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03 Dec 2021, 07:07
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If \(x^4 > 50\), then which of the following must be true?
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x|} > 0.4\)
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x|} > 0.4\)
03 Dec 2021, 07:07
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Official Solution:
If \(x^4 > 50\), then which of the following must be true?
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x|} > 0.4\)
\(x^4 > 50\) means that \(x < -\sqrt[4]{50}\) or \(x > \sqrt[4]{50}\).
Check each option:
A. \(|x| > 3\). Take to the fourth power: \(x^4 > 81\). This one is not necessarily true. For example, consider \(x^4=60\).
B. \(x > 2.5\). This one is not not necessarily true. For example, consider \(x=-10\).
C. \(x < 2.5\). This one is not necessarily true. For example, consider \(x=10\).
D. \(\frac{1}{|x|} < 0.4\). Simplify: \(|x| > \frac{5}{2}\). Take to the fourth power: \(x^4 > 40\) (\((\frac{5}{2})^4=\frac{625}{16}\approx 40\)). Since given that \(x^4\) is greater than 50, then it's obviously greater than 40. This one is true.
E. \(\frac{1}{|x|} > 0.4\). Simplify: \(|x| < \frac{5}{2}\). Take to the fourth power: \(x^4 < 40\). This one is NOT true.
Answer: D
If \(x^4 > 50\), then which of the following must be true?
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x|} > 0.4\)
\(x^4 > 50\) means that \(x < -\sqrt[4]{50}\) or \(x > \sqrt[4]{50}\).
Check each option:
A. \(|x| > 3\). Take to the fourth power: \(x^4 > 81\). This one is not necessarily true. For example, consider \(x^4=60\).
B. \(x > 2.5\). This one is not not necessarily true. For example, consider \(x=-10\).
C. \(x < 2.5\). This one is not necessarily true. For example, consider \(x=10\).
D. \(\frac{1}{|x|} < 0.4\). Simplify: \(|x| > \frac{5}{2}\). Take to the fourth power: \(x^4 > 40\) (\((\frac{5}{2})^4=\frac{625}{16}\approx 40\)). Since given that \(x^4\) is greater than 50, then it's obviously greater than 40. This one is true.
E. \(\frac{1}{|x|} > 0.4\). Simplify: \(|x| < \frac{5}{2}\). Take to the fourth power: \(x^4 < 40\). This one is NOT true.
Answer: D
08 Jan 2024, 07:00
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