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: Make k the subject of the relation. Given the relation: y = (4m(k+x))/(k+2x) Multiply both sides by (k+2x): y(k+2x) = 4m(k+x) Expand both sides: yk + 2xy = 4mk + 4mx Gather terms containing k on one side and terms without k on the other side: 2xy - 4mx = 4mk - yk Factor out k from the right side: 2xy - 4mx = k(4m - y) Divide by (4m - y) to isolate k: k = (2xy - 4mx)/(4m - y) So, the subject of the relation is k = (2xy - 4mx)/(4m - y). Step 2: Find the value of k. Substitute the given values x=3, y=-2, and m=1 into the expression for k: k = (2(3)(-2) - 4(1)(3))/(4(1) - (-2)) Calculate the numerator: 2(3)(-2) - 4(1)(3) = -12 - 12 = -24 Calculate the denominator: 4(1) - (-2) = 4 + 2 = 6 Now, divide the numerator by the denominator: k = (-24)/(6) k = -4 The value of k is -4. Send me the next one 📸