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The number aa is irrational. Which statement about a38a^{38} is true?

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Properties of operations on rational and irrational numbersright chevron icon

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A leaky 10-kg10\text{-kg} bucket is lifted from the ground to a height of 14 m14\, \text{m} at a constant speed with a rope that weighs 0.6 kg/m0.6\, \text{kg/m}. Initially the bucket contains 42 kg42\, \text{kg} of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14 m14\, \text{m} level. How much work is done? (Use 9.8 m/s29.8\, \text{m/s}^2 for gg.) Show how to approximate the required work (in J\text{J}) by a Riemann sum. (Let xx be the height in meters above the ground. Enter xi∗x_i^* as xix_i.)
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A leaky 10−kg 10-\mathrm{kg} bucket is lifted from the ground to a height of 1414 m at a constant speed with a rope that weighs 0.6 kg/m 0.6 \mathrm{~kg} / \mathrm{m} . Initially the bucket contains 4242 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14−m 14-\mathrm{m} level. How much work is done? (Use 9.8 m/s2 9.8 \mathrm{~m} / \mathrm{s}^{2} for g .)\newlineShow how to approximate the required work (in J) by a Riemann sum. (Let x x be the height in meters above the ground. Enter xi∗∗ x_{i}^{* *} as xi x_{i} )\newlinelim⁡n→∞∑i=1n(98+35.28xi)Δx\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x\newlineExpress the work (in J) as an integral in terms of x x (in m).\newline∫014(98+35.28x\int_{0}^{14}(98+35.28 x\newlineEvaluate the integral (in J). (Round your answer to the nearest integer.)
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