This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Establish the relationship between P, Q, and R. The problem states that P varies directly as Q and inversely as the square root of R. This can be written as: P = (kQ)/(sqrt(R)) where k is the constant of proportionality. Step 2: Calculate the constant of proportionality k. We are given the values P = 8, Q = 10, and R = 16. Substitute these values into the equation: 8 = (k · 10)/(sqrt(16)) 8 = (10k)/(4) 8 = 2.5k Divide both sides by 2.5 to solve for k: k = (8)/(2.5) k = 3.2 Step 3: Determine the equation connecting P, Q, and R. Substitute the calculated value of k = 3.2 back into the general variation equation: P = (3.2Q)/(sqrt(R)) The equation connecting P, Q, and R is P = 3.2Q / √R. P = (3.2Q)/(sqrt(R)) Last free one today — make it count tomorrow, or type /upgrade for unlimited.