Math 154 Chapter 7.7: Applications of Quadratic Equations Objectives:
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1 Math 154 Chapter 7.7: Applications of Quadratic Equations Objectives: Products of numbers Areas of rectangles Falling objects Cost/Profit formulas Products of Numbers Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles E: The product of two positive numbers is 135. One number is 3 less than twice the other number. Find the numbers. Let = Then = ( ) the other number times the one number product of the numbers Answer: 9 = the other number 15 = the one number 1. The product of two positive numbers is 13. One number is 4 more than three times the other number. Find the numbers. Let = Then = ( ) the other number times the one number product of the numbers Answer: 6 = the other number = the one number
2 Areas of Rectangles Area of a rectangle formula: area = (length)(width) E: The length of a rectangle is 7 feet more than twice the width. The rectangle has an area of 85 square feet. Find the length and width of the rectangle. Let = Then = ( ) the width times the length area of the rectangle Answer: 5 feet = the width 17 feet = the length 1. The width of a rectangle is 9 feet less than 5 times the length. The rectangle has an area of 48 square feet. Find the length and width of the rectangle. Let = Then = ( ) the width times the length area of the rectangle Answer: 8 feet = the length 31 feet = the width
3 Falling Objects Falling objects formula: feet 16(seconds) d 16t E: An object falls from a 64-foot building. How long does it take for the object to hit the ground? Let = distance 16 times time squared Answer: seconds = time it takes to hit the ground 1. An object falls from a 56-foot building. How long does it take for the object to hit the ground? Let = distance 16 times time squared Answer: 4 seconds = time it takes to hit the ground
4 Cost/Profit Formulas E: A company calculated its daily profit, P, to be P 14 35, where is the number widgets sold. How many widgets must be sold in one day if you want a daily profit of $05? Let = daily profit profit formula Answer: 4 = number of widgets that must be sold to make $05 1. A company calculated its daily cost, C, to be C 13 38, where is the number widgets produced. How many widgets must be produced if you want the daily cost to be $30? Let = daily cost cost formula Answer: 17 = number of widgets that must be produced to cost $30.
5 Pythagorean Theorem Finding Legs of Right Triangles E: Find the missing leg by using the Pythagorean Theorem, a b c Let = Answer: 8 = the missing leg 1. Find the missing leg by using the Pythagorean Theorem, a b c Let = Answer: 4 = the missing leg
6 Finding Hypotenuses of Right Triangles 1. E: Find the missing hypotenuse by using the Pythagorean Theorem, a b c Let = Answer: 5 = the missing hypotenuse. Find the missing hypotenuse by using the Pythagorean Theorem, a b c. 8 6 Let = Answer: 10 feet = the missing hypotenuse
7 Application Problems Involving Right Triangles E: One leg of a right triangle is four inches more than twice the other leg. The hypotenuse is 6 inches. Find the lengths of the three sides of the triangle. Let = Then _= 6 +4 Answer: 10 inches = the other leg 4 inches = the one leg. The diagonal of a rectangle is 5 inches. Find the length and width of the rectangle if the length is three more than three times the width. Let = Then _= Answer: 7 inches = the other leg 4 inches = the one leg
8 Application Problems Involving Right Triangles E: A ladder is leaning against a building. The distance of the ground between the bottom of the ladder to the building is 18 feet less than the length of the ladder. Also, the ladder reaches up the wall 4 feet less than the length of the ladder. Find the length of the ladder, distance of the ground between the bottom of the ladder to the building, and distance the ladder reaches up the wall. Let = Then _= Then _= Answer: 34 feet = the length of the ladder 16 feet = distance of the ground between the bottom of the ladder to the building 30 feet = distance the ladder reaches up the wall 1. A tree is supported by ropes. One rope goes from the top of the tree to a point on the ground. The height of the tree is 1 foot more than the distance between the base of the tree and the rope anchored in the ground. The length of the rope is 1 foot less than twice the distance between the base of the tree and the rope anchored in the ground. Find the distance between the base of the tree and the rope anchored in the ground, the height of the tree, and the length of the rope. Let = Then _= Then _= Answer: 3 feet = the distance between the base of the tree and the rope anchored in the ground 4 feet = the height of the tree 5 feet = the length of the rope
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