If-Q-2-x-y-1-5-x-lt-1-5-y-lt-6-Find-Q-max-

Question Number 192054 by cortano12 last updated on 07/May/23

If Q = \frac{2 - x}{y - 1}; - 5 ⩽ x < - 1, 5 ⩽ y < 6

Find Q_{\max} .

Answered by mehdee42 last updated on 07/May/23

- 5 ⩽ x < - 1 \overset{\times - 1}{\Rightarrow} 1 < - x ⩽ 5 \overset{+ 2}{\Rightarrow} 3 < 2 - x ⩽ 7 (i)

5 ⩽ y < 6 \overset{- 1}{\Rightarrow} 4 ⩽ y - 1 < 5 \overset{}{\Rightarrow} \frac{1}{5} < \frac{1}{y - 1} ⩽ \frac{1}{4} (i i)

(i) \times (i i) \Rightarrow \frac{3}{5} < \frac{2 - x}{y - 1} ⩽ \frac{7}{4} \Rightarrow Q_{m a x} = \frac{7}{4} ✓

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