Problem-Solving Scenarios in Mathematics

Explore various mathematical problems including rational functions, equations, time and distance calculations, exam grades, and cost analysis. Work through scenarios such as solving equations, finding wind speed, improving grades, and determining annual costs. Enhance your problem-solving skills with practical mathematical applications.

• Mathematics
• Problem-solving
• Equations
• Rational functions
• Time calculations

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Uploaded on Sep 14, 2024 | 0 Views

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Presentation Transcript

1. Warm Up. State the end behavior of the following functions:

2. Warm Up Identify the transformations and graph the following functions

3. 8-6 Solving Rational Functions Today s Objective: I can solve a rational equation.

4. Solving Rational Equations Multiply to eliminate the fractions. 6 ?+? 2 ? (? + 2)(? 2) (2?) 2= 4 ? + 2+ ? 2= 1 ? 2= 2?(4) 6 ? +2? 2? 2(? 2) +?(? + 2) = (? + 2)(? 2) +?2 2? 4 + ?2+ 2? = ?2 4 = 8? 12 ?2 8? + 12 = 0 4? = 0 (? 2)(? 6) = 0 ? = 2or ? = 6 ? = 0

5. I can clean my garage in 4 hours. My son, Ethan, can clean it in 9 hours. How long will it take if we work together? 1 What fraction of the garage will be cleaned by me in 1 hour? 4 x What fraction of the garage will be cleaned by me in x hour? 4 x What fraction of the garage will be cleaned by Ethan in x hour? What expression can we write if we work together? 9 + x 13 = = 9 4 36 36 . 2 = x x x 2 hours 45 minutes + = ( ) 1 x x 36 4 9 77

6. A flight across the U.S. takes longer going west than it does going east. The time for a round trip Chicago to San Francisco (1850 miles one way) is 7.75 hours. If the airplane cruises at 480 miles per hour, what is the speed of the wind? x = the speed of the wind ???????? ???? Distance = Rate time Time = 1850 480 + ?+ 1850 480 ?= 7.75 ? = 35 ?? Distance Rate Time 1850 480 + ? 1850 480 + x Eastbound p.546:15-29 odd, 37, 39, 43, 45 p.526:21-22 1850 480 ? 1850 Westbound 480 x

7. Grades You earned an 82% on your first test. How many consecutive 100% test scores do you need to bring your average up to 97%. So you don t have to take the final. Assume that each test has equal impact on the average grade. 82 100? + 100 + 100? = 0.97 ? = 5

8. Cost over Time Problems A new High Definition TV costs $1600 and uses $15 of electricity a year. How long do I have to own the TV to have an average annual cost of $100 or less? + 5 15 5 What would be the average annual cost of owning the TV for 5 years? 1600 = 335 1600 + 15 x What would be the average annual cost of owning the TV for x years? = 100 x 18 = 82 . years x

9. If Elaine is working alone, she can complete a job in 10 minutes. If she works with Jose, they can complete the job in 6 minutes. How long will it Jose to complete the job alone? Fraction of the job for Elaine in 6 minutes? 10 ( Fraction of the job for Jose in 6 minutes? 1 = ) x 10 = x 4 60 = x = 15 6 6 + x 10 x x + 6 60 15 minutes

10. Pg. 538 problem 5 Gas mileage