Let's evaluate the expression step by step:
1. Evaluate [tex]\( 23.45 \cos 67.89^\circ \)[/tex]:
- Calculating [tex]\( \cos 67.89^\circ \)[/tex], we find that it equals approximately 0.3765.
- Multiply this value by 23.45:
[tex]\[
23.45 \times 0.3765 \approx 8.8263
\][/tex]
2. Calculate [tex]\( 31.6^2 \)[/tex]:
- [tex]\( 31.6^2 = 998.56 \)[/tex]
3. Divide the results from steps 1 and 2:
- We need to find the fraction:
[tex]\[
\frac{8.8263}{998.56} \approx 0.008839
\][/tex]
4. Calculate the cube root of the fraction:
- We then find the cube root of 0.008839:
[tex]\[
\sqrt[3]{0.008839} \approx 0.2068
\][/tex]
So, the step-by-step detailed solution for the given expression is as follows:
- [tex]\( 23.45 \cos 67.89^\circ \approx 8.8263 \)[/tex]
- [tex]\( 31.6^2 = 998.56 \)[/tex]
- [tex]\(\frac{8.8263}{998.56} \approx 0.008839 \)[/tex]
- [tex]\(\sqrt[3]{0.008839} \approx 0.2068 \)[/tex]
Thus, the evaluated result is approximately [tex]\(0.2068\)[/tex].
