
Concept explainers
a.
Explain the maximum and minimum points mean in the context of the situation.
a.

Answer to Problem 40PPS
The maximum point means that the rope is the highest at
The minimum point means that the rope is the lowest at
Explanation of Solution
Given:
It is given in the question that the graph shows the approximates the height of a jump rope h in inches as a function of time t in seconds. A Maximum point on the graph is
Concept Used:
In this, use the concept of study the graph and describe the maximum and minimum points.
Calculation:
Since, from the graph
The x − coordinate represents the time.
The y − coordinate represents the height.
The maximum point means that the rope is the highest at
The minimum point means that the rope is the lowest at
Conclusion:
The maximum point means that the rope is the highest at
The minimum point means that the rope is the lowest at
b.
Calculate the equation for the midline, the amplitude and the period of the function.
b.

Answer to Problem 40PPS
The midline, amplitude and the period are
Explanation of Solution
Given:
It is given in the question that the graph shows the approximates the height of a jump rope h in inches as a function of time t in seconds. A Maximum point on the graph is
Concept Used:
In this, use the concept of general equation of sine
Calculation: Let the equation be
Firstly find the midline, d :
Now, the amplitude is the difference between the midline and maximum value:
Since, it takes
Now, it is known that the period is
Let’s find b:
Conclusion:
The midline, amplitude and the period are
c.
Find the equation for the function.
c.

Answer to Problem 40PPS
The equation for the function is
Explanation of Solution
Given: It is given in the question that amplitude, period and midline are
Concept Used:
In this, use the general equation of the sine function
Calculation: Let the function be
Now,
Put the above value in the equation,
The equation is
Conclusion:
The equation is
Chapter 13 Solutions
Algebra 2
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