To find the approximate air pressure at the center of a hurricane given a sustained wind velocity of 64 meters per second, we will use the equation provided:
[tex]\[ v = 6.3 \cdot \sqrt{\text{pressure}} \][/tex]
Here, [tex]\( v \)[/tex] is the sustained wind velocity, which is 64 meters per second. We will solve for the pressure step-by-step:
1. Start with the given equation:
[tex]\[ 64 = 6.3 \cdot \sqrt{\text{pressure}} \][/tex]
2. To isolate the square root term, divide both sides of the equation by 6.3:
[tex]\[ \frac{64}{6.3} = \sqrt{\text{pressure}} \][/tex]
3. Simplify the fraction on the left-hand side:
[tex]\[ \frac{64}{6.3} \approx 10.1587 \][/tex]
4. To remove the square root, square both sides of the equation:
[tex]\[ \left( \frac{64}{6.3} \right)^2 = \text{pressure} \][/tex]
5. Calculate the square of the simplified fraction:
[tex]\[ (10.1587)^2 \approx 103.20 \][/tex]
Thus, the approximate air pressure at the given sustained wind velocity of 64 meters per second is about 103 millibars. Therefore, the correct answer from the given options is:
[tex]\[ \boxed{103 \ \text{millibars}} \][/tex]
