Chapter 3.4, Problem 26AYU

(a)

To determine

To draw: a scatter diagram of the given data

Answer to Problem 26AYU

  

Explanation of Solution

Given:

  

Calculation:

draw scatter diagram of the data and find the type of relation that may existbetween the two variables.

  

From the above scatter graph of data it is found that there is quadratic relation between the twovariables.

Conclusion:

Thus, the scatter diagram is drawn.

(b)

To determine

To find: the quadratic function of best fit

Answer to Problem 26AYU

The relation between distance and height is $h=-\frac{49}{13200}{x}^2+\frac{227}{220}x+\frac{17}{3}$

Explanation of Solution

Calculation:

Using the graph utility, the quadratic function of best fit that models the relation between

distance and height is

  $h=-\frac{49}{13200}{x}^2+\frac{227}{220}x+\frac{17}{3}$

Conclusion:

The relation between distance and height is

  $h=-\frac{49}{13200}{x}^2+\frac{227}{220}x+\frac{17}{3}$

(c)

To determine

the distance that the ball will travel before it reaches its maximum height.

Answer to Problem 26AYU

Hence, the distance is $138.97$

Explanation of Solution

Calculation:

To determine the distance the ball will travel before it reaches its maximum height, take the

derivative of $h$ with respect to $x$ and set it to zero.

  $\frac{dh}{dx}=0$

  $\begin{array}{r}\hfill \begin{array}{l}-\frac{49}{13200}2x+\frac{227}{220}=0\\ -\frac{49}{6600}x=-\frac{227}{220}\end{array}\\ \hfill x=138.97\end{array}$

Hence, the distance is $138.97$

Conclusion:

Hence, the distance is $138.97$

(d)

To determine

To find: the maximum height of the ball.

Answer to Problem 26AYU

Hence, the height is $77.35$

Explanation of Solution

Calculation:

To find the maximum height, substitute $x=138.97$ in the quadratic function that relates distance and height.

  $h=-\frac{49}{13200}{(138.97)}^2+\frac{227}{220}(138.97)+\frac{17}{3}=-71.70+143.39+5.66=77.35$

Hence, the height is $77.35$

Conclusion:

Hence, the height is $77.35$

(e)

To determine

To graph: the quadratic function of best fit on the scatter diagram.

Answer to Problem 26AYU

  

Explanation of Solution

Calculation:

Using the graph utility the quadratic function of best fit on the scatter diagram is given below:

  

Conclusion:

Thus, the required graph is drawn.