Certainly! Let's go through the calculations step by step:
1. Calculating [tex]\(2\pi\)[/tex]:
- We need to compute [tex]\(2\)[/tex] times [tex]\(\pi\)[/tex].
- The value of [tex]\(\pi\)[/tex] (pi) is approximately [tex]\(3.141592653589793\)[/tex].
- [tex]\(2 \times \pi = 2 \times 3.141592653589793 = 6.283185307179586\)[/tex].
Therefore, [tex]\(2\pi = 6.283185307179586\)[/tex].
2. Calculating [tex]\(\frac{\pi}{4}\)[/tex]:
- We need to compute [tex]\(\frac{\pi}{4}\)[/tex], which is [tex]\(0.25\)[/tex] times [tex]\(\pi\)[/tex].
- The value of [tex]\(\pi\)[/tex] is approximately [tex]\(3.141592653589793\)[/tex].
- [tex]\(0.25 \times \pi = 0.25 \times 3.141592653589793 = 0.7853981633974483\)[/tex].
Therefore, [tex]\(\frac{\pi}{4} = 0.7853981633974483\)[/tex].
3. Calculating [tex]\(5.2e\)[/tex]:
- We need to compute [tex]\(5.2\)[/tex] times [tex]\(e\)[/tex].
- The value of [tex]\(e\)[/tex] (Euler's number) is approximately [tex]\(2.718281828459045\)[/tex].
- [tex]\(5.2 \times e = 5.2 \times 2.718281828459045 = 14.135065507987035\)[/tex].
Therefore, [tex]\(5.2e = 14.135065507987035\)[/tex].
4. Calculating [tex]\(8\phi\)[/tex]:
- We need to compute [tex]\(8\)[/tex] times [tex]\(\phi\)[/tex].
- The value of [tex]\(\phi\)[/tex] (the golden ratio) is [tex]\(\frac{1 + \sqrt{5}}{2}\)[/tex], which is approximately [tex]\(1.618033988749895\)[/tex].
- [tex]\(8 \times \phi = 8 \times 1.618033988749895 = 12.94427190999916\)[/tex].
Therefore, [tex]\(8\phi = 12.94427190999916\)[/tex].
In summary:
[tex]\[
\begin{array}{l}
2 \pi = 2 \times 3.141592653589793 = 6.283185307179586 \\
\frac{\pi}{4} = 0.25 \times 3.141592653589793 = 0.7853981633974483 \\
5.2 e = 5.2 \times 2.718281828459045 = 14.135065507987035 \\
8 \varphi = 8 \times 1.618033988749895 = 12.94427190999916 \\
\end{array}
\][/tex]
