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12 Nov 2024, 03:47
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Minimum: 949
Maximum: 1264
Raphael works as a caretaker at a zoo, where his responsibilities include bathing and feeding the animals. According to the guidelines, an animal’s daily water requirement is directly proportional to the square root of its weight.
Based on this, a tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water. Similarly, an elephant weighing 4000 kg requires \(x\) liters of water, where \(x\) is an integer.
Select for Minimum the least possible value of \(x\), and for Maximum the greatest possible value of \(x\). Make only two selections, one in each column.
Based on this, a tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water. Similarly, an elephant weighing 4000 kg requires \(x\) liters of water, where \(x\) is an integer.
Select for Minimum the least possible value of \(x\), and for Maximum the greatest possible value of \(x\). Make only two selections, one in each column.
| Minimum | Maximum | |
| 947 | ||
| 948 | ||
| 949 | ||
| 1263 | ||
| 1264 | ||
| 1265 |
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Official Answer
Minimum: 949
Maximum: 1264
12 Nov 2024, 03:47
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Official Solution:
An animal’s daily water requirement being directly proportional to the square root of its weight implies that the water requirement equals \(\sqrt{weight} * k\) for some constant \(k\).
Given that a tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water, we have:
\(300 < \sqrt{400} * k < 400\)
\(300 < 20k < 400\)
\(15 < k < 20\)
An elephant weighing 4000 kg would require \(x = \sqrt{4000} * k\) liters. Multiplying the above inequality by \(\sqrt{4000}\) gives:
\(15\sqrt{4000} < \sqrt{4000} * k < 20\sqrt{4000}\)
\(15\sqrt{4000} < x < 20\sqrt{4000}\)
Evaluating \(15\sqrt{4000}\) using a calculator, we get approximately 948.7.
Evaluating \(20\sqrt{4000}\) using a calculator, we get approximately 1264.9.
Thus:
\(948.7 < x < 1264.9\)
Since \(x\) is an integer, the least possible value of \(x\) is 949, and the greatest possible value of \(x\) is 1264.
Correct answer:
Minimum "949"
Maximum "1264"
Bunuel
An animal’s daily water requirement being directly proportional to the square root of its weight implies that the water requirement equals \(\sqrt{weight} * k\) for some constant \(k\).
Given that a tiger weighing 400 kg requires more than 300 liters but less than 400 liters of water, we have:
\(300 < \sqrt{400} * k < 400\)
\(300 < 20k < 400\)
\(15 < k < 20\)
An elephant weighing 4000 kg would require \(x = \sqrt{4000} * k\) liters. Multiplying the above inequality by \(\sqrt{4000}\) gives:
\(15\sqrt{4000} < \sqrt{4000} * k < 20\sqrt{4000}\)
\(15\sqrt{4000} < x < 20\sqrt{4000}\)
Evaluating \(15\sqrt{4000}\) using a calculator, we get approximately 948.7.
Evaluating \(20\sqrt{4000}\) using a calculator, we get approximately 1264.9.
Thus:
\(948.7 < x < 1264.9\)
Since \(x\) is an integer, the least possible value of \(x\) is 949, and the greatest possible value of \(x\) is 1264.
Correct answer:
Minimum "949"
Maximum "1264"
03 Feb 2025, 16:32
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
