Mathematics: Find the length of an arc of 40° in a circle with an 8 inch radius. 8/9 inches 16/9 inches 64/9 inches

Question:Which is the value of the expression A. 1 B. 2 C. 8 D. 10 B. 2Step-by-step explanation:GivenRequiredEvaluateSplit FractionFrom Laws of IndicesApplying this law to the above expression, we haveAlso, from Laws of IndicesApplying this law to the above expression, we haveMultiply 10 by 1Hence,...

Find the length of an arc of 40° in a circle with

Ответ:

rustalex6045

14.03.2022

Mathematics

To understand how to obtain arc length, you have to understand first that the ratio between the arc length and the circumference is equal to the ratio between the angle that forms that arc length and 360 degrees(a full circle).

So, the equation for arc length is the following:
$\frac{s}{2\pi r}= \frac{x}{360}$
Where s is the arc length, r is the radius, and x is the angle.

So just substitute the information in the question into the equation:
$\frac{s}{2\pi *8}= \frac{40}{360} \\ \\ \frac{s}{16\pi}= \frac{1}{9} \\ \\ s= \frac{16\pi}{9} inches$