= squaref eet. 1 centimeter = 0.01 meters; 1 meter = yards. = 79.49liters

Transcription

1 Homework Section 2B Solutions Week of 9/10/12 Math Warm-up: Convert 3.5 miles to units of feet. 1 mile = 5280 feet 3.5miles 5280feet 1mile = 18480feet Convert 6 hours to units of seconds. 1 hour = 60 minutes; 1 minute = 60 seconds 6hours 60minutes 1hour 60seconds 1minute = 21600seconds Convert 4 acres to units of square feet. 1 acre = square feet 4acres 43560squarefeet 1acre = squaref eet Convert 125 centimeters to yards. 1 centimeter = 0.01 meters; 1 meter = yards 125centimeters 0.01meters 1centimeter 1.094yards = yards 1meter Convert 84 quarts to liters. 1 quart = 0.25 gallons, 1 gallon = 3.79 liters 84quarts 0.25gallons 1quart 3.79liters 1gallon = 79.49liters 1

2 2. Fun with Units: The bed of a pickup truck is 3.5 feet deep, 12 feet long, and 5 feet wide. What is the area of the bed s floor? What is its volume? Area = length width = 12feet 5feet = 60ft 2 or 60squarefeet V olume = length width height = 12feet 5feet 3.5feet = 210ft 3 or 210cubicfeet The film Shrek 2 grossed $436 million. If the tickets cost $8 each, approximately how many people saw the film? 1 person = $ dollars 1person = 54, 500, 000people 8dollars There are approximately 3 million births in the United States each year. Find the birth rate in births per minute births 1year 1year 365days 1day 24hours 1hour 60minutes = 5.7births minute How many liquid pints does a 2-gallon container hold? How many cubic inches does it hold? 8 pints = 1 gallon; 1 pint = cubic inches Part 1: If there are 8 pints in a gallon, then 2 gallons contains 2gallons 16pints 8pints 1gallon = Part 2: From part 1, 2 gallons = 16 pints, so: 16pints in3 1pint = 462in 3 A 40-gram pebble has a volume of 10 cubic centimeters. What is its density? Will it float or sink in water? 2

3 Density is measured in grams per cubic centimeter, so no conversion is needed here. The density is: 40grams 10cm 3 = 4grams 1cm 3 We know that water has a density of 1gram cm 3, so the pebble is more dense than water and will sink. 3. The fearsome pirate Captain Bartolomeo needs to buy a new ship. He knows that a good ship these days (in the 16th century, that is) will cost him 125 Pirate Doubloons. Unfortunately most of his money is in swindled Spanish Reales. Using the chart below, determine many Spanish Reales a good ship will cost. Table 1: Currency Exchange Rates Currency US Dollars per Foreign Foreign per US Dollar Pirate Doubloons Spanish Reales From the table, you can obtain these two conversions: 1 Dollar = 20 Doubloons and 4 Dollars= 1 Reales. Use this to convert 125 Doubloons to Reales. 125Doubloons 1dollar 20Doubloons 1Reales 4dollars = Reales Bartolomeo has already pillaged 7,258 Spanish Reales. Does he have enough to buy his ship? If not, how much more does he need? Note: this question was written before I changed the conversion factors in the chart and I forgot to change this part, so the magnitude of the numbers are quite different from those obtained in the first part of the question. But certainly based on what you calculated in part 1, he has more than enough. 4. Bartolomeo has obtained his ship, The Conversion Maker. The dimensions of the living quarters are 22 meters in length and 9 meters in width. Bartolomeo s crew is 77 pirates. What is the population density of the living quarters in pirates per square foot? How much space (in feet) is available per pirate? 3

4 This is a population density problem, and we know population density is measured in people (or pirates) per square unit area. The area of the living quarters is length times width, i.e. 22meters 9meters = 198m 2. 77pirates 198m 2 = 0.39pirates m 2 Next we need to convert this to square feet, using the conversion 1 meter = 3.28 feet, so 1 square meter = 3.28feet 3.28feet = ft pirates 1m 2 m ft 2 = 0.036pirates 1squaref eet To find the amount of square feet for 1 pirate, divide the top and bottom by the amount of pirates, i.e. divide by to get: 1pirate 27.77ft 2 or 27 square feet for each pirate. 5. Salty Sam quickly drinks 6 ounces of rum, which contains 57 grams of alcohol. Given that Salty Sam weighs 200 pounds and has 6 liters of blood, what is his blood alcohol content in grams per milliliter? Should Bartolomeo let Salty Sam drive The Conversion Maker? Blood alcohol content is measured in grams of alcohol per 100 ml of blood, so first we need to convert liters to milliliters and then find the value for 100 ml. 57grams 6Liters = 9.5grams 1liter 1Liter 1000mL = grams 1mL Now multiply top and bottom by 100 to get grams per 100 ml: 0.95grams 100mL This is an extremely high BAC, certainly not fit for driving (or anything else for that matter). Remember that this is based on the somewhat unreasonable assumption that alcohol is absorbed immediately. 6. Salty Sam challenges Bartolomeo to a sword fight, which incidentally burns 408 Calories per hour. How many watts of power is generated from an hour of sword fighting? Considering 4

5 that Salty Sam just had 388 Calories of rum, how long does he need to sword fight to burn off those calories? Power is measured in watts, which is joules. First convert Calories into joules by mul- seconds tiplying by 4184: 408Cal 4184joules 1Cal = joules This is after one hour of activity, so power is: joules Now convert hours to seconds to get power in Watts joules = W atts. 3600s For the second part, convert calories into hours in the following manner: 388Calories 408Cal = 0.95hours 7. Bartolomeo orders Salty Sam to walk the plank. Salty Sam knows that it will take him 2 hours to swim to the closest shore, and that to survive for two hours the water temperature needs to be at least 60 F. Arr, you ll never make it, says Bartolomeo, the water is only 17 C. Salty Sam says, I ll take my chances. Does Salty Sam survive? Calculate the water temperature in Fahrenheit using the conversion equation: 9 5 C + 32 = F 9 (17) + 32 = F 5 Solve to see that the water temperature is 62.6 F. Thus Salty Sam survives! 8. Read section 2C for problem solving tips. 5