The total revenue r (in dollars) is directly proportional to the number of units sold x. when 500 units are sold, the total revenue is $4825. write a mathematical model that relates the total revenue r to the number of units sold x.

y = 9.65x

Step-by-step explanation:

Given that total revenue is directly proportional to the number of units sold

Let the number of units sold be represented by x and the total revenue be represented by y

Given y∝x

y = kx where k is some constant

Also given that when 500 units are sold, the total revenue is $4825.

Here y=4825 and x=500

Now

k=9.65

Therefore the equation representing the relation between the total revenue and the number of units sold is

y = 9.65x

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18