(section 6.1) Find the length of the small arc formed by the intersection of the unit circle a circle centered at the origin with a radius of 1: x2 + y2 = 1 and the line 2 y=1/2​

The length of the arc is approximately 2.0944

Step-by-step explanation:

The given parameters are;

The equation of the circle = x² + y² = 1

The radius of the circle, r = 1

The equation of the line, y = 1/2

Therefore, we point where the line intersects with the circle are given as the points 'y = 1/2' as follows;

When y = 1/2, the equation of the circle becomes;

x² + (1/2)² = 1

x² = 1 - (1/2)² = 3/4

x = ±√3/2

The angle subtended by the arc, θ = 2 × arctan((√3/2)/(1/2)) = 120°

The circumference of the circle, C = 2·π·r

∴ C = 2 × π × 1 = 2·π

The length of the arc, l = (θ/360) × C

∴ l = (120/360) × 2·π = (2/3)·π

The length of the arc, l = (2/3)·π ≈ 2.0944

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation:

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c