IDNLearn.com provides a comprehensive solution for all your question and answer needs. Discover in-depth and trustworthy answers to all your questions from our experienced community members.
Sagot :
Let's solve this problem step-by-step.
Given the equation for mean sustained wind velocity:
[tex]\[ v = 6.3 \sqrt{1013 - \rho} \][/tex]
We need to find the air pressure [tex]\( \rho \)[/tex] when the mean sustained wind velocity [tex]\( v \)[/tex] is 64 meters per second.
1. Substitute [tex]\( v = 64 \)[/tex] into the equation:
[tex]\[ 64 = 6.3 \sqrt{1013 - \rho} \][/tex]
2. Isolate the square root term by dividing both sides of the equation by 6.3:
[tex]\[ \frac{64}{6.3} = \sqrt{1013 - \rho} \][/tex]
3. Calculate the left-hand side:
[tex]\[ \frac{64}{6.3} \approx 10.1587 \][/tex]
4. Now, square both sides to eliminate the square root:
[tex]\[ \left(10.1587\right)^2 = 1013 - \rho \][/tex]
[tex]\[ 103.202 \approx 1013 - \rho \][/tex]
5. Solve for [tex]\( \rho \)[/tex]:
[tex]\[ \rho = 1013 - 103.202 \][/tex]
[tex]\[ \rho \approx 909.8 \][/tex]
So the air pressure at the center of the hurricane when the mean sustained wind velocity is 64 meters per second is approximately 910 millibars.
Among the given options, the closest value is:
- 103 millibars
- 194 millibars
- 363 millibars
- [tex]\( \boxed{910 \text{ millibars}} \)[/tex]
Given the equation for mean sustained wind velocity:
[tex]\[ v = 6.3 \sqrt{1013 - \rho} \][/tex]
We need to find the air pressure [tex]\( \rho \)[/tex] when the mean sustained wind velocity [tex]\( v \)[/tex] is 64 meters per second.
1. Substitute [tex]\( v = 64 \)[/tex] into the equation:
[tex]\[ 64 = 6.3 \sqrt{1013 - \rho} \][/tex]
2. Isolate the square root term by dividing both sides of the equation by 6.3:
[tex]\[ \frac{64}{6.3} = \sqrt{1013 - \rho} \][/tex]
3. Calculate the left-hand side:
[tex]\[ \frac{64}{6.3} \approx 10.1587 \][/tex]
4. Now, square both sides to eliminate the square root:
[tex]\[ \left(10.1587\right)^2 = 1013 - \rho \][/tex]
[tex]\[ 103.202 \approx 1013 - \rho \][/tex]
5. Solve for [tex]\( \rho \)[/tex]:
[tex]\[ \rho = 1013 - 103.202 \][/tex]
[tex]\[ \rho \approx 909.8 \][/tex]
So the air pressure at the center of the hurricane when the mean sustained wind velocity is 64 meters per second is approximately 910 millibars.
Among the given options, the closest value is:
- 103 millibars
- 194 millibars
- 363 millibars
- [tex]\( \boxed{910 \text{ millibars}} \)[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.