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1 The height, in metres, of a ball is given by the equation h = 16t – 4r, where t is time in seconds. Find when the ball will reach its maximum height, and what the maximum height will be.

1 The height, in metres, of a ball is given by the equation h = 16t – 4r, where t is time in seconds. Find when the ball will reach its maximum height, and what the maximum height will be.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 15CYU
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1 The height, in metres, of a ball is given by the equation h= 16t - 4r, where t is time in seconds. Find when the ball will reach its maximum height, and what the maximum height will be. %3D 2 The cost per hour of a bike ride is given by the formula C=x - 15x + 70, where x is the distance travelled in km. Find the distance that gives the minimum cost. 3 The perimeter of a rectangle is 60 m and its length is x m. Show that the area of the rectangle is given by the equation A = 30x -x. b. b Hence find the maximum area of the rectangle. a. 4 A farmer wants to make a rectangular paddock with an area of 4000 m?. To minimise fencing costs she wants the paddock to have a minimum perimeter. 8000 Show that the perimeter is given by the equation P= 2x + a. b Find the dimensions of the rectangle that will give the minimum perimeter, correct to 1 decimal place. Calculate the cost of fencing the paddock, at $48.75 per metre.
Transcribed Image Text:1 The height, in metres, of a ball is given by the equation h= 16t - 4r, where t is time in seconds. Find when the ball will reach its maximum height, and what the maximum height will be. %3D 2 The cost per hour of a bike ride is given by the formula C=x - 15x + 70, where x is the distance travelled in km. Find the distance that gives the minimum cost. 3 The perimeter of a rectangle is 60 m and its length is x m. Show that the area of the rectangle is given by the equation A = 30x -x. b. b Hence find the maximum area of the rectangle. a. 4 A farmer wants to make a rectangular paddock with an area of 4000 m?. To minimise fencing costs she wants the paddock to have a minimum perimeter. 8000 Show that the perimeter is given by the equation P= 2x + a. b Find the dimensions of the rectangle that will give the minimum perimeter, correct to 1 decimal place. Calculate the cost of fencing the paddock, at $48.75 per metre.
5 Bill wants to put a small rectangular vegetable garden in his backyard using 2 existing walls as part of its border. He has 8 m of garden edging for the border on the other 2 sides. Find the dimensions of the garden bed that will give the greatest area. 6 Find 2 numbers whose sum is 28 and whose product is a maximum. 7 The difference of 2 numbers is 5. Find these numbers if their product is to be minimum. 8 Apiece of wire 10 m long is broken into 2 parts, which are bent into the shape of a rectangle and a square as shown. Find the dimensions x and y that make the total area a maximum. y.
Transcribed Image Text:5 Bill wants to put a small rectangular vegetable garden in his backyard using 2 existing walls as part of its border. He has 8 m of garden edging for the border on the other 2 sides. Find the dimensions of the garden bed that will give the greatest area. 6 Find 2 numbers whose sum is 28 and whose product is a maximum. 7 The difference of 2 numbers is 5. Find these numbers if their product is to be minimum. 8 Apiece of wire 10 m long is broken into 2 parts, which are bent into the shape of a rectangle and a square as shown. Find the dimensions x and y that make the total area a maximum. y.
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