6. A landscaping company is trying to create a formula to predict the amount of time, t, required to mow a yard based on the area of the yard, A, the speed of the mower, v, and the width of the mower, w. One employee suggests a formula of t = 1.15 * A/(vw) Does this formula make sense? Explain .

The formula makes sense

Step-by-step explanation:

For illustration purposes, we will assume the yard is a rectangle ( such assumption does not in any way invalid the arguments that follows

Dimensions of the yard

L = 10 m

w = 4 m

A = 40 m²

Arguments:

1.- The required time (t)  is proportional to the area (A). That means ( keeping all parameters fixed but Area ) we need more time to mow a bigger area yard. Then  t ∝ A

You can see that if the yard is 40 m²  you will take let´s say 0,5 day and you will need more time if the area is 100 m² ( it seems obvious )

2.- Let´s now assume the width of the mower is 1 m if you move along the length you will need to go forward and backward  4 times. Now think about a mower of 4 m ( it does not matter if that machine exists or no, is just a mental experiment) in that case you only need one pass, then the required time is inversely proportional to the width of the mower. That means a bigger width of the mower minor required time. Then t ∝ 1/w

3.-If now we keep the width of the mower but increased the speed of the machine we will reduce the working time. Time is an inversely proportional function of the speed of the machine since each required pass will take less time. Then  t ∝ 1/v

We have evaluated three parameters A, w, and v ( area, the width of the mower,  and speed ) and demonstrated the way each of these parameters influences the time, so far we don´t know how much each of them contributes  in the total output, for that we have to measure and get conclusions, Furthermore coefficient 1,15 (in formula seems to take into account the hole combinations of the factors)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

i use my brain for prombles like this maybe you could try it

step-by-step explanation: