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: Determine the fraction of the circle represented by the minor sector. The circle is divided into two sectors in the ratio 3:7. The total number of parts is 3 + 7 = 10. The minor sector corresponds to the smaller ratio, which is 3. So, the minor sector represents (3)/(10) of the entire circle. Step 2: Calculate the angle of the minor sector in radians. A full circle is 2 radians. The angle of the minor sector is: = (3)/(10) × 2 = (6)/(10) = (3)/(5) radians Step 3: Calculate the length of the minor arc. The formula for the arc length L of a sector is L = r, where r is the radius and is the angle in radians. Given radius r = 7 cm. Substitute the values: L = 7 × (3)/(5) L = (21)/(5) Using ≈ 3.14159: L ≈ (21 × 3.14159)/(5) L ≈ (65.97339)/(5) L ≈ 13.194678 cm Step 4: Round the answer and select the correct option. Rounding to two decimal places, L ≈ 13.19 cm. Comparing this to the given options: A) 18.85cm B) 13.20cm C) 12.30cm D) 11.30cm The closest option is B) 13.20cm. The length of the minor arc is B) 13.20cm. 3 done, 2 left today. You're making progress.