Answer:
Part A
The height of the stack made of 8 containers is 19.6 cm
Part B
When the tower is 40.6 cm tall, the number of containers in the set are 22 containers
Part C
(Disagree) The height of a single container is 9.1
Step-by-step explanation:
The question relates to containers, stacked one inside the other such that the height increases by only the wider top edge of the containers
The given expression that gives the height of the stack is presented as follows;
1.5·c + 7.6
Where;
c = The number of containers in the stack
Part A
When there are 8 containers, we have;
h(8) = 1.5 × 8 + 7.6 = 19.6
The height of the stack made of 8 containers, h(8) = 19.6 cm
Part B
When the tower (height of the stack set) is 40.6 cm tall, we have;
h(c) = 1.5·c + 7.6 = 40.6
∴ The number of containers, c = (40.6 - 7.6)/1.5 = 22
When the tower is 40.6 cm tall, the number of containers in the set, c = 22 containers
Part C
Given that the height stack increases only by the thickness of the wider rim of each added container, we have;
The expression for the height of the stack , 1.5·c + 7.6, is the expression for a straight line equation, m·x + c
The thickness of each rim = The slope, of the line, m = The increase in height with number of containers = 1.5
The number of containers (The independent variable, x) = The number of stacked rims = c
The minimum height = The height of a single container = 1.5 × 1 + 7.6 = 9.1
Therefore, the height of a single container = 9.1 not 7.6
= 17/2
