Final answer:
To find the constant of proportionality k when m is jointly proportional to u and q with given values for these variables, substitute the values into the equation m = k · u · q and solve for k. The calculated value is approximately 0.1905.
Step-by-step explanation:
When it is said that m is jointly proportional to u and q, we can write an equation m = k · u · q, where k is the constant of proportionality. To find the value of k, use the given values of m, u, and q. Since m is 8 when u is 6 and q is 7, we can plug these values into the equation and solve for k: 8 = k · 6 · 7. Solving for k, we get k = 8 / (6 × 7), which simplifies to k = 8 / 42, or k = 1 / 5.25. Therefore, the constant of proportionality k is 1/5.25 or approximately 0.1905.