a cup is 6.4cm tall, not including a 0.6cm lip. cups are stacked inside one another. you may want to draw a diagram to help you see how the height of the stack of cups increases. select the function that represents the height of a stack of cups in terms of the numbers of cups in the stack.
H(c)=
the number of cups in a 18.4cm high stack is:
To find the function that represents the height of a stack of cups in terms of the number of cups in the stack, we need to analyze the pattern and determine the relationship between the height of the stack and the number of cups.
From the given information, we know that each cup is 6.4cm tall and has a 0.6cm lip. This means that the effective height of each cup is 6.4cm - 0.6cm = 5.8cm.
If we stack only one cup, the height of the stack would be 5.8cm.
If we stack two cups, the height of the stack would be 5.8cm + 5.8cm = 11.6cm.
If we stack three cups, the height of the stack would be 5.8cm + 5.8cm + 5.8cm = 17.4cm.
We can see that the height of the stack increases by 5.8cm for each additional cup added.
Based on this pattern, we can formulate the following function:
H(c) = 5.8c
where H(c) represents the height of the stack of cups in centimeters and c represents the number of cups in the stack.
To determine the number of cups in an 18.4cm high stack, we need to solve the equation H(c) = 18.4 for c:
5.8c = 18.4
Divide both sides of the equation by 5.8:
c = 18.4 / 5.8
c ≈ 3.17
Therefore, the number of cups in an 18.4cm high stack is approximately 3 cups.