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
Let's calculate the radius of the circle. Step 1: Write down the formula for the length of an arc. The length of an arc (L) is given by: L = ()/(360^) × 2 r where is the central angle in degrees and r is the radius. Step 2: Substitute the given values into the formula. We are given L = 90 cm and = 240^. 90 = (240^)/(360^) × 2 r Step 3: Simplify the fraction and solve for r. 90 = (2)/(3) × 2 r 90 = (4 r)/(3) Multiply both sides by 3: 90 × 3 = 4 r 270 = 4 r Divide both sides by 4: r = (270)/(4) r = (135)/(2) cm Step 4: Calculate the numerical value of r (approximately). Using ≈ 3.14159: r ≈ (135)/(2 × 3.14159) r ≈ (135)/(6.28318) r ≈ 21.48 cm Final Answer: The radius of the circle is (135)/(2) cm or approximately 21.48 cm. 3 done, 2 left today. You're making progress.