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
Here are the solutions to the problems: 1. Find ^2 \, d. Step 1: Use substitution. Let u = . Step 2: Differentiate u with respect to : du = \, d. Step 3: Substitute u and du into the integral: u^2 \, du Step 4: Integrate with respect to u: u^2+12+1 + C = (u^3)/(3) + C Step 5: Substitute back u = : (^3 )/(3) + C The final answer is (^3 )/(3) + C. 2. Use the matrix method to solve the following simultaneous equations: 3x + 4y = 2 5x - 6y = 16 Step 1: Write the system in matrix form AX = B: 3 & 4 \\ 5 & -6 x \\ y = 2 \\ 16 Step 2: Find the determinant of matrix A: (A) = (3)(-6) - (4)(5) = -18 - 20 = -38 Step 3: Find the inverse of matrix A, A^-1: A^-1 = (1)/((A)) -6 & -4 \\ -5 & 3 = (1)/(-38) -6 & -4 \\ -5 & 3 = (3)/(19) & (2)/(19) \\ (5)/(38) & -(3)/(38) Step 4: Calculate X = A^-1B: x \\ y = (3)/(19)