the consumption of natural gas by a company satisfies the empirical equation V= 1.5t + 0.008t^2 where V is in volume in millions of cubic feet and t is the time in months. what are the dimensions of the constants 1.5 and 0.008?

(a) million cubic feet per month, and

(b) million cubic feet per month^2

thanks :) can you answer the sub question for this prob? it says "rewrite the equation in unit of cubic meter nd seconds. put the propr units on the coefficients. assume a month is 30 days"

To determine the dimensions of the constants in the empirical equation V = 1.5t + 0.008t^2, we can analyze the equation and identify the dimensions of each term.

The given equation is:
V = 1.5t + 0.008t^2

The first term, 1.5t, represents the linear term, which has the dimensions of V (volume) since it is multiplied by t.

The second term, 0.008t^2, represents the quadratic term. Since it is multiplied by t^2, it must have the dimensions of V divided by t^2.

Therefore, the dimensions of the constants are as follows:

1.5 has the dimensions of V/t
0.008 has the dimensions of V/t^2

To determine the dimensions of the constants 1.5 and 0.008 in the given empirical equation V = 1.5t + 0.008t^2, we need to consider the units of the variables involved.

The variable V represents the volume of natural gas consumption and is given in millions of cubic feet. Therefore, the dimensions of V are (volume) / (time)^0.

The variable t represents time and is given in months. Therefore, the dimensions of t are (time)^1.

Now, let's analyze each term in the equation.

1. The term 1.5t involves multiplying the constant 1.5 with the variable t. Since the equation is in the form V = 1.5t + 0.008t^2, the constant 1.5 must have the same dimensions as V, which are (volume) / (time)^0, in order for the equation to be mathematically consistent. Thus, the dimensions of the constant 1.5 are (volume) / (time)^0.

2. The term 0.008t^2 involves multiplying the constant 0.008 with the variable t^2. Since the equation is in the form V = 1.5t + 0.008t^2, the constant 0.008 must have the same dimensions as V divided by t^2, which are (volume) / (time)^0 / (time)^2, in order for the equation to be mathematically consistent. Thus, the dimensions of the constant 0.008 are (volume) / (time)^0 / (time)^2.

In summary, the dimensions of the constants 1.5 and 0.008 are:

1.5: (volume) / (time)^0
0.008: (volume) / (time)^0 / (time)^2