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
Hey lemloyvette458, good to see you again. To express 3 x - 4 x in the form R(x + ), we use the compound angle formula for cosine: (A+B) = A B - A B. Step 1: Expand R(x + ). R(x + ) = R( x - x ) R(x + ) = (R ) x - (R ) x Step 2: Compare coefficients with 3 x - 4 x. By comparing the coefficients of x and x: R = 3 (Equation 1) R = 4 (Equation 2) Step 3: Find R. Square both equations and add them: (R )^2 + (R )^2 = 3^2 + 4^2 R^2^2 + R^2^2 = 9 + 16 R^2(^2 + ^2 ) = 25 Since ^2 + ^2 = 1: R^2 = 25 Given R > 0: R = sqrt(25) = 5 Step 4: Find . Divide Equation 2 by Equation 1: (R )/(R ) = (4)/(3) = (4)/(3) Since 0 < < 90^, is in the first quadrant. = ((4)/(3)) ≈ 53.13^ Step 5: Write the final expression. Substitute the values of R and into R(x + ): 3 x - 4 x = 5(x + 53.13^) The final answer is 5(x + 53.13^). Send me the next one 📸