)\\ d=10\end{array}$

Table is

Distance whale can swim
Time (min)	5	10	15	20
Distance (mile)	3.50	7.00	10.50	14.00

Conclusion:

Hence, required table is

Distance whale can swim
Time (min)	5	10	15	20
Distance (mile)	3.50	7.00	10.50	14.00

(b)

To determine

To calculate: To find the difference between the output values.

Answer to Problem 34PPS

Different between the output values increase by the same amount and difference is $3.50$

Explanation of Solution

Given information: A whale can swim half a mile per minute

Calculation:

Given that a whale can swim half a mile per minute. Table is

Distance whale can swim
Time (min)	5	10	15	20
Distance (mile)	3.50	7.00	10.50	14.00

Difference between the distance is

  $\begin{array}{l}7-3.50=3.50\\ 10.50-7=3.50\\ 14-10.50=3.50\end{array}$

Conclusion:

Hence, Different between the output values increase by the same amount and difference is $3.50$

(c)

To determine

To calculate: To graph the ordered pairs (time, distance) and then draw a line through the points

Answer to Problem 34PPS

Ordered pairs are plotted.

Explanation of Solution

Given information: A whale can swim half a mile per minute

Calculation:

Given that a whale can swim half a mile per minute. Table is

Distance whale can swim
Time (min)	5	10	15	20
Distance (mile)	3.50	7.00	10.50	14.00

Set of Ordered pairs (time, distance) is as below:

  $\left\{\left(5,3.5\right),\left(10,5.0\right),\left(15,7.5\right),\left(20,10.0\right)\right\}$

Plotting the point on graph:

  

Conclusion:

Hence, ordered pairs are plotted

(d)

To determine

To calculate: To write the equation to represent the relationship between the time $x$ and number of miles $y$

Answer to Problem 34PPS

The equation to represent the relationship between the time $x$ and number of miles $y$ is $10y-7x=0$

Explanation of Solution

Given information: A whale can swim half a mile per minute

Formula Used:

Equation of line is given as

  $\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given that a whale can swim half a mile per minute. Table is

Distance whale can swim
Time (min)	5	10	15	20
Distance (mile)	3.50	7.00	10.50	14.00

Set of Ordered pairs (time, distance) is as below:

  $\left\{\left(5,3.5\right),\left(10,7.0\right),\left(15,10.5\right),\left(20,14.0\right)\right\}$

Equation of line passing through the points $\left(5,3.5\right),\left(10,7.0\right)$ is given as

  $\begin{array}{l}y-7=\frac{7-3.5}{10-5}\left(x-10\right)\\ y-7=\frac{3.5}{5}\left(x-10\right)\\ y-7=\frac{35}{50}\left(x-10\right)\\ y-7=\frac{7}{10}\left(x-10\right)\\ 10y-70=7x-70\\ 10y-7x=0\end{array}$

Conclusion:

Hence, the equation to represent the relationship between the time $x$ and number of miles $y$ is $10y-7x=0$