Cost Versus Quantity
The metric BWGZ gravel supply business charges the amount
|
C = $20.00 + w· |
$15.00
50 kg |
|
|
for each amount w of gravel purchased. (For each order of gravel, the BWGZ gravel company charges $0.30
per kilogram plus $20.00. The latter could be a handling
or order setup charge.)
The graph of
cost or price C versus the amount w follows.
The slope of this straight-line graph is
|
m = |
$15.00
50 kg |
= |
$30.00
100 kg |
= 0.30 |
$
kg |
|
|
There are several possible ways to write m. Pick the one
you like or favor.
For w = 2000 lbs of gravel, the cost would be
|
|
|
|
$20.00 + 2000 lbs· |
$15.00
50 kg |
|
| |
|
|
$20.00 + 2000 · |
15.00
50 |
$· |
lbs
kg |
|
| |
|
|
$20.00 + 2000 · |
15.00
50 |
$· |
lbs
2.2046 lbs |
|
| |
|
|
$20.00 + |
æ
ç
è
|
2000· |
15.00
50
|
· |
1
2.2046
|
ö
÷
ø
|
$ |
| |
|
| $20.00 + $272.16 = $292.16 |
|
|
since 1 kg = 2.2046 lbs at the surface of the earth.
FOOTNOTE: At the earth surface, a one pound mass and one pound
weight are identical measures of material. There is a distinction
between mass and weight that has to be considered for calculations
away from the earth surface. Students of physics should know
why.
In computations, we follow the
convention that units can appear before or after the number
in it. In contrast, in the presentation of results, the
placement of the unit before or after depends on
grammatical or cultural preferences of a cosmetic nature.
| |
Why Slopes
and
More Math
understanding & explaining
Reason and Math
Volume 3
Printed in Canada
ISBN 0-9697564-3-7
|
Content Guide
Foreword
Chapter Descriptions
1. Introduction
Preview -why slopes in 1983
2. Second Preview Begins
2 Skier in Motion (V)
2 The Skier (V)
2. Position Dependent (V)
3 Slope & Extrema (V)
4 Single Factor Analysis (V)
4 Two Factor (V)
4 More Factors (V)
4 With Divisors (V)
5 Maxima & Minima Tests
6 Jumps & Discontinuities
8 Review (optional)
9 On Calculus Studies
11 Slope of Slope
13 Acceleration
14 Limits & Error Control (V)
14 Limit of a Fn.
14. Limited Error Control
14 Signif. Digits
14 Cauchy Limits
14 Sequence Limits
14 Decimal Arith.
15 What is Slope (V)
15 Slope Calculation (V)
15 Slope, a Limit
15 Tangent Lines
15 Linear Approx.,
15 Limits via Algebra (V)
15 Recap.
PS.Chain Rule for Polys
PS Chain Rule- General (V) -
PS More Chain Rule (V)
PS - Sign Analysis (V)
16 What is Velocity
17 What is Area
18 Integration
18 Area Calculation
18 Fn DefN, 6 Ways
19 Logs & Powers
19 Natural Log.
19 Exponential Fn.
20 What's Next
21 Add Vectors
22 Complex #'s
23 Complex #'s
23 Trig Identity
23 Proofs of.
24 Complex Logs etc
Units in Calculations:
7 Velocity
7 Varying Velocity Example
7. Velocity Calculation
7 Changing Units
7 Same Velocity Motions
10 Slopes without Units.
10 Units & Slopes
10 Units in Cost vs. Quantity
10 How Units Appear
10 Unit Elimination
10 Partial Elimination
10 Interest & Units
12 More on Units
Enriched material: The Appendices of Volume
3 are located in the Real
Analysis Area.
Pigeon Hole Principle
Constant Difference Thm
Continuous Functions
Rational Functions
Mean Value Theorem
One Side Range Theorem
Range On One Side
Theorem
Integration
& Lipschitz
Continuity
These appendices continue the
decimal viewpoint of limits, error
control and continuity begun
in Chapter 14. The One Sided
Range Theorem is a postscript,
not in printed version.
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