Let's break down the expression step-by-step to find the solution for [tex]\( c \tau \times 2 \pi \tau \div 9 \)[/tex].
1. Understand the Constants:
- [tex]\( \tau \)[/tex] (tau) is a mathematical constant equivalent to [tex]\( 2\pi \)[/tex], where [tex]\( \pi \)[/tex] is approximately [tex]\( 3.14159 \)[/tex]. Therefore, [tex]\( \tau \approx 6.28318 \)[/tex].
- Assume [tex]\( c = 1 \)[/tex] as no specific value is provided.
2. Substitute the Constants:
- Replace [tex]\( \tau \)[/tex] with [tex]\( 2\pi \)[/tex] in the expression:
[tex]\[
c \times (2\pi) \times 2\pi \times (2\pi) \div 9
\][/tex]
3. Simplify the Expression:
- Substitute [tex]\( c = 1 \)[/tex]:
[tex]\[
1 \times (2\pi) \times 2\pi \times 2\pi \div 9
\][/tex]
4. Combine Like Terms:
- Multiply the terms inside the expression:
[tex]\[
2\pi \times 2\pi \times 2\pi = 8\pi^3
\][/tex]
So the expression becomes:
[tex]\[
\frac{8\pi^3}{9}
\][/tex]
5. Calculate the Numerical Value:
- Evaluate [tex]\( \pi \)[/tex] as approximately [tex]\( 3.14159 \)[/tex]:
[tex]\[
\pi^3 \approx (3.14159)^3 \approx 31.00627
\][/tex]
6. Substitute back:
- Plug in the value of [tex]\( \pi^3 \)[/tex]:
[tex]\[
\frac{8 \times 31.00627}{9} \approx 27.56113482693317
\][/tex]
Therefore, the value of the expression [tex]\( c \tau \times 2 \pi \tau \div 9 \)[/tex] is approximately [tex]\( 27.56113482693317 \)[/tex].
