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 the formula for the perimeter of a sector. The total rope length represents the perimeter of the sector. The perimeter P of a sector is given by the formula P = 2r + L, where r is the radius and L is the arc length. Given: Perimeter P = 18 cm Radius r = 2 cm (interpreting "c.2 cm" as 2 cm) Step 2: Calculate the arc length L. Substitute the given values into the perimeter formula: 18 = 2(2) + L 18 = 4 + L Subtract 4 from both sides to find L: L = 18 - 4 L = 14 cm Step 3: Calculate the angle of the sector in radians. The formula for arc length is L = r, where is the angle in radians. Substitute the values for L and r: 14 = 2 Divide by 2 to find : = (14)/(2) = 7 radians The size of the angle of the sector is 7 radians. Send me the next one 📸