To find the altitude of the plane after 30 minutes, we need to add the altitude gain to the initial altitude of the plane.
- Initial altitude: \( 20683 \frac{2}{3} \) feet
- Altitude gain: \( 6733 \frac{3}{8} \) feet
Let's first convert these mixed numbers into improper fractions.
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Convert \( 20683 \frac{2}{3} \): \[ 20683 \frac{2}{3} = 20683 + \frac{2}{3} = \frac{20683 \times 3}{3} + \frac{2}{3} = \frac{62049 + 2}{3} = \frac{62051}{3} \]
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Convert \( 6733 \frac{3}{8} \): \[ 6733 \frac{3}{8} = 6733 + \frac{3}{8} = \frac{6733 \times 8}{8} + \frac{3}{8} = \frac{53864 + 3}{8} = \frac{53867}{8} \]
Next, we will find a common denominator to add these fractions. The least common multiple (LCM) of 3 and 8 is 24.
Now, we convert both fractions to have a denominator of 24.
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Convert \( \frac{62051}{3} \): \[ \frac{62051}{3} \times \frac{8}{8} = \frac{496408}{24} \]
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Convert \( \frac{53867}{8} \): \[ \frac{53867}{8} \times \frac{3}{3} = \frac{161601}{24} \]
Now, we can add these two fractions: \[ \frac{496408}{24} + \frac{161601}{24} = \frac{496408 + 161601}{24} = \frac{658009}{24} \]
Next, convert the improper fraction back to a mixed number. We can divide: \[ 658009 \div 24 = 27417 \quad \text{(whole number part)} \] To find the remainder: \[ 658009 - (27417 \times 24) = 658009 - 657999 = 10 \] So, the mixed number is: \[ 27417 \frac{10}{24} \] Now simplify \( \frac{10}{24} \) to \( \frac{5}{12} \): \[ 27417 \frac{5}{12} \]
Therefore, the altitude of the plane after 30 minutes is \( 27417 \frac{5}{12} \) feet.
So, the true statement is that the altitude of the plane after 30 minutes is 27417 5/12 feet above ground level.
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