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Module 1: Basic Skills of Algebraic Expressions Lesson 3: Dimensional Analysis Objectives: I can change quantities from one unit to a different unit using dimensional analysis. I can solve real-life application using dimensional analysis. Vocabulary: Dimensional Analysis, Unit Agenda: - Quiz 1 - Worm up - Dimensional Analysis Notes - Practice Focus Questions: How can I use dimensional analysis to change quantities from one unit to another? How can I use Dimensional Analysis to compare two quantities? More Practice: http://www.alysion.org/dimensional/fun.htm Practice the examples available and check your answers Homework: HW 1-3 1 Mathematician:________________ Algebra I Quiz 1 Combine the following polynomials: 1. (4𝑥 2 + 𝑥 + 7) + (2𝑥 2 + 3𝑥 + 1). 2. (3𝑥 3 − 𝑥 2 + 8) − (𝑥 3 + 5𝑥 2 + 4𝑥 − 7) Find: 3. The sum of (5 − 𝑡 − 𝑡 2 ) and (9𝑡 + 𝑡 2 ). 4. Subtract (2𝑥 3 + 24) from (3𝑥 3 + 8𝑥). 5. What is the perimeter of the triangle below? 2𝑥 + 5 7𝑥 4 + 9𝑥 2𝑥 4 + 26 2 Warm Up: Conserving Fuel: Discuss with your partner In cold climates, conservation of fuel is always a high priority. This is especially true regarding gasoline for vehicles and heating fuel for homes. Consider this! 1. Gas stations can become very creative when trying to make their product sound cheaper than their competitors. Three stations list the price of their gasoline as seen below. Which station is really offering the cheapest gasoline? $0.72 a quart $2.95 per gallon $0.37 a pint Information you may need: 1 gallon = 4 Quarts, 1 gallon = 8 pints 3 Dimensional Analysis: Examples 1: How many miles will a person run during a 10 kilometer race? This is what we need to change 10 𝑘𝑚. 0.62 𝑚𝑖𝑙𝑒𝑠 = 6.2 𝑚𝑖𝑙𝑒𝑠 1 𝑘𝑚 The ratio allow us to change the unit that we have to another unit Example 2: Convert 25 yards to inches Example 3: Convert 84 miles to kilometers Now Your Turn: 1) Covert 10 gallons to cups. 2) 16 kilograms to ounces. 4 3) A kiddy pool holds 10 gallons of water. How many cubic meters is this? 4) A car weighs 34005 Kilograms, How much the car weigh in tons? Think about This Situation: 5. An image of a building in a photograph is 6 centimeters wide and 11 centimeters tall. If the image is similar to the actual building and the actual building is 174 meters wide, how tall is the actual building, in meters? More Practice: https://www.khanacademy.org/math/algebra/introduction-to-algebra/units-algebra/e/workingwith-units 5 Mathematician: ________________ Date: Homework: Lesson 1-3 Answer the following questions: 1. (REGENTS) Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below. Which ratio is incorrectly written to convert his speed? 3 𝑓𝑡 5280 𝑓𝑡 60 𝑠𝑒𝑐 60 𝑚𝑖𝑛 (1) (2) (3) (4) 1 𝑦𝑑 1 𝑚𝑖 1 𝑚𝑖𝑛 1 ℎ𝑟 3. Covert the following units: (a) 33 feet to yards (b) 3 liters to gallons. (c) 3 Kilograms to ounces. 6 4) Ally is baking cake on her mom’s birthday; she needs .75 quart of milk to make the cake. How many cups of milk does Ally need? 5) The moon is 250,000 miles away. How many feet is it from earth? 6) Bob and Latoya both drove to a baseball game at a college stadium. Bob lives 70 miles from the stadium and Latoya lives 60 miles from it, as shown in the accompanying diagram. Bob drove at a rate of 50 miles per hour, and Latoya drove at a rate of 40 miles per hour. If they both left home at the same time, who got to the stadium first? 7