Answer:
Approximately 59 stacked cups.
Step-by-step explanation:
Given,
Height of a cup = 12.5 cm,
Two stacked cups = 14 cm,
Three stacked cups = 15.5 cm,
........, so on,....
Thus, there is an AP that represents the given situation,
12.5, 14, 15.5,....
First term is, a = 12.5,
Common difference, d = 1.5 cm,
Thus, the height of x cups is,
[tex]h(x) = a+(x-1)d = 12.5 + (x-1)1.5 = 1.5x + 11[/tex]
According to the question,
h(x) = 200
⇒ 1.5x + 11 = 200
⇒ 1.5x = 189
⇒ x = 59.3333333333 ≈ 59,
Hence, approximately 59 stacked cups will need.
Answer:
hx = 1.5cm . x + 11 cm
126 cups
Step-by-step explanation:
We have the following ordered pairs (x, hx).
We are looking for a linear equation of the form:
hx = a.x + b
where,
a is the slope
b is the y-intercept
To find the slope, we take any pair of ordered values and replace their values in the following expression.
[tex]a=\frac{\Delta hx }{\Delta x} =\frac{h2-h1}{2-1} =\frac{14cm-12.5cm}{2-1} =1.5cm[/tex]
Now, the general form is:
hx = 1.5cm . x + b
We can take any ordered pair and replace it in this expression to find b. Let's use h1.
h1 = 1.5cm . x1 + b
12.5 cm = 1.5 cm . 1 + b
b = 11 cm
The final equation is:
hx = 1.5cm . x + 11 cm
If hx = 200 cm,
200 cm = 1.5cm . x + 11 cm
189 cm = 1.5cm . x
x = 126
