Question

Окружность с радиусом 1 разбита на три дуги так что величины соответствующих им центральных углов пропорциональны числам 1 2 и 3 Найдите длину наибольшей дуги

Answer 1

L=2πR=6.28*1=6.28мдлина всей
1+2+3=6 частей всего
6,28:6≈1,04м одна часть
1,04*3=3,12м  длина большей дуги

Answer 2

Все эти углы центральные. Длину окружности можно измерять в градусах.
1+2+3=6(частей)
360:6=60 градусов-одна часть, или меньшая дуга
60 *2=120 градусов средняя дуга
60*3=180 градусов -наибольшая дуга

Answer 3

Problem Analysis

We are given a circle with a radius of 1, divided into three arcs such that the central angles of the arcs are proportional to the numbers 1, 2, and 3. We need to find the length of the largest arc.

Solution

Let's denote the central angles of the arcs as A, 2A, and 3A, where A is a constant. The sum of the central angles in a circle is 360 degrees.

So, A + 2A + 3A = 360 6A = 360 A = 60

Now, we can calculate the central angles: - Arc 1: A = 60 degrees - Arc 2: 2A = 120 degrees - Arc 3: 3A = 180 degrees

The length of an arc can be calculated using the formula: Arc Length = (Central Angle / 360) * 2 * π * r

Where: - r is the radius of the circle - π is a mathematical constant approximately equal to 3.14159

Let's calculate the lengths of the arcs.

For Arc 1: Arc Length 1 = (60 / 360) * 2 * π * 1 Arc Length 1 = (1/6) * 2 * π Arc Length 1 = (1/3) * π

For Arc 2: Arc Length 2 = (120 / 360) * 2 * π * 1 Arc Length 2 = (1/3) * 2 * π Arc Length 2 = (2/3) * π

For Arc 3: Arc Length 3 = (180 / 360) * 2 * π * 1 Arc Length 3 = (1/2) * 2 * π Arc Length 3 = π

Conclusion

The length of the largest arc is π.