Concept explainers
Height of a Rail A shot-putter throws a hall at an inclination of to the horizontal. The following data represent the height of the ball , in feet, at the instant that it has traveled feet horizontally:
(a) Use a graphing utility to draw a
(b) Use a graphing utility to find the quadratic function of best fit that models the relation between distance and height.
(c) Use the function found in part (b) to determine how far the ball will travel before it reaches its maximum height.
(d) Use the function found in part (b) to find the maximum height of the ball.
(e) With a graphing utility, graph the quadratic function of best fit on the scatter diagram.
To calculate:
a. Graph a scattered diagram and determine the type of relation that exists between the 2 variables.
b. Find the quadratic function of best fit.
c. Determine how far the ball will travel before it reaches the maximum height.
d. Find the maximum height of the ball.
e. Graph the quadratic function of best fit.
Answer to Problem 26AYU
a. The graph is given below.
b. The equation of best fit is .
c. The ball will travel feet before it reaches the maximum height.
d. The maximum height attained by the ball is about .
e. The graph is given below.
Explanation of Solution
Given:
A shot putter throws a ball at an inclination of 45 degree to the horizontal. The given data represents the relation between the height of the ball thrown and the distance it travels.
Formula used:
For a quadratic equation if is positive, then the vertex is the minimum point and if is negative, the vertex is the maximum point.
Calculation:
We can draw the scatter diagram using Microsoft Excel.
Thus, on entering the and the values on excel, we have to choose the Scatter diagram form the insert option.
Then for getting the equation of best fit, we have to choose the Layout option and then Trendline and then more Trendline option. Then choose the option polynomial and then display the equation.
Thus, we get the scatter diagram with the equation of best fit as
a. The scatter diagram is drawn above and we can see that the given variables exhibit a non-linear polynomial relationship.
b. The equation of best fit is .
c. We can see that the equation of best fit is a quadratic equation with .
Here, is negative, therefore, the vertex is the maximum point.
The value for maximum is
Thus, the ball will travel feet before it reaches the maximum height.
d. The maximum income earned is
The maximum height attained by the ball is about feet.
e. The graph is drawn above.
Chapter 3 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)
Calculus: Early Transcendentals (3rd Edition)
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