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Today’s Daily Quiz will be given at the end of the hour. Please close your laptops

Today’s Daily Quiz will be given at the end of the hour. Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials. Coming up : Today: Lecture on Section 6.7 (HW 37) Tomorrow: Review for Test 3

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Today’s Daily Quiz will be given at the end of the hour. Please close your laptops

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  1. Today’s Daily Quiz will be given at the end of the hour. Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials.

  2. Coming up: • Today: Lecture on Section 6.7 (HW 37) • Tomorrow: Review for Test 3 • Practice Test 3 available now, due Thursday. • Thursday: Test 3 (150 points) • 100 points on new material • 50 points on Units 1 & 2 (Test 1 & Test 2 material) • Next week: • Monday: Section 7.1 (Rational expressions) • Daily Quiz (no makeups), HW 38 due Tuesday • Tuesday:Section 10.1 (Radicals and radical functions) • AND Weekly Quiz 9 (no makeups) HW 39 due Mon. 12/2 • Although there are no classes Wed.-Fri. (Thanksgiving break), these lectures cover the two toughest sections so far, and no makeups will be given if you miss either quiz next week.

  3. Section 6.7 Applications of Polynomial Equations

  4. General strategy for solving applied (word) problems: • Understand the problem: • Read and reread the problem. • Choose a variable to represent the unknown. • Construct a drawing, whenever possible. • Translate the problem into an equation. • Solve the equation. • Check your answers in the original equation. • Interpret the result: • Determine if any or all of the proposed solutions make sensein terms of the applied problem. • Convert your answer(s) into the appropriate form to answer the specific question(s) asked in the word problem.

  5. Example Understand The product of two consecutive positive integers is 132. Find the two integers. Read and reread the problem and choose a variable to represent the unknown quanitity. If we let x = one of the unknown positive integers, then x + 1 = the next consecutive positive integer.

  6. Example (cont.) Now translate this into an equation: The product of is 132 two consecutive positive integers 132 x (x + 1) • =

  7. Example (cont.) Solve x(x + 1) = 132 x2 + x = 132 (distributive property) x2 + x – 132 = 0 (write equation in standard form) (x + 12)(x – 11) = 0 (factor quadratic polynomial) x + 12 = 0 or x – 11 = 0 (set factors equal to 0) x = -12 or x = 11 (solve each factor for x)

  8. Example (cont.) Interpret Possible solutions: x = -12 or x = 11 Remember that x is supposed to represent a positive integer. So, although x = -12 satisfies our equation, it cannot be a solution for the problem we were presented. If we let x = 11 (the first integer), then the next consecutive integer is x + 1 = 12. Check: The product of the two numbers is 11 · 12 = 132, our desired result. State Solution:The two positive integers are 11 and 12.

  9. Pythagorean Theorem(used in some homework problems in today’s assignment) In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. (leg a)2 + (leg b)2 = (hypotenuse)2 Weekend for-fun homework: See if you can find the two mistakes in the Scarecrow’s recitation of the Pythagorean theorem in this clip from the Wizard of Oz movie: http://www.youtube.com/watch?v=ky7DMCHQJZY

  10. Example Find the length of the shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotenuse is 10 miles less than twice the shorter leg.

  11. Example (cont.) Understand Read and reread the problem. If we let x = the length of the shorter leg, then x + 10 = the length of the longer leg and 2x – 10 = the length of the hypotenuse. Now draw a diagram:

  12. Example (cont.) Translate By the Pythagorean Theorem, (leg a)2 + (leg b)2 = (hypotenuse)2 x2 + (x + 10)2 = (2x – 10)2

  13. Example (cont.) Solve x2 + x2 + 20x + 100 = 4x2 – 40x + 100 (multiply the binomials) 2x2 + 20x + 100 = 4x2 – 40x + 100 (simplify left side) 0 = 2x2 – 60x (subtract 2x2 + 20x + 100 from both sides) 0 = 2x(x – 30) (factor right side) x = 0 or x = 30 (set each factor = 0 and solve) x2 + (x + 10)2 = (2x – 10)2

  14. Example (cont.) Interpret Check: Remember that x is supposed to represent the length of the shorter side. So, although x = 0 satisfies our equation, it cannot be a solution for the problem we were presented. If we let x = 30, then x + 10 = 40 and 2x – 10 = 50. Since 302 + 402 = 900 + 1600 = 2500 = 502, the Pythagorean Theorem checks out. State Solution: The length of the shorter leg is 30 miles. (Remember that is all we were asked for in this problem.)

  15. To solve this problem, we set h = 0 (since 0 = ground level). Then we solve the equation -16t2 + 144t = 0 Factoring this equation gives two answers: t = 0, which means the rocket is at ground level when it is launched, and t = 9, which tells us that the rocket returns to the ground 9 seconds after it is launched. Note: There are several problems like this in today’s homework. New question: How long will it take for the rocket to reach its peak height of 324 feet? ANSWER: Solve 324 = -16t2 + 144t Factoring gives: 4(2t – 9)(2t - 9)= 0 Answer: t = 4.5 sec.

  16. Please Note: You DO NOT have to memorize formulas for the word problems. You will have the sheet of formulas to use during quizzes and tests on this material. Also, you’ll get more out of tomorrow’s review lecture if you try Practice Test 3 once before class tomorrow. It’s not due till Thursday, but it’s open and available now.

  17. REMINDER: The assignment on today’s material (HW 37) is due at the start of the next class session. Please open your laptops and start working on the homework assignment until it is time to take the quiz at the end of the class session. You can keep your yellow formula sheets out when you take the quiz. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in on the Math 110 clipboard by the front door of the lab

  18. Please open Daily Quiz 31. If you have any time left after finishing the quiz problems, CHECK YOUR FACTORING ANSWERSbefore you submit the quiz. • A scientific calculator may be used on this quiz. • Remember to turn in your answer sheetto the TA when the quiz time is up.

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