Find a mathematical model representing the statement. (Determine the constant of proportionality.)

v varies jointly as p and q and inversely as the square of s. (v = 2.1 when p = 4.2, q = 5.4 and s = 2.4.)

v =

kpq/s^2 or v = kpq/s^2

To determine the constant of proportionality, substitute the given values into the equation:

2.1 = k(4.2)(5.4)/(2.4)^2

Simplifying the equation:

2.1 = k(22.68)/5.76

2.1 * 5.76 = 22.68k

12.096 = 22.68k

Divide both sides by 22.68:

k = 12.096 / 22.68

k ≈ 0.533

To find the mathematical model representing the statement, "v varies jointly as p and q and inversely as the square of s," we can use the formula for direct variation and inverse variation.

Direct Variation: When two quantities vary directly, one quantity is a constant multiple of the other. In this case, v varies directly with both p and q.

Inverse Variation: When two quantities vary inversely, their product is a constant. In this case, v varies inversely with the square of s.

Based on these relationships, we can write the mathematical model as:

v = k * (p * q) / (s^2)

Now, we need to find the constant of proportionality, k. To do this, we can use the given information: "v = 2.1 when p = 4.2, q = 5.4, and s = 2.4."

Substituting these values into the equation, we have:

2.1 = k * (4.2 * 5.4) / (2.4^2)

Simplifying this equation, we can calculate the value of k.

v = k*pq/s^2

Now just plug in the numbers to find k.