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
37. Given that b varies directly as the square root of a, and b=2 when a=9, then the equation connecting b and a is: Step 1: Write the direct variation relationship. If b varies directly as the square root of a, we can write this relationship as: b = ksqrt(a) where k is the constant of proportionality. Step 2: Use the given values to find the constant k. We are given that b=2 when a=9. Substitute these values into the equation: 2 = ksqrt(9) 2 = k · 3 Step 3: Solve for k. Divide both sides by 3: k = (2)/(3) Step 4: Write the final equation connecting b and a. Substitute the value of k back into the direct variation equation: b = (2)/(3)sqrt(a) The correct option is [C] b = (2)/(3)sqrt(a).