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Exam 1 Postmortem
(What went wrong?)
CSI MATH 111.122 YCP
Definitions (continued)
A proposition makes a claim that may be either true or false.
A claim may be either
assertion
denial
A proposition must have the structure of a complete sentence
(i.e., questions are not propositions!)
Copyright © 2008 Pearson Education, Inc. Slide 1-12
1-A
If . . . Then Statements(Conditionals)
Copyright © 2008 Pearson Education, Inc. Slide 1-3
p q if p, then q
T T T T F F F T T F F T
Note: Conditional is true unless p is true and q is false.
1-B
Conditional Negation
Conditional
if p, then q
If you are sleeping, then you are breathing.
Conditional Negation
p and ~q
(why this is true will be shown later)
You are sleeping and you are not breathing.
epw 9/15/2008 Slide 1-4
1-B
Units
The units of a quantity describe what is being measured or counted.
Copyright © 2008 Pearson Education, Inc. Slide 2-5
Read kilowatts hours as “kilowatt-hours.”
hyphenMultiplication
Read ft ft ft or ft3, as“cubic feet” or “feet cubed”
cube or cubicRaising to a third power
Read ft ft, or ft2, as“square feet” or “feet squared”
squareRaising to a second power
Read miles hours as “miles per hour”
perDivision
ExampleKey word or symbol
Operation
2-A
Using Units
Always keep units along with their quantities! Example
► 2500 watts x 3 hours = 7500 watt-hours► Not 2500 x 3 = 7500 watt-hours
Example► 1000 watt-hours = 1 kilowatt-hour► 500 watt-hours = 0.5 kilowatt-hour = 0.5 kw-hr
epw 9/25/06 2 - 6
1 watt x 1000 hours = 1 w x 1000 hr = 1000 w-hr
1000 watts x 1 hour = 1000 w x 1 hr = 1000 w-hr
REMEMBER: 1000 watts = 1 kilowatt, and
1000 w = 1 1 kw = 1 1 kw 1000 w
1 watt x 1000 hours = 1 w x 1000 hr = 1000 w-hr = 1 kw-hr
1000 watts x 1 hour = 1000 w x 1 hr = 1000 w-hr = 1 kw-hr
Examples
epw 9/24/2008 Slide 2-7
Conversions
• Multiply, divide, or what?• Simplify by multiplying by 1 • Depends on what the problem is• The key to solving the problem is knowing
what units the solution should be• Example, if the answer should be
square yards (yd2), and your solution produces
yd4, then your solution is incorrectepw 9/25/06 8
Using Units
Know the units to expect Examples
The question asks for a cost in $
when using conversions, all units, except for dollars,
should cancel! The question asks for speed in km/hr
when using conversions, all units, except for km/hr,
should cancel!
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Conversion Format
ft
in. 12 or
foot 1
inches 12
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• There are 12 inches per 1 foot:
• Also, there is 1 foot per 12 inches:
Use whatever produces the desired units!
in. 12
ft or
inches 12
foot 1
Chain of Units Conversions
How many seconds are in one day?
Copyright © 2008 Pearson Education, Inc. Slide 2-11
2-A
24 hr 60 min 60 s
1 day 86,400 s1 day 1 hr 1 min
Cubic Units
How many cubic yards of soil are needed to fill a
planter that is 20 feet long by 3 feet wide by 4 feet tall?
Copyright © 2008 Pearson Education, Inc. Slide 2-12
The volume is 20 ft × 3 ft × 4 ft = 240 ft3
1 yd = 3 ft, so (1 yd)3 = (3 ft)3 = 27 ft3 or 1 yd3 = 1 27 ft3
2-A
U.S. Customary System
Copyright © 2008 Pearson Education, Inc. Slide 2-13
2-B
Knots and Nots
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A nautical mile is a unit of length on land, sea, and it the air. It corresponds approximately to one minute of latitude along any meridian (one minute of arc length on the Earth’s surface).
A knot is a measure of speed: 1 knot = 1 nautical mile hour
3.5 knots per hour = 3.5 nautical miles ÷ hour = 3.5 nautical miles hour hour2
Knots and Nots
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Which is faster, 1 mile per hour or 1 knot?
1 mile = 5280 feet hour hour
1 nautical mile = 6076.1 feet hour hour
Metric Conversions
Copyright © 2008 Pearson Education, Inc. Slide 2-16
2-B
Moving between metric units requires shifting the decimal placeone to the right when going to the next smaller unit and one to theleft when going to the next larger unit.
(Example: 5.23 cm = 52.3 mm)
Temperature Conversions
The conversions are given in both words and with formulas in which C, F, and K are Celsius, Fahrenheit, and Kelvin temperatures, respectively.
Copyright © 2008 Pearson Education, Inc. Slide 2-17
C = K 273.15Subtract 273.15Kelvin to Celsius
K = C + 273.15Add 273.15.Celsius to Kelvin
Subtract 32. Then divide by 1.8
Fahrenheit to Celsius
F = 1.8c + 32Multiply by 1.8. Then add 32.
Celsius to Fahrenheit
Conversion FormulaConversion in WordsTo Convert from
2-B
Units of Density and Concentration
Density describes compactness or crowding.
Material density – given in units of mass per unit volume; i.e., g/cm3
Population density – given by the number of people per unit area
Information density – how much information can be stored by digital media
Copyright © 2008 Pearson Education, Inc. Slide 2-18
2-B
Conversion Factors
epw 9/17/2008 Slide 2-19
Every Conversion Factor can be Written Three Different Ways
1 in. = 2.54 cm
1 in. = 1
2.54 cm
2.54 cm = 1
1 in.
Convert Miles to Kilometers
• Given 1 in. = 2.54 cm• Calculate how many cm are in 1 foot• 1 ft = 12 in.• 1 ft = 12 in. x 2.54 cm = 30.48 cm
1 in.• 1 mile = 5280 ft x 30.48 cm = 160934.4 cm
ft
• 1 mile = 1.6093 km
epw 9/17/2008 Slide 2-20
How Many Square Kilometers are in One Square Mile?
1 mi = 1.6093 km
(1 mi)2 = (1.6093 km)2
1 mi2 = 2.5898 km2
One square mile is 2.5898 square kilometers
epw 9/17/2008 Slide 2-21