Joel has a summer job cutting lawns. The relationship between his profit, P , in dollars and the number of lawns cut, n , is shown by the graph below. What type of variation is the relationship, and
what is its initial value?

There is a direct relationship between the profit P and the number of lawns cut

The initial value is (0,-100)

Step-by-step explanation:

Firstly, we want to know the type of variation that is between the profit and the number of lawns.

Now, looking at the graph, we can see that as the number of lawns increase, there is a corresponding increase in the profit causing a sharp rise in the graph.

What this represents is that there is a direct relationship between the two quantities.

Now, we are told to get the initial value.

Looking at the plot, we can see that the number of lawns is the x axis while the profit is the y axis

The initial value is that point at which we have the graph intersecting the y-axis which is below the x-axis

This point is the point (0,-100)

This point gives the initial value of the relationship

the balls meet at the starting point at every 60 mins interval.

Step-by-step explanation: It is given that the speed of A is 4 rotations / 120 second

This is equal to 1 rotation / 30 sec Similarly , the speed of B is 3 rotations / 60 sec

or 1 rotation / 20 second

Now, let us take the HCF of the time taken by both the balls A and B.

i.e. HCF of 30 and 20 is 60.

Therefore , the balls meet at the starting point at every 60 mins interval.