what is the length of a radius of a circle with a central angle of 3π/5 and an arc length of 24π/5

The length of a radius of the circle is units.

s = r * T

24pi/5 = r * 3pi/5
(24pi/5) * (5/(3pi)) = r
(24/3) * (pi/pi) * (5/5) = r
8 * 1 * 1 = r
r = 8

Casayuran

Oh, radius, my old friend, always there to measure the distance and keep things circular. Now, let's tackle your question.

So, we've got a central angle of 3π/5 and an arc length of 24π/5. Cool beans! In a perfect world, the formula to figure out the length of a radius given an arc length and central angle is:

Radius = (Arc Length) / (Central Angle)

Now, we just need to plug in the numbers and do some math magic.

Radius = (24π/5) / (3π/5)

Now, let's cancel out those pesky π's.

Radius = (24/5) / (3/5)

Ah, the glory of math when things start canceling out. So, let's simplify further.

Radius = 24/5 * 5/3

Now, it's time for some multiplication.

Radius = 8

There you have it, my friend! The length of the radius of the circle is 8 units. Ta-dah!

To find the length of the radius, you can use the formula:

Arc Length = radius * central angle

Given that the arc length is 24π/5 and the central angle is 3π/5, we can substitute these values into the formula:

24π/5 = radius * (3π/5)

To solve for the radius, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by (3π/5):

(24π/5) / (3π/5) = radius

Simplifying the equation:

(24π/5) * (5/3π) = radius

The π's cancel out:

(24/1) * (1/3) = radius

Multiplying and simplifying:

8 = radius

Therefore, the length of the radius is 8 units.

To find the length of the radius of a circle given the central angle and arc length, we can use the formula:

arc length = radius * central angle

In this case, we have the arc length as 24π/5 and the central angle as 3π/5. Let's substitute these values into the formula and solve for the radius.

24π/5 = radius * 3π/5

To solve for the radius, we can cancel out the π/5 terms on both sides of the equation:

24 = radius * 3

Now, divide both sides of the equation by 3 to isolate the radius:

radius = 24/3
radius = 8

Therefore, the length of the radius of the circle is 8 units.