Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10.8, Problem 12CFU

To determine

Find the system of second degree equations that models the situation.

Expert Solution

Answer to Problem 12CFU

x2+y2=680 and y2−x2=288

Explanation of Solution

Given information:

A garden is having two square flowerbeds. The total area of the flowerbed is 680 sq. feet and the second bed has 288 sq. feet more than the first.

Calculation:

Here, let us suppose that the two square flowerbeds have sides x and y .

Now, we will make the system of equations according to the given situation:

x2+y2=680..........(1)y2−x2=288..........(2)

Hence, the required answer is x2+y2=680 and y2−x2=288 .

To determine

Estimate the solution and make the graph.

Expert Solution

Answer to Problem 12CFU

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 12CFU , additional homework tip 1

Explanation of Solution

Given information:

A garden is having two square flowerbeds. The total area of the flowerbed is 680 sq. feet and the second bed has 288 sq. feet more than the first.

Calculation:

Here, we will make the graph using the equations:

x2+y2=680..........(1)y2−x2=288..........(2)

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 12CFU , additional homework tip 2

Now,The point of intersection=(14,22)∴ First flower bed=14 ft by 14 ftSecond flower bed=22 ft by 22ft

Hence, the results are shown in the above graph.

To determine

Find the length of each flowerbed within the garden.

Expert Solution

Answer to Problem 12CFU

x=14, y=22

Explanation of Solution

Given information:

A garden is having two square flowerbeds. The total area of the flowerbed is 680 sq. feet and the second bed has 288 sq. feet more than the first.

Calculation:

Here,Add both the equations:x2+y2+y2−x2=680+2882y2=968y2=484y=484∴y=22Put 22 in:x2+484=680x2=680−484x2=196x=196∴x=14

Hence, the required answer is x=14, y=22 .

Chapter 10.8, Problem 11CFU

Chapter 10.8, Problem 13E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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