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: Write the variation equation. The problem states that y is directly proportional to sqrt(x). This can be written as: y = ksqrt(x) where k is the constant of proportionality. Step 2: Use the given information to find the constant k. We are given that y=12 when x=4. Substitute these values into the equation: 12 = ksqrt(4) 12 = k(2) Divide by 2 to find k: k = (12)/(2) k = 6 Step 3: State the law connecting y and x. Substitute the value of k back into the variation equation from Step 1: y = 6sqrt(x) Step 4: Find y when x=25. Substitute x=25 into the law found in Step 3: y = 6sqrt(25) y = 6 × 5 y = 30 The law connecting y and x is y = 6sqrt(x). When x=25, y = 30. 3 done, 2 left today. You're making progress.