MATHEMATICS COLLEGE

The cube of a number is less than five times the square of the number. For what set of numbers is this true?(–ꝏ, 5)
(5, ꝏ)
(–ꝏ, 0) U (0, 5)
(–ꝏ, 5) U (5, ꝏ)

Answers

Answer 1
Answer:

Answer:

  (–ꝏ, 0) U (0, 5)

Step-by-step explanation:

The relation can be written as ...

  x³ < 5x²

  x³ -5x² < 0

  x²(x -5) < 0

This is not true for x = 0. It is true for x < 5, otherwise. Then the solution set is ...

  x ∈ {(–ꝏ, 0) U (0, 5)}
Answer 2
Answer:

The cube of any number from the set (-∞, 0) ∪ (0, 5) is less than five times the square of the number. So, the third option is correct.

Mathematically, a set is a collection of distinct, well-defined objects forming a group.

Let the number be x.

Then, according to the question:

x³ > 5x²

x³ - 5x² > 0

x²(x - 5) > 0

x² > 0 or x - 5 > 0

x > 0 or x > 5

This implies that

x ∈ (-∞, 0) ∪ (0, 5)

Hence, the correct answer is the third option, (-∞, 0) ∪ (0, 5).

Learn more about Set here:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answer:

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Answers

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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