Exam 1 Postmortem (What went wrong?) CSI MATH 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 A

If... Then Statements (Conditionals) Copyright © 2008 Pearson Education, Inc. Slide 1-3 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 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 ft 3, as “cubic feet” or “feet cubed” cube or cubicRaising to a third power Read ft  ft, or ft 2, 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/

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 (yd 2 ), and your solution produces yd 4, then your solution is incorrect epw 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! epw 9/25/06 9

Conversion Format epw 9/25/06 10 There are 12 inches per 1 foot: Also, there is 1 foot per 12 inches:  Use whatever produces the desired units!

Chain of Units Conversions How many seconds are in one day? Copyright © 2008 Pearson Education, Inc. Slide A

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 ft 3 1 yd = 3 ft, so (1 yd) 3 = (3 ft) 3 = 27 ft 3 or 1 yd 3 = 1 27 ft 3 2-A

U.S. Customary System Copyright © 2008 Pearson Education, Inc. Slide B

Knots and Nots epw 9/24/2008 Slide 1-14 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 hour 2

Knots and Nots epw 9/24/2008 Slide 2-15 Which is faster, 1 mile per hour or 1 knot? 1 mile = 5280 feet hour hour 1 nautical mile = feet hour hour

Metric Conversions Copyright © 2008 Pearson Education, Inc. Slide B Moving between metric units requires shifting the decimal place one to the right when going to the next smaller unit and one to the left 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  Subtract Kelvin to Celsius K = C Add 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 Words To 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/cm 3 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 B

Conversion Factors epw 9/17/2008 Slide 2-19 Every Conversion Factor can be Written Three Different Ways

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 = cm 1 in. 1 mile = 5280 ft x cm = cm ft  1 mile = km epw 9/17/2008 Slide 2-20

How Many Square Kilometers are in One Square Mile? 1 mi = km (1 mi) 2 = ( km) 2 1 mi 2 = km 2 One square mile is square kilometers epw 9/17/2008 Slide 2-21