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 varies as 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 the sum of the values of y when x=4 and x=100 is 15. When x=4, let y_1 = ksqrt(4) = k × 2 = 2k. When x=100, let y_2 = ksqrt(100) = k × 10 = 10k. The sum of these values is 15: y_1 + y_2 = 15 2k + 10k = 15 12k = 15 Divide by 12 to find k: k = (15)/(12) k = (5)/(4) Step 3: State the law connecting y and x. Substitute the value of k back into the variation equation from Step 1: y = (5)/(4)sqrt(x) The law connecting y and x is y = (5)/(4)sqrt(x). Last free one today — make it count tomorrow, or type /upgrade for unlimited.