Question

the mean sustained wind velocity, \\(v\\), can be determined by the equation \\(v = 6.3 \sqrt{1013 - p}\\), where \\(p\\) is the air pressure, in millibars, at the center of the hurricane. what is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second?

103 millibars
194 millibars
363 millibars
910 millibars

Explanation:

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<reasoning>

Substitute the given wind velocity

Using the Solving Radical Equations knowledge point
\[
64 = 6.3\sqrt{1013 - p}
\]

Isolate the radical expression

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} \sqrt{1013 - p} &= \frac{64}{6.3} \\ \sqrt{1013 - p} &\approx 10.1587 \end{aligned}$$

\]

Square both sides of the equation

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} 1013 - p &= (10.1587)^2 \\ 1013 - p &\approx 103.199 \end{aligned}$$

\]

Solve for the air pressure p

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} -p &\approx 103.199 - 1013 \\ -p &\approx -909.801 \\ p &\approx 910 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>103 millibars</mcq-option>
<mcq-option>194 millibars</mcq-option>
<mcq-option>363 millibars</mcq-option>
<mcq-correct>910 millibars</mcq-correct>
</answer>

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"Mathematics",
"Algebra",
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Answer:

<pre_analysis>
{
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</pre_analysis>

<reasoning>

Substitute the given wind velocity

Using the Solving Radical Equations knowledge point
\[
64 = 6.3\sqrt{1013 - p}
\]

Isolate the radical expression

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} \sqrt{1013 - p} &= \frac{64}{6.3} \\ \sqrt{1013 - p} &\approx 10.1587 \end{aligned}$$

\]

Square both sides of the equation

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} 1013 - p &= (10.1587)^2 \\ 1013 - p &\approx 103.199 \end{aligned}$$

\]

Solve for the air pressure p

Using the Solving Radical Equations knowledge point
\[

$$\begin{aligned} -p &\approx 103.199 - 1013 \\ -p &\approx -909.801 \\ p &\approx 910 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>103 millibars</mcq-option>
<mcq-option>194 millibars</mcq-option>
<mcq-option>363 millibars</mcq-option>
<mcq-correct>910 millibars</mcq-correct>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Radical Equations"
]
}
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