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kap26 [50]
2 years ago
7

Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!​

Mathematics
1 answer:
FromTheMoon [43]2 years ago
3 0

Answer: t\in [\dfrac{1}{4},2]

Step-by-step explanation:

Given

Inequality is 4t^2\leq9t-2

Taking variables one side

\Rightarrow 4t^2-9t+2\leq0\\\Rightarrow 4t^2-8t-t+2\leq0\\\Rightarrow 4t(t-2)-1(t-2)\leq0\\\Rightarrow (4t-1)(t-2)\leq0

Using wavy curve method

t\in [\dfrac{1}{4},2]

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-a^2=(-1)\cdot a\cdot a

Regardless of the sign of a, we have a\cdot a=a^2\ge0 (never negative). But multiplying by -1 makes it negative.

On the other hand,

(-a)^2=((-1)\cdot a)^2=(-1)^2\cdot a^2=1\cdot a^2=a^2

which can never be negative for real a.
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