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Section 7.6: More Applications of Quadratic Equations

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7.6 Lecture Guide: More Applications of Quadratic Equations Objective: Use quadratic equations to solve word problems.

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Strategy for Solving Word Problems: Step 1: Read the problem carefully to determine what you are being asked to find. Step 2: Select a variable to represent each unknown quantity. Specify precisely what each variable represents. Example Find two consecutive even integers whose product is 48.

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Strategy for Solving Word Problems: Example Find two consecutive even integers whose product is 48. Step 3: If necessary, translate the problem into word equations. Then translate the word equations into algebraic equations.

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Strategy for Solving Word Problems: Example Find two consecutive even integers whose product is 48. Step 4: Solve the equation(s), and answer the question asked by the problem. Step 5: Check the reasonableness of your answer.

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If triangle ABC is a right triangle, then: The Pythagorean Theorem Algebraically Verbally The sum of the areas of the squares formed on the legs of a right triangle is equal to the area of the square formed on the hypotenuse. (The converse of this theorem is also true. If, then triangle ABC is a right triangle.)

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Use the Pythagorean Theorem to find the length of the side that is not given. 1. b 7 4

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Use the Pythagorean Theorem to find the length of the side that is not given. 2. 6 c 3

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Use the Pythagorean Theorem to find the length of the side that is not given. 3. b 26 24

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Use the Pythagorean Theorem to find the length of the side that is not given. 4. 36 c 15

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5. The hypotenuse of a right triangle is 4 centimeters less than three times length of the shortest leg. The longer leg is 4 centimeters more than twice the length of the shortest leg. What is the length of each side? Applying the Pythagorean Theorem

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6. A 42-inch wide screen television is advertised as having a 8:5 aspect ratio. (The aspect ratio is the ratio of the width to the height of the screen.) Determine the actual dimensions and the viewable area of this television.

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7. Two airplanes depart simultaneously from an airport. One flies due south; the other flies due east at a rate 20 miles per hour faster than that of the first airplane. After 4 hours radar indicates that the airplanes are 800 miles apart. What is the ground speed of each airplane? Round the speed to the nearest whole number. Applying the Pythagorean Theorem

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Finding Dimensions 8. If each side of a square is increased by 10 inches, the total area of both the new square and the original square will be 210 square inches. What is the length of each side of the original square? Round to the nearest tenth of an inch.

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Determining Height 9. The height in feet of a ball thrown off the roof of a building is given by, where t represents the time in seconds since the ball was thrown. This function is also represented in the graph and table below. Answer each question below algebraically. Use the graph and the table to verify your results. Time (sec) Height (ft) Time (sec)Height (ft) 0.075 0.5101 1.0119 1.5129 2.0131 2.5125 3.0111 3.589 4.059 4.521

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(a) Determine the initial height of the ball. 9. The height in feet of a ball thrown off the roof of a building is given by, where t represents the time in seconds since the ball was thrown. (b) Determine the time when the ball hit the ground.

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(c) Determine the time when the ball reaches is maximum height. 9. The height in feet of a ball thrown off the roof of a building is given by, where t represents the time in seconds since the ball was thrown. (d) Determine the maximum height of the ball.

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(e) Determine time interval when the height of the ball is increasing. 9. The height in feet of a ball thrown off the roof of a building is given by, where t represents the time in seconds since the ball was thrown. (f) Determine time interval when the height of the ball is decreasing.

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(g) Determine the time interval when the ball is above 100 ft. 9. The height in feet of a ball thrown off the roof of a building is given by, where t represents the time in seconds since the ball was thrown.

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Calculating an Interest Rate rate is necessary for $12,000 to grow to $12,484.80? what interest 10. If the formula computing the amount A of an investment of principal P invested at interest rate r for 1 year and compounded semiannually is

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