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: Calculate 2q. Given vector q = -6 \\ 5 , multiply each component by 2: 2q = 2 -6 \\ 5 = 2 × (-6) \\ 2 × 5 = -12 \\ 10 Step 2: Calculate p + 2q. Given vector p = -2 \\ 5 and 2q = -12 \\ 10 , add the corresponding components: p + 2q = -2 \\ 5 + -12 \\ 10 = -2 + (-12) \\ 5 + 10 = -14 \\ 15 Step 3: Calculate the magnitude of p + 2q. The magnitude of a vector x \\ y is given by sqrt(x^2 + y^2). For p + 2q = -14 \\ 15 : |p + 2q| = sqrt((-14)^2 + (15)^2) |p + 2q| = sqrt(196 + 225) |p + 2q| = sqrt(421) Step 4: Evaluate the square root and round to two decimal places. sqrt(421) ≈ 20.5182845 Rounding to two decimal places: |p + 2q| ≈ 20.52 The value of |p + 2q| to two decimal places is: 20.52 3 done, 2 left today. You're making progress.