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Category: Geometry

I-have-seen-a-relationship-in-the-curve-path-of-a-thrown-object-at-while-the-total-passed-distance-D-v-and-highest-point-had-passedD-u-then-arctan-4D-u-D-v-but-cant-find-the-proof-I-w

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Question Number 217148 by Marzuk last updated on 03/Mar/25 $${I}\:{have}\:{seen}\:{a}\:{relationship}\:{in}\:{the}\:{curve} \\ $$$${path}\:{of}\:{a}\:{thrown}\:{object}\:{at}\:\beta\: \\ $$$${while}\:{the}\:{total}\:{passed}\:{distance}\:{D}_{{v}} \:{and} \\ $$$${highest}\:{point}\:{had}\:{passedD}_{{u}} \\ $$$${then}\:\beta\:=\:{arctan}\left(\frac{\mathrm{4}{D}_{{u}} }{{D}_{{v}} }\right) \\ $$$${but}\:{cant}\:{find}\:{the}\:{proof}. \\ $$$${I}\:{would}\:{like}\:{to}\:{say}\:{would}\:{anyone}\:{like}…

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Solve-for-x-in-i-x-2-

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Question Number 216485 by Tawa11 last updated on 08/Feb/25 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\:\mathrm{in}:\:\:\:\mathrm{i}^{\mathrm{x}} \:\:=\:\:\mathrm{2} \\ $$ Answered by issac last updated on 09/Feb/25 $${x}\centerdot\mathrm{ln}\left({i}\right)=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{ln}\left({i}\right)=\frac{\pi}{\mathrm{2}}{i} \\ $$$$\therefore\:{x}=−\frac{\mathrm{2}}{\pi}{i}\centerdot\mathrm{ln}\left(\mathrm{2}\right)…

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