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.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56df9dae-fefa-42d0-9d05-38b84ce2f9c0%2F6e063f5b-7d3b-47f3-949f-47ffe1d5311e%2Fa46w9d_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56df9dae-fefa-42d0-9d05-38b84ce2f9c0%2F6e063f5b-7d3b-47f3-949f-47ffe1d5311e%2F4we2alh_processed.jpeg&w=3840&q=75)
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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