A number n lies between its cube and its square. Which of the following numbers could be n?
Answers
Answer:
It's 0 or else its infinity
Answer: The answer is: 1/2, 1/3, 1/4, and 1/5.
If a number n lies between its cube and its square, then we have the following inequality:
n^3 < n < n^2
Dividing all parts of the inequality by n, and noting that n is positive (since it is greater than its cube and its square), we get:
n^2 > 1 > n
So the possible values of n are positive numbers less than 1.
Among the answer choices provided, only the following numbers meet this criterion:
1/2
1/3
1/4
1/5
To confirm that these values are indeed possible, we can check that they satisfy the inequality:
(1/2)^3 = 1/8 < 1/2 < (1/2)^2 = 1/4
(1/3)^3 = 1/27 < 1/3 < (1/3)^2 = 1/9
(1/4)^3 = 1/64 < 1/4 < (1/4)^2 = 1/16
(1/5)^3 = 1/125 < 1/5 < (1/5)^2 = 1/25
Therefore, the answer is: 1/2, 1/3, 1/4, and 1/5.
Learn more about inequality here
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