Do you have to install a fence around the square tomato patch. Do you have enough material to create a 70 foot long fence And you need at least 49 ft.² of space for planting.

Question

A. Write a function that represents the perimeter of the garden.

b. Identify the independent and dependent variable

c. Describe the domain and range of the function.

Answer 1

Let x = length and y = width

Then, 2x + 2y = 70 and xy = 49.

Since 2x + 2y = 70, y = 35 - x

y = 35 - x

x is the independent variable

domain: 0 < x < 35

range: 0 < y < 35

x(35 - x) = 49

x² - 35x + 49 = 0

x = [35 ± √1029] / 2 = 33.539 or 1.461

The dimensions of the tomato patch would be 33.539 ft by 1.461 ft for a 70 square foot patch (There is enough fencing for maybe 1 row of tomato plants)

Answer 2

The easiest way to lay out this garden is by 7^2=49sq/ft. You'll need 7*4=28'.

To lay out a length of 70' your width would be 70*.7=49sq/ft.

7, 4, 70 independant

49, 28, 7 dependant

domain x for 49sq/ft, d=7, r=7

70 " 70 .7

range y