Stackable polystyrene cups have a height h1=12.5 cm. Two stacked cups have a height of h2=14 cm. Three stacked cups have a heigh

Answer:

hx = 1.5 cm·x + 11 cm

126 cups

Step-by-step explanation:

We define the following ordered pairs (x, hx).

• (1, 12.5 cm)

• (2, 14 cm)

• (3, 15.5 cm)

We need to find a linear equation represented as:

hx = a·x + b

where,

a is the slope

b is the y-intercept

In order to determine the slope, we select any pair of values to insert into a specific expression.

hx = 1.5 cm·x + b

Next, we can substitute in an ordered pair to find b. Let's utilize h1.

h1 = 1.5 cm·x1 + b

12.5 cm = 1.5 cm·1 + b

b = 11 cm

The final equation is:

hx = 1.5 cm·x + 11 cm

200 cm = 1.5 cm·x + 11 cm

189 cm = 1.5 cm·x

x = 126

Answer:

Approximately 59 stacked cups.

Step-by-step explanation:

We have the following measurements:

Height of one cup = 12.5 cm,

Height of two cups stacked = 14 cm,

Height of three cups stacked = 15.5 cm,

...and so on.

This situation can be described by an arithmetic sequence,

12.5, 14, 15.5,....

The first term is defined as a = 12.5,

with a common difference of d = 1.5 cm.

Thus, the height of x stacked cups is given by

As per the problem,

h(x) = 200

⇒ 1.5x + 11 = 200

⇒ 1.5x = 189

⇒ x = 59.3333333333 ≈ 59.

Therefore, you will need approximately 59 stacked cups.