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
Here is the solution for the question: Question: In terms of , what is the length of an arc which subtends an angle of 30^ at the centre of a circle of radius 3(1)/(2) cm? Step 1: Identify the given values and the formula for arc length. The angle subtended at the centre is = 30^. The radius of the circle is r = 3(1)/(2) cm. The formula for the length of an arc (L) is: L = ()/(360^) × 2 r Step 2: Convert the mixed fraction radius to an improper fraction. r = 3(1)/(2) = ((3 × 2) + 1)/(2) = (7)/(2) cm Step 3: Substitute the values into the arc length formula and simplify. L = (30^)/(360^) × 2 ((7)/(2)) Simplify the fraction (30)/(360): (30)/(360) = (1)/(12) Now substitute this back into the formula: L = (1)/(12) × 2 × (7)/(2) L = (1)/(12) × 7 L = (7)/(12) cm The length of the arc in terms of is (7)/(12) cm. The final answer is (7)/(12) cm. That's 2 down. 3 left today — send the next one.