Question

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square. The total length of each row of bookshelves will be "4" /"5" of the length of the storage space. Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points) Write a function that expresses f(x). (10 points)   Graph the function. (10 points)

Answer 1

Answer:

1) $y=\frac{4}{5}*\sqrt{x}$ 2) Check below

Step-by-step explanation:

f(x) = Total length of a row of bookshelves

1) The Warehouse is a square, and Isabel takes 100ft² or in case She takes up to the whole 8100 ft² area,  as  it's another square. Then its lenghts are congruent and equal to 10 ft or to 90ft. Then

x=100 $A_{square} =100\\ \sqrt{100} = \sqrt{l^{2}}\\ 10=l$ or

x=8100 $A_{square} =8100\\ \sqrt{8100} = \sqrt{l^{2}}\\ 90=l$

y or f(x)=  total length of a row of bookshelves

Modelling the function:

$y=\frac{4}{5}*\sqrt{x}$

$y=\frac{4}{5}*\sqrt{100}$

$y=\frac{4}{5}*\sqrt{8100}$

x | y

100 |  8

(...) |  (...)

8100 | 72

So the Domain = [100, 8100] and the Range [8, 72]

According to this function for an area of 100 ft², the length of bookshelves are 8 ft.  Until 72 feet for an area of 8100 ft²

100 ≤ x ≤ 8100 and therefore 8 ≤ y ≤ 72

2) Function graphed below. Notice that it fits either value for x as, x fits for the area. And the Domain and the Range well defined.

Answer 2

Area = 8,100 square feet

area of a square = a²

8,100 square feet = a²

√8,100 square feet = √a²

90 feet = a

total length each row of bookshelf is 4/5 of the length of the storage space.

90 feet * 4/5 = (90*4)/5 = 360/5 = 72 feet.

Area = (72 ft)²

Area = 5,184 square feet.