Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
6th Edition
ISBN: 9781418300203
Author: Prentice Hall
Publisher: Prentice Hall
Question
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Chapter 2.1, Problem 30E

(a.)

To determine

To sketch: a graph of elevation y as a function of distance downriver x .

(a.)

Expert Solution
Check Mark

Answer to Problem 30E

The required graph is shown.

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.1, Problem 30E , additional homework tip 1

Explanation of Solution

Given:

    Elevation Along Bear Creek
    Distance DownriverRiver Elevation
    0.001577
    0.561512
    0.921448
    1.191384
    1.301319
    1.391255
    1.571191
    1.741126
    1.981062
    2.18998
    2.41933
    2.64869
    3.24805

Calculation:

Plot the points on graph and join them 0,1577,0.56,1512,0.92,1448,1.19,1384,1.30,1319,1.39,1255,1.57,1191,1.74,1126,1.98,1062,2.18,998,2.41,933,2.64,869,3.24,805

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.1, Problem 30E , additional homework tip 2

(b.)

To determine

To obtain: an approximate graph of the derivative.

(b.)

Expert Solution
Check Mark

Answer to Problem 30E

The graph of the derivative is shown.

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.1, Problem 30E , additional homework tip 3

Explanation of Solution

Given:

    Elevation Along Bear Creek
    Distance DownriverRiver Elevation
    0.001577
    0.561512
    0.921448
    1.191384
    1.301319
    1.391255
    1.571191
    1.741126
    1.981062
    2.18998
    2.41933
    2.64869
    3.24805

Concept used:

The derivative of a function is represented by slope of graph.

  Slope=change in ychnage in x

Calculation:

Create a table with mid point of each interval and their respective slopes.

    Elevation Along Bear Creek
    Distance DownriverRiver Elevation
    0.00+0.562=0.281512−15770.56−0=−116.07
    0.56+0.922=0.741488−15120.92−0.56=−177.78
    0.92+1.192=1.0551348−14481.19−0.92=−237.04
    1.19+1.302=1.2451319−13841.30−1.19=−590.91
    1.30+1.392=1.3451255−13191.39−1.30=−711.11
    1.39+1.572=1.481191−12551.57−1.39=−355.56
    1.57+1.742=1.6551126−11911.74−1.57=−382.35
    1.74+1.982=1.861062−11261.98−1.74=−266.67
    1.98+2.182=2.08998−10622.18−1.98=−320
    2.18+2.412=2.295933−9982.41−2.18=−282.61
    2.41+2.642=2.525869−9332.64−2.41=−278.26
    2.64+3.242=2.94805−8693.24−2.64=−106.67

Now plot the above points on the graph and join them.

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.1, Problem 30E , additional homework tip 4

(c.)

To determine

The units of measure would be appropriate for a gradient in this problem.

(c.)

Expert Solution
Check Mark

Answer to Problem 30E

The unit of gradient is feet per mile.

Explanation of Solution

Given:

    Elevation Along Bear Creek
    Distance Downriver (miles)River Elevation (feet)
    0.001577
    0.561512
    0.921448
    1.191384
    1.301319
    1.391255
    1.571191
    1.741126
    1.981062
    2.18998
    2.41933
    2.64869
    3.24805

Concept used:

The average change in elevation over a given distance is called a gradient.

Conclusion:

Here, the elevation is given in feet and the distance down the river is given in miles.

Thus, the units of the gradient will be feet per mile.

(d.)

To determine

The units of measure would be appropriate for derivative.

(d.)

Expert Solution
Check Mark

Answer to Problem 30E

The units of the gradient will be feet per mile.

Explanation of Solution

Given:

    Elevation Along Bear Creek
    Distance Downriver (miles)River Elevation (feet)
    0.001577
    0.561512
    0.921448
    1.191384
    1.301319
    1.391255
    1.571191
    1.741126
    1.981062
    2.18998
    2.41933
    2.64869
    3.24805

Concept used:

Derivative is given by the slope.

Here, the average change in elevation over a given distance is slope.

Conclusion:

Here, the elevation is given in feet and the distance down the river is given in miles.

Thus, the units of the gradient will be feet per mile.

(e)

To determine

To identify: The most dangerous section of the river by analyzing the graph in (a).

(e)

Expert Solution
Check Mark

Answer to Problem 30E

The most dangerous section of the river is from 1.2 to 1.5 miles.

Explanation of Solution

Given:

    Elevation Along Bear Creek
    Distance Downriver (miles)River Elevation (feet)
    0.001577
    0.561512
    0.921448
    1.191384
    1.301319
    1.391255
    1.571191
    1.741126
    1.981062
    2.18998
    2.41933
    2.64869
    3.24805

Conclusion:

In the graph, the steepest part which is from 1.2 to 1.5 miles.

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.1, Problem 30E , additional homework tip 5

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Chapter 2.1, Problem 29E
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Chapter 2.1, Problem 31E

Chapter 2 Solutions

Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

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