The interval forms of the inequations are: a) x ∈ (20.5, + ∞), b) t ∈ (- ∞, 102], c) y ∈ (- ∞, - 8) ∪ (6, + ∞).
The simplified forms of the radical expressions are: a) m³ · n⁴, b) - 2√(2 · a), c) 3∛ 2 / 20.
How to analyze and modify inequalities and radical expressions
In the first part of this question we must transform inequalities into interval notation:
a) x > 20.5, inequalities of the form x > a are equivalent to x ∈ (a, + ∞). Thus, x > 20.5 is equivalent to x ∈ (20.5, + ∞).
b) t ≤ 102, inequalities of the form t ≤ a are equivalent to t ∈ (- ∞, a]. Thus, t ≤ 102 is equivalent to t ∈ (- ∞, 102].
c) y ≥ 6 or y ≤ - 8, the conditional "or" used in logics is equivalent to the operator ∪ used in set theory. Thus, y ≥ 6 or y ≤ - 8 is equivalent to y ∈ (- ∞, - 8) ∪ (6, + ∞).
The second part of this questions consists in simplifying radical expressions by algebraic handling:
- ∛(m⁹ · n¹²)
- m³ · n⁴
- 3√(2 · a) - √(8 · a) - √(18 · a)
- √9 · [√2 · √a] - √8 · √a - √18 · √a
- √18 · √a - √8 · √a - √18 · √a
- [√18 · √a - (√18 · √a)] - √8 · √a
- (√18 - √18) · √a - √8 · √a
- 0 · √a - √8 · √a
- (0 - √8) · √a
- - √8 · √a
- - 2√2 · √a
- - 2√(2 · a)
- 3∛250 / 100
- 3∛(2 · 125) / 100
- 3∛2 · (5 / 100)
- 3∛2 · (1 / 20)
- 3∛ 2 / 20
To learn more on inequalities: https://brainly.com/question/20383699
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