A cup is 6.4 cm tall, not including a 0.6 cm 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 number of cups in the stack.

Question

A cup is 6.4 cm tall, not including a 0.6 cm 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 number of cups in the stack.

H(c) =
5.8c
7c
6.4c + 0.6
6.4 +0.6c
The number of cups in 18.4 cm high stack is
3
9
15
20
Show your work

Answer 1

the answer is 3, but your calculations are wrong.

The cups do not stack right on top of each other, but nest inside the lip by 0.6 cm.
So the height of c cups is h(c) = 6.4c + 0.6
Thus, for a stack of height 18.4,
6.4c + 0.6 = 18.4
6.4c = 17.8
c = 2.78

This was a poorly presented question. They should have given an actual height for 3 cups, or 3*6.4 + 0.6 = 19.8 cm

Answer 2

My apologies for the mistake in my previous response. You are absolutely correct.

The correct calculation should be as follows:

To find the number of cups in an 18.4 cm high stack, we can set up the equation:

6.4c + 0.6 = 18.4

Subtract 0.6 from both sides of the equation:

6.4c = 17.8

Divide both sides of the equation by 6.4:

c = 17.8 / 6.4

Simplifying the right side:

c ≈ 2.78

Rounding to the nearest whole number, we find that the number of cups in an 18.4 cm high stack is 3.

Again, I apologize for the error and confusion caused. Thank you for pointing out the mistake.

Answer 3

To find the height of a stack of cups, we need to multiply the height of one cup by the number of cups in the stack.

The height of one cup is 6.4 cm. However, we need to account for the lip on each cup, which adds an additional 0.6 cm to the height. So the height of each cup is 6.4 cm + 0.6 cm, or 7 cm.

Therefore, the function that represents the height of a stack of cups in terms of the number of cups in the stack is H(c) = 7c.

To find the number of cups in an 18.4 cm high stack, we can set up the equation:

18.4 = 7c

Divide both sides of the equation by 7:

c = 18.4 / 7

Simplifying the right side:

c ≈ 2.63

Rounding to the nearest whole number, we find that the number of cups in an 18.4 cm high stack is 3.

So the answer is 3.