A) 32
B) \[31\frac{3}{4}\]
C) \[30\frac{1}{2}\]
D) \[31\frac{1}{4}\]
Correct Answer: D
Solution :
\[\Delta \,ABC\,\,=\,\,\frac{1}{2}\,\left| \begin{align} & 4\,\,\,\,\,\,-4\,\,\,\,\,\,\,\,1 \\ & 9\,\,\,\,\,\,\,\,\,\,6\,\,\,\,\,\,\,\,\,1 \\ & {{t}^{2\,\,\,\,\,\,}}\,\,\,\,\,2t\,\,\,\,\,\,\,1 \\ \end{align} \right|\] \[D=60+10t-10{{t}^{2}}\] \[\frac{d\,\Delta }{dt}\,=\,0\,\,\Rightarrow \,\,t=\frac{1}{2}\] \[\frac{{{d}^{2}}\,\Delta }{d{{t}^{2}}}\,=\,\,-20\,\,<\,\,0\] \[\therefore \,\,\,\text{ }max\text{ }at\text{ }t=\frac{1}{2}\] max area \[\Delta =65-\frac{5}{2}\] \[=\,\,\,\frac{125}{2}\,\,\,=\,\,31\frac{1}{4}\]You need to login to perform this action.
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