A tennis player's swing moves along the path of an arc. If the radius of the arc's circle is 4 feet and the power and the angle of rotation is 100 degrees, what is the length of the arc?

7ft.

s = rθ, where θ is in radians

so, 4*100*pi/180

To find the length of the arc, we can use the formula:

Arc Length = (θ/360) * 2πr

where:
θ is the angle of rotation in degrees,
r is the radius of the arc's circle.

In this case, θ = 100 degrees and r = 4 feet.

Let's substitute these values into the formula:

Arc Length = (100/360) * 2π(4)

Arc Length = (5/18) * (2π) * 4

Now, let's simplify:

Arc Length = (5/18) * (8π)

Arc Length = (40π/18)

Arc Length ≈ 6.98 feet

Therefore, the length of the arc is approximately 6.98 feet.

To find the length of the arc, we need to know the circumference of the circle that represents the arc's path.

The circumference of a circle is calculated using the formula:
C = 2πr

In this case, the radius (r) of the circle is given as 4 feet.

Substituting the value of the radius into the formula, we get:
C = 2π(4) = 8π

We also know that the angle of rotation is 100 degrees.

To find the length of the arc, we need to calculate what fraction of the total circumference is represented by an angle of 100 degrees.

Since a circle has a total angle of 360 degrees, we can set up a proportion to find the fraction of the circumference represented by 100 degrees:

100 degrees / 360 degrees = x / 8π

Simplifying the proportion, we get:
0.2778 = x / 8π

Now, we can solve for x, which represents the length of the arc.

Multiplying both sides of the equation by 8π, we get:
x = 8π * 0.2778 = 2.219 feet

Therefore, the length of the arc is approximately 2.219 feet.