Question 184676
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\frac{h - 57.5}{2}\right| \leq 3.25]


Means:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \frac{h - 57.5}{2} \leq 3.25 \ \ \Rightarrow\ \ h - 57.5 \leq 6.5 \ \ \Rightarrow\ \ h \leq 64.0 \text{ inches}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ -\frac{h - 57.5}{2} \leq 3.25 \ \ \Rightarrow\ \ -h + 57.5 \leq 6.5 \ \ \Rightarrow\ \ -h \leq -51.0 \ \ \Rightarrow\ \ h \geq 51.0\text{ inches}]


Note change of inequality sense when multiplying by a negative.


Putting it all together:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ 51.0\text{ in.} \leq h \leq 64.0\text{ in.}]


Converting to feet:  *[tex \Large 51.0 \div 12 \approx 4.3] feet and *[tex \Large 64.0 \div 12 \approx 5.3] feet, so:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ 4.3\text{ ft.}  \leq h \leq 5.3\text{ ft.} ]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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