An arc subtends an angle of 1050 at the center of a circle of a circle of radius 6 cm. find the length of the arc, if the π is 22/7

set ε={3,6,9,12,15,18,21,24,27,30}

What is n(ε)?

s = rθ

There are only 360° in a full circle, so I'm not sure how your arc can subtend an angle of 1050. Anyway, just express θ and multiply by r.

n(ε) is just the number of elements in the set. Surely you can count ...

To find the length of the arc, we need to use the formula:

Length of Arc = (θ/360) × 2πr

Where:
- θ is the angle in degrees subtended by the arc
- 360 is the total measure of angles in a complete circle
- πr is the circumference of the circle
- r is the radius of the circle

Given:
- θ = 1050 degrees
- r = 6 cm
- π = 22/7

First, we need to convert the angle from degrees to radians, as the formula requires the angle to be in radians.

To convert degrees to radians, we use the formula:
Radians = (π/180) × Degrees

Converting the given angle into radians:
θ_radians = (22/7 × 1050)/180

Now we can plug the values into the formula:

Length of Arc = (θ_radians/360) × 2πr
Length of Arc = ((22/7 × 1050)/180 × 1/360) × (2 × 22/7 × 6)

Simplifying the expression:
Length of Arc = (22/7 × 1050 × 1 × 1) / (180 × 360) × (2 × 22 × 6/7)
Length of Arc = (22 × 1050 × 1 × 1) / (7 × 180 × 360) × (2 × 22 × 6)
Length of Arc = (23100) / (45360) × (528)
Length of Arc = 27052800/45360
Length of Arc ≈ 595.227 cm

Therefore, the length of the arc is approximately 595.227 cm.