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
You're on a roll — Step 1: Round each number to 2 significant figures. • 44.08 ≈ 44 • 79.06 ≈ 79 • 19.54 ≈ 20 Step 2: Evaluate the estimated value. Estimated Value = (44)/(79 - 20) = (44)/(59) Estimated Value ≈ 0.74576 Step 3: Calculate the actual value of the expression. Actual Value = (44.08)/(79.06 - 19.54) = (44.08)/(59.52) Actual Value ≈ 0.74059 Step 4: Determine the percentage error. The formula for percentage error is | Actual Value - Estimated ValueActual Value | × 100\%. Percentage Error = | (0.74059 - 0.74576)/(0.74059) | × 100\% Percentage Error = | (-0.00517)/(0.74059) | × 100\% Percentage Error = 0.006981 × 100\% Percentage Error ≈ 0.698\% The estimated value is 0.74576 and the percentage error is 0.698\%. Step 1: Rearrange the equation of the circle by grouping x terms and y terms, and moving the constant to the right side. The given equation is x^2 + y^2 + 6x - 8y - 2 = 0. (x^2 + 6x) + (y^2 - 8y) = 2 Step 2: Complete the square for the x terms and y terms. For x^2 + 6x, add ((6)/(2))^2 = 3^2 = 9. For y^2 - 8y, add ((-8)/(2))^2 = (-4)^2 = 16. Add these values to both sides of the equation. (x^2 + 6x + 9) + (y^2 - 8y + 16) = 2 + 9 + 16 Step 3: Rewrite the expressions as squared terms. (x + 3)^2 + (y - 4)^2 = 27 Step 4: Identify the coordinates of the center and the radius. The standard form of a circle's equation is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius. Comparing with (x + 3)^2 + (y - 4)^2 = 27: The center (h,k) is (-3, 4). The radius squared r^2 = 27, so the radius r = sqrt(27) = sqrt(9 × 3) = 3sqrt(3). The coordinates of the center are (-3, 4) and the radius is 3sqrt(3). Got more? Send 'em!