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: Identify the given values and their absolute errors. We are given: x = -1.73 with an absolute error x = 0.002 y = 2.17 with an absolute error y = 0.009 We need to find the error in the determination of the term Z = x^2 - y^2. Step 2: Calculate the nominal value of Z. Z = x^2 - y^2 Z = (-1.73)^2 - (2.17)^2 Z = 2.9929 - 4.7089 Z = -1.716 Step 3: Determine the absolute error for x^2 and y^2. For a function f(u) = u^n, the absolute error is given by f = |n u^n-1| u. For x^2: (x^2) = |2x| x (x^2) = 2 × |-1.73| × 0.002 (x^2) = 2 × 1.73 × 0.002 (x^2) = 0.00692 For y^2: (y^2) = |2y| y (y^2) = 2 × |2.17| × 0.009 (y^2) = 2 × 2.17 × 0.009 (y^2) = 0.03906 Step 4: Calculate the total absolute error for Z = x^2 - y^2. When quantities are added or subtracted, their absolute errors add up to give the maximum possible absolute error. Z = (x^2) + (y^2) Z = 0.00692 + 0.03906 Z = 0.04598 Step 5: Round the error to an appropriate number of significant figures. The input errors (0.002 and 0.009) are given to one significant figure. It is common practice to round the final absolute error to one significant figure. Z ≈ 0.05 The error in the determination of the term x^2 - y^2 is 0.05. Last free one today — make it count tomorrow, or type /upgrade for unlimited.