Concept explainers
(a)
To find:The slope of the uphill and downhill portion of the trip.
(a)
Answer to Problem 60HP
The slope of the uphill trip is ¼ and the slope of the downhill trip is -(1/4).
Explanation of Solution
Given:
The vertical cross-section of the hill is modelled by the equation
Calculation:
Plot the function of the hill.
For the range
Calculate the slope of the uphill of the trip:
Calculate the slope of the downhill trip:
Therefore, the slope of the uphill trip is ¼ and the slope of the downhill trip is (-1/4).
(b)
To plot:The graph of the function.
(b)
Answer to Problem 60HP
The graph of the function is drawn below.
Explanation of Solution
Given:
The vertical cross-section of the hill is modelled by the equation
Calculation:
In the given function, a vertical shift of 100 is observed from the equation. Since the function is negative, the graph of the function opens in the downward direction.
Plot the function of the hill.
Therefore, the graph of the function is drawn above.
(c)
To find:The domain and the range of the function of the hill.
(c)
Answer to Problem 60HP
The domain of the function is
Explanation of Solution
Given:
The vertical cross-section of the hill is modelled by the equation
Calculation:
Plot the function of the hill.
For the range
The set of input or argument values for which the function gives real and defined output is termed as the domain of the function. Find the domain from the given graph. In the given graph domain constraints and the undefined points are not observed. Therefore the domain of the graph is
The range is defined as the set of values of the dependent variables for which the function has defined values.
The range of the given function is
Therefore the domain of the graph is
Chapter 4 Solutions
Algebra 1
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