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: Divide both sides by 2. h = 2 sqrt((l-U)/(g-U)) (h)/(2) = sqrt((l-U)/(g-U)) Step 2: Square both sides of the equation to remove the square root. ((h)/(2))^2 = (sqrt((l-U)/(g-U)))^2 (h^2)/(4^2) = (l-U)/(g-U) Step 3: Multiply both sides by (g-U) to eliminate the denominator. (h^2)/(4^2)(g-U) = l-U Step 4: Expand the left side of the equation. (h^2g)/(4^2) - (h^2U)/(4^2) = l-U Step 5: Collect all terms containing U on one side and terms not containing U on the other side. Add (h^2U)/(4^2) to both sides and subtract l from both sides. (h^2g)/(4^2) - l = (h^2U)/(4^2) - U Step 6: Factor out U from the terms on the right side. (h^2g)/(4^2) - l = U((h^2)/(4^2) - 1) Step 7: Divide both sides by ((h^2)/(4^2) - 1) to isolate U. U = (h^2g)/(4^2) - l(h^2)/(4^2) - 1 Step 8: Simplify the expression by multiplying the numerator and the denominator by 4^2. U = (4^2(h^2g)/(4^2) - l)4^2((h^2)/(4^2) - 1) U = (h^2g - 4^2l)/(h^2 - 4^2) The final answer is U = (h^2g - 4^2l)/(h^2 - 4^2).