Sure, let's solve the given expression step-by-step.
We need to evaluate:
[tex]\[ gh = \left( \frac{6371 \, \text{km}}{6371 \, \text{km} + 2640 \, \text{km}} \right)^2 \][/tex]
1. Calculate the denominator:
Add [tex]\( 6371 \, \text{km} \)[/tex] and [tex]\( 2640 \, \text{km} \)[/tex]:
[tex]\[ 6371 \, \text{km} + 2640 \, \text{km} = 9011 \, \text{km} \][/tex]
2. Form the fraction:
Now, place [tex]\( 6371 \, \text{km} \)[/tex] in the numerator and the sum [tex]\( 9011 \, \text{km} \)[/tex] in the denominator:
[tex]\[ \frac{6371 \, \text{km}}{9011 \, \text{km}} \][/tex]
3. Evaluate the fraction:
The value of the fraction is:
[tex]\[ \frac{6371}{9011} \approx 0.7070247475307957 \][/tex]
4. Square the fraction:
Now square the value obtained in the previous step:
[tex]\[ \left(0.7070247475307957\right)^2 \][/tex]
5. Compute the squared value:
The squared value is:
[tex]\[ 0.7070247475307957^2 \approx 0.4998839936209854 \][/tex]
Therefore, the final result for [tex]\( gh \)[/tex] is:
[tex]\[ gh \approx 0.4998839936209854 \][/tex]
