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A ball is thrown downward from a window from a tall building. Its position at time t in seconds is s = 16t^2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 161 feet.

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alexeylizunok

if I understood correctly:
s = 16t^2 + 32t, s=161
16t^2 + 32t=161
16t^2 + 32t-161=0
t=(-32+8√177)/32=-1+√177/4≈2,326≈2,3

\(s=16t^2+32t;\ s=161\\\\16t^2+32t=161\\\\16t^2+32t-161=0\\\\a=16;\ b=32;\ c=-161\\\\\Delta=b^2-4ac\to\Delta=32^2-4\cdot16\cdot(-161)=1024+10304=11328\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt{11328}=\sqrt{64\cdot177}=8\sqrt{177}\approx106.4\\\\x_1=\frac{-32-106.4}{2\cdot16}< 0;\ x_2=\frac{-32+106.4}{2\cdot16}=\frac{74.4}{32}=2.325\approx2.3\ (ft)\)

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