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
You're on a roll — To make k the subject of the formula r = (2v+4)/(sqrt(2kv+k)) and simplify, we need to isolate k. Step 1: Multiply both sides by sqrt(2kv+k). rsqrt(2kv+k) = 2v+4 Step 2: Square both sides to eliminate the square root. (rsqrt(2kv+k))^2 = (2v+4)^2 r^2(2kv+k) = (2v+4)^2 Step 3: Expand the left side and factor out k. 2kvr^2 + kr^2 = (2v+4)^2 k(2vr^2 + r^2) = (2v+4)^2 Step 4: Isolate k by dividing both sides by (2vr^2 + r^2). k = ((2v+4)^2)/(2vr^2 + r^2) Step 5: Simplify the denominator by factoring out r^2. k = ((2v+4)^2)/(r^2(2v+1)) The expression for k is: k = ((2v+4)^2)/(r^2(2v+1)) 4 down, 1 left today. What's next?