Answer :
To determine the approximate air pressure at the center of a hurricane given that the mean sustained wind velocity is 64 meters per second, we need to use the given equation:
[tex]\[ v = 6.3 \sqrt{1013 - p} \][/tex]
Given:
[tex]\[ v = 64 \, \text{meters per second} \][/tex]
We will isolate [tex]\( p \)[/tex] in the equation to find the air pressure. Here's the step-by-step solution:
1. Start with the given equation:
[tex]\[ v = 6.3 \sqrt{1013 - p} \][/tex]
2. Substitute the given wind velocity [tex]\( v = 64 \)[/tex]:
[tex]\[ 64 = 6.3 \sqrt{1013 - p} \][/tex]
3. Divide both sides by 6.3 to isolate the square root term:
[tex]\[ \frac{64}{6.3} = \sqrt{1013 - p} \][/tex]
4. Calculate the left side:
[tex]\[ \frac{64}{6.3} \approx 10.1587 \][/tex]
5. Square both sides to remove the square root:
[tex]\[ (10.1587)^2 = 1013 - p \][/tex]
6. Perform the squaring operation:
[tex]\[ 103.196 = 1013 - p \][/tex]
7. Rearrange to solve for [tex]\( p \)[/tex]:
[tex]\[ p = 1013 - 103.196 \][/tex]
8. Subtract to find [tex]\( p \)[/tex]:
[tex]\[ p \approx 909.804 \][/tex]
Therefore, the approximate air pressure at the center of the hurricane is [tex]\( 910 \)[/tex] millibars when rounded to the nearest whole number. Among the given choices, the closest answer is:
[tex]\[ \boxed{910 \text{ millibars}} \][/tex]
[tex]\[ v = 6.3 \sqrt{1013 - p} \][/tex]
Given:
[tex]\[ v = 64 \, \text{meters per second} \][/tex]
We will isolate [tex]\( p \)[/tex] in the equation to find the air pressure. Here's the step-by-step solution:
1. Start with the given equation:
[tex]\[ v = 6.3 \sqrt{1013 - p} \][/tex]
2. Substitute the given wind velocity [tex]\( v = 64 \)[/tex]:
[tex]\[ 64 = 6.3 \sqrt{1013 - p} \][/tex]
3. Divide both sides by 6.3 to isolate the square root term:
[tex]\[ \frac{64}{6.3} = \sqrt{1013 - p} \][/tex]
4. Calculate the left side:
[tex]\[ \frac{64}{6.3} \approx 10.1587 \][/tex]
5. Square both sides to remove the square root:
[tex]\[ (10.1587)^2 = 1013 - p \][/tex]
6. Perform the squaring operation:
[tex]\[ 103.196 = 1013 - p \][/tex]
7. Rearrange to solve for [tex]\( p \)[/tex]:
[tex]\[ p = 1013 - 103.196 \][/tex]
8. Subtract to find [tex]\( p \)[/tex]:
[tex]\[ p \approx 909.804 \][/tex]
Therefore, the approximate air pressure at the center of the hurricane is [tex]\( 910 \)[/tex] millibars when rounded to the nearest whole number. Among the given choices, the closest answer is:
[tex]\[ \boxed{910 \text{ millibars}} \][/tex]