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Author: Tinku Tara

Question-224665

Question Number 224665 by ajfour last updated on 24/Sep/25 Commented by ajfour last updated on 24/Sep/25 $${At}\:{the}\:{instant}\:{shown}\:{rotating} \\ $$$${frame}\:{plane}\:{lies}\:{in}\:{yz}\:{plane}. \\ $$$${Angular}\:{acceleration}\:\left({constant}\right) \\ $$$${is}\:\boldsymbol{\alpha},\:{angular}\:{velocity}\:\boldsymbol{\omega}.\:{Find}\:\boldsymbol{\theta} \\ $$$${and}\:\boldsymbol{\phi}.\:{String}\:{length}\:{is}\:{L}.…

Prove-that-sin-54-5-1-4-

Question Number 224635 by hardmath last updated on 23/Sep/25 $$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{sin}\left(\mathrm{54}°\right)\:=\:\:\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\mathrm{4}} \\ $$ Answered by som(math1967) last updated on 23/Sep/25 $$\:{let}\:\mathrm{54}=\alpha \\ $$$$\therefore\mathrm{5}\alpha=\mathrm{270} \\ $$$$\Rightarrow\mathrm{3}\alpha=\mathrm{270}−\mathrm{2}\alpha \\…

Question-224642

Question Number 224642 by Rogerkeyter last updated on 23/Sep/25 Answered by som(math1967) last updated on 24/Sep/25 $$\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\frac{\boldsymbol{{e}}^{\sqrt{\mathrm{1}−\boldsymbol{{x}}}} }{\boldsymbol{{e}}^{\sqrt{\boldsymbol{{x}}}} }} \\ $$$$\:\:\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{e}}^{\sqrt{\boldsymbol{{x}}}}…