Mathematics, 05.10.2019 20:30 cynone8254
After t seconds, the height of a weight attached to a spring is s(t)= -3 cos 2t inches. when is the first time that the weight reaches its maximum height?
Answers: 1
![\bf s(t)=-3cos(2\pi t)\implies 0=-3cos(2\pi t)\implies 0=cos(2\pi t) \\\\\\ cos^{-1}(0)=cos^{-1}[cos(2\pi t)]\implies cos^{-1}(0)=2\pi t \\\\\\ \cfrac{cos^{-1}(0)}{2\pi }=t \\\\\\ \textit{now, on the interval of }[0,2\pi ]\ where\ cos^{-1}(0)? \\\\\\ well\qquad \frac{\pi }{2}\ ,\ \frac{3\pi }{2}\qquad thus \\\\\\ t= \begin{cases} \cfrac{\frac{\pi }{2}}{2\pi }\implies \cfrac{1}{4}\\\\ \cfrac{\frac{3\pi }{2}}{2\pi }\implies \cfrac{3}{4} \end{cases}](/tpl/images/0290/7821/c72b5.png)
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After t seconds, the height of a weight attached to a spring is s(t)= -3 cos 2t inches. when is the...
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