Use the given circle. Find the length s to the nearest tenth. The circle has an outer circle of 5π/3 and a inner circle of 6 in
It is not clear what is meant by "outer circle of 5π/3". However, assuming that the problem is referring to the circumference of the circle:
The length s can be found by subtracting the circumference of the inner circle from the circumference of the outer circle and then dividing by 2π (since s represents half the distance around the circle):
s = (5π/3 - 2πr) / (2π)
where r is the radius of the inner circle. To find r, we can use the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius. Solving for r, we get:
r = C / 2π = 6 / 2π = 3 / π
Substituting this value into the formula for s:
s = (5π/3 - 2π(r)) / (2π)
= (5π/3 - 2π(3/π)) / (2π)
= (5π/3 - 6) / (2π)
≈ -0.5
This answer doesn't make sense, since s represents a length and cannot be negative. Therefore, there may be an error in the given information or the problem statement.
To find the length s, we first need to determine the radius of the circle. Let's call the radius r.
The outer circle has a circumference of 5π/3. The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius.
So we have 5π/3 = 2πr.
To simplify, we can divide both sides of the equation by 2π:
(5π/3) / (2π) = r.
Simplifying further, we get:
5/6 = r.
Therefore, the radius of the circle is 5/6.
Now, let's find the length of s. Since the circle has an outer and inner circle, the length of s is equal to the difference between the outer and inner circumferences.
The outer circumference is 5π/3, and we need to find the circumference of the inner circle. The formula for the circumference is still C = 2πr.
For the inner circle, the radius is given as 6 inches. So the inner circumference is:
C = 2π(6) = 12π.
Now, we can find the length s:
s = (5π/3) - (12π).
To subtract the two values, we need a common denominator:
s = (5π/3) - (12π/1).
Changing the fractions to have a common denominator of 3, we get:
s = (5π/3) - (36π/3).
Combine the two fractions:
s = (5π - 36π)/3.
Simplify the numerator:
s = (-31π)/3.
To find the length s to the nearest tenth, we can use a calculator to approximate the decimal value for π (pi) and compute the result.