Question

Help please am stuck​ tap on picture for full question

Answer 1

h = 9n

Explanation:

Since h (height) is a function of number of DVDs then we can express in the form of:

`\displaystyle{h = an+b}`

where h is height, a is rate of change, n is number of DVD and b is the initial height which of course is 0 (proportional). Henceforth, we will be with the equation:

`\displaystyle{h = an}`

Next, we will be finding the rate of change of how much the dependent values change with respect to the independent values. That can be expressed as:

`\displaystyle{a = (h_2 - h_1)/(n_2-n_1) = (\Delta h)/(\Delta n)}`

delta means "change of/in"

We will pick
`\displaystyle{(n_1,h_1) = (2,18)}` and
`\displaystyle{(n_2, h_2) = (3,27)}`. Therefore, substitute in the rate of change formula:

`\displaystyle{a = (27-18)/(3-2)}\\\\\displaystyle{a = (9)/(1)}\\\\\displaystyle{a = 9}`

Therefore, the rate of change is 9. Substitute a = 9 in and therefore, the equation for the table is:

`\displaystyle{h = 9n}`