Create a visually engaging image representing a mathematical scenario, where an object is traveling along a circular path defined by 32pi/5 radians. The image should hint towards the challenge of converting radians to degrees, without containing any text. The image could potentially include a circular path, a simple object moving along this path, and tick marks or graphic design elements to reflect the complex calculation needed. Do not include the actual question and solutions or any other text.

If an object travels in a circle 32pi/5 radians, at what degree measure is it, relative to where it started?

a) 1052°
b) 144°
c) 72°
d) 98.6°

I got 1152° but there is no option for the answer, what did I wrong?

32/5 = 6 2/5

so we have gone 6 pi radians + 2/5 of a radian
but 6 pi radians is 3 whole circles
so we end up at (2/5)pi radian
(2/5)pi(180/pi) = 72 degrees

6 remainder 2

Tricky :)

Why is 32/5 = 6 2/5?

Jake, division

5 ( 6 + 2/5)/5 = (30 + 2)/5 = 32/5

Thank you~

the body breaks down both physically and?

Well mine is pretty cooked mentally.

To convert radians to degrees, you need to use the conversion factor that 1 radian is equal to 180/π (approximately 57.2958) degrees.

In this case, the object travels in a circle of 32π/5 radians. Using the conversion factor, the degree measure would be:

(32π/5) × (180/π) = 1152 degrees

Since 1152 degrees is not one of the given options, it seems that you cannot find a match for your answer. It's possible that there may be a mistake in the options provided or that there is another approach or requirement for the problem that is not mentioned. Double-check the question and options to see if any additional information or context was given.

32PI/5 rad* 180 deg/PI= 32/5*180=32*36

You are right.