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

Question

3 months ago

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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

t of h3=15.5 cm. Find the equation for hx= 1.5 x+ Your friend is 200 cm tall. Find out how many cups you will need to reach the height of your friend. cups

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-03-02T17:41:25+03:00

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.

$a=\frac{\Delta hx }{\Delta x} =\frac{h2-h1}{2-1} =\frac{14cm-12.5cm}{2-1} =1.5cm$

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

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AnnZ [12.3K] · Answer 2 · 2026-03-02T17:42:08+03:00

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

$h(x) = a+(x-1)d = 12.5 + (x-1)1.5 = 1.5x + 11$

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.