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U of U MATH 1030 - Lecture Notes

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Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BSection B.1: Standardized Unit Systems: U.S. and MetricDifferent system of standardized unitsThere are different systems of standardized units: the international metric system, called SI (from the FrenchSyst`eme International d’Unit´es) and the English system, called the U.S. customary system (USCS).The U.S. Customary SystemThe U.S. Customary System• To measure the lengths of objects we have: inches, feet, yards, miles and others.• To measure weights of objects we have three different ways: Avoirdupois measures, Troy measuresand Apothecary measures. The Avoirdupois measures are commonly used today.• To measure volumes we have two kinds of measures: Liquid measures and Dry measures. Theliquid measures are used in the case of liquid objects as water, beer and so on. The Dry measuresare used in the case of solid objects such as flour.Notice that 1 dry pint = 33.60 in3> 1 liquid pint = 28.88 in3.Ex.1 The Kentucky Derby.In the Kentucky Derby, horses race a distance of 10 furlongs. How many miles is the race?1Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BEx.2 20, 000 Leagues Under the Sea.In the Jules Verne’s novel 20, 000 Leagues Under the Sea, does the title refer to an ocean depth? How doyou know?The International Metric SystemThe International Metric SystemThe basic units of length, mass, time and volume in the metric system are• the meter for length (m);• the kilogram for mass (kg);• the second for time (s);• the liter for volume (L).In the international metric system we use powers of 10 to find all the other units ad we write the new unitsadding a prefix which indicates multiplication by a power of 10.2Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BEx.3(1) Convert 2759 centimeters to metes.(2) How many nanoseconds are in a microsecond?Metric-USCS ConversionsThis is a table of conversions:USCS to Metric Metric to USCS1 in. = 2.54 cm 1 cm = 0.3937 in.1 ft = 0.3048 m 1 m = 3.28 ft1 yd = 0.9144 m 1 m = 1.094 yd1 mi = 1.6093 km 1 km = 0.6214 mi1 lb = 0.4536 kg 1 kg = 2.205 lb1 gal = 3.785 L 1 L = 0.2642 gal3Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BFor example, if you remember that a kilometer is about 0.6 mile, you will know that a 10-kilometer roadrace is about 6 miles.Ex.4 Gas Price per Liter.At a gas station in Mexico, the price of gasoline is 8 pesos per liter. What is the price in dollars per gallons?We know that 1 peso = $0.09136.Ex.5 Square Kilometers to Square Miles.How many square kilometers are in a square mile?4Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BTemperature Units: Fahrenheit, Celsius and KelvinTemperature UnitsThere are three temperature scales commonly used today: Fahrenheit, Celsius and Kelvin.• The Fahrenheit scale is used in the United States and it is defined so that water freezes at 32◦F andboils at 212◦F .• Internationally, temperature is measured on the Celsius scale, which places the freezing point ofwater at 0◦C and the boiling point at 100◦C.• The Kelvin scale is used in science and is the same as the Celsius scale except for its zero point: atemperature of 0 K is the coldest possible temperature, known as absolute zero and it correspondto −273.15◦C or −459.67◦F .The conversions are:• from Celsius to Fahrenheit:F = 1.8 C + 32• from Fahrenheit to Celsius:C =F − 321.8• from Celsius to Kelvin:K = C + 273.15• from Kelvin to Celsius:C = K − 273.15.5Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BEx.6 Human Body Temperature.Average human body temperature is 98.6◦F . What is it in Celsius and Kelvin?Ex.7The local weather report says that tomorrow the temperature will be 59◦, but does not specify whether itis in Celsius or Fahrenheit. Can you tell which it is? Why?6Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BSection B.2: Units of Energy and PowerDefinition of energyEnergy is what makes matter move or heat up. The international metric unit of energy is the joule.CaloriesFor example, we need energy from food to walk or run. The most familiar energy unit is the food Calorieused to measure the energy our body can draw from food:1 Calorie = 4184 joules.Definition of powerPower is the rate at which energy is used. The international metric unit of energy is the watt:1 watt = 1joules.Ex.8You are riding an exercise bicycle at a fitness center. The readout states that you are using 500 Caloriesper hour. Are you generating enough power to light a 100-watt bulb?7Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BDefinition of kilowatt-hourA kilowatt-hour is a unit of energy:1 kilowatt-hour =1000 joule1 s× 1 hr =1000 joule1 s× 3, 600 s = 3, 600, 000 joule.Ex.9Your utility company charges 8 cents per kilowatt-hour of electricity. How much does it cost to keep a100-watt light bulb on for a week?8Chapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section BSection B.3: Units of Density and ConcentrationDefinition of densityDensity describes compactness or crowding. There are three different kinds of densities:• Material density is given in units of mass per unit volume, such as grams per cubic centimeter (gcm3).For example, the density of water is 1gcm3. Objects with densities less than 1gcm3float in the water,while objects with densities more than 1gcm3sink.• Polpulation density is given by the number of people per unit area. For example, if 500 people live ina square region that is 2 miles on a side, the population density of the area is500 people4mi2= 125peoplemi2.• Information density is used to describe how much memory can be stored by digital media. For exam-ple, each square inch surface of a DVD hold about 100 megabytes of information, so we say that aDVD has an information density of 100MBin2.Definition of concentrationConcentration describes the amount of one substance mixed with another. There are many types of concen-tration, for example:• The concentration of an air pollutant is often measured by the numbers of molecules of the pollutantper million molecules of air. For example, if there are 20 molecules of carbon monoxide in each 1million molecules of air, we state the carbon monoxide concentration as 20 parts per million (ppm).• Blood alcohol content (BAC) describes the concentration of alcohol in a person’s body.


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