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
Welcome back Klazzy — missed you this week. Here are the calculations for the given problem: Step 1: Identify the radius of the semicircle. The figure shows a semicircle with diameter AB. M is the center of the circle. The line segment MN is perpendicular to AB, and N is a point on the semicircle. Therefore, MN is the radius (r) of the semicircle. Given |MN| = 2 cm. So, the radius r = 2 cm. Step 2: Calculate |AB| (Part a). The length of AB is the diameter of the semicircle, which is twice the radius. |AB| = 2r |AB| = 2 × 2 cm |AB| = 4 cm The length of AB is 4 cm. Step 3: Calculate the angle subtended by arc ANB at the center (Part b). Arc ANB represents the entire semicircle. The angle subtended by a semicircle at its center is 180^. The angle is 180^. Step 4: Calculate the difference in length between AB and arc ANB (Part c). The length of the line segment AB is the diameter, which is 4 cm. The length of arc ANB is the circumference of a semicircle, given by the formula r. Length of arc ANB = × 2 cm = 2 cm. The difference in length is the absolute difference between the arc length and the diameter: Difference = | Length of arc ANB - Length of AB | Difference = | 2 cm - 4 cm | Difference = (2 - 4) cm Using ≈ 3.14159: Difference ≈ (2 × 3.14159 - 4) cm Difference ≈ (6.28318 - 4) cm Difference ≈ 2.28318 cm To convert this to millimeters, multiply by 10 (since 1 cm = 10 mm): Difference ≈ 2.28318 × 10 mm Difference ≈ 22.8318 mm Rounding to the nearest millimeter: Difference ≈ 23 mm The difference in length is 23 mm. Send me the next one 📸