Let's solve the given problem step-by-step to find [tex]\( E \)[/tex]. The expression to evaluate is:
[tex]\[
E = \frac{\frac{2 \pi}{5} \text{ rad} + 60^8 \text{ minutes}}{9}
\][/tex]
We need to convert the terms in the numerator, [tex]\(\frac{2 \pi}{5}\)[/tex] radians and [tex]\(60^8\)[/tex] minutes, before summing them and then dividing by 9.
1. Convert [tex]\(\frac{2 \pi}{5}\)[/tex] radians into degrees:
Since there are [tex]\( \pi \)[/tex] radians in 180 degrees,
[tex]\[
\frac{2 \pi}{5} \text{ radians} = \frac{2 \times 180^\circ}{5} = 72^\circ
\][/tex]
This results in approximately [tex]\( 1.2566370614359172 \)[/tex] when computed.
2. Convert [tex]\(60^8\)[/tex] to degrees:
To convert minutes to degrees, we note that 1 degree is equal to 60 minutes. Thus,
[tex]\[
60^8 \text{ minutes} = \frac{60}{8} \text{ degrees}
\][/tex]
When computed, this gives us:
[tex]\[
\frac{60}{8} = 7.5^\circ
\][/tex]
3. Sum the converted values:
Summing the two values from steps 1 and 2, we obtain:
[tex]\[
1.2566370614359172 + 7.5 = 8.7566370614359172
\][/tex]
4. Divide by 9:
Finally, we divide the result by 9:
[tex]\[
E = \frac{8.7566370614359172}{9} \approx 0.9729596734928797
\][/tex]
Thus, the value of [tex]\( E \)[/tex] is approximately [tex]\( 0.9729596734928797 \)[/tex].
