Question Number 216613 by ajfour last updated on 12/Feb/25 $$\int_{{a}} ^{\:{x}} \frac{\mathrm{1}−{b}\mathrm{ln}\:\frac{{x}}{{a}}}{\:\sqrt{\mathrm{1}−\left(\mathrm{1}−{b}\mathrm{ln}\:\frac{{x}}{{a}}\right)^{\mathrm{2}} }}\:{dx} \\ $$ Commented by ajfour last updated on 12/Feb/25 https://youtu.be/Kq4VqD0azog?si=K_P6MADAgm8CXegJ Terms of…
Question Number 216615 by EmGent last updated on 12/Feb/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{sin}\:{n}\pi{x}\:{J}_{\mathrm{0}} \left({j}_{\mathrm{0}{m}} {x}\right){dx} \\ $$ Answered by EmGent last updated on 12/Feb/25 $$\mathrm{Does}\:\mathrm{anyone}\:\mathrm{knows}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:? \\…
Question Number 216585 by MathematicalUser2357 last updated on 11/Feb/25 $$\mathrm{is}\:\mathrm{this}\:\mathrm{right}? \\ $$$$\mathrm{i}\:\mathrm{had}\:\mathrm{let}\:\theta=\begin{cases}{\mathrm{tan}^{−\mathrm{1}} \left(\frac{{d}}{{c}}\right)}&{\left({c}>\mathrm{0},{d}>\mathrm{0}\right)}\\{\pi−\mathrm{tan}^{−\mathrm{1}} \left(\frac{{d}}{{c}}\right)}&{\left({c}<\mathrm{0},{d}>\mathrm{0}\right)}\\{−\pi+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{d}}{{c}}\right)}&{\left({c}<\mathrm{0},{d}<\mathrm{0}\right)}\\{−\mathrm{tan}^{−\mathrm{1}} \left(\frac{{d}}{{c}}\right)}&{\left({c}>\mathrm{0},{d}<\mathrm{0}\right)}\end{cases}\:\mathrm{before}\:\mathrm{i}\:\mathrm{calculated}\:\mathrm{below} \\ $$$$\left({a}+{bi}\right)^{{c}+{di}} =\mid{a}+{di}\mid^{{c}+{di}} {e}^{{i}\left({c}+{di}\right)\theta} \\ $$$$=\mid{a}+{bi}\mid^{{c}} \mid{a}+{bi}\mid^{{di}} {e}^{{ic}\theta} {e}^{−{d}\theta}…
Question Number 216587 by Tawa11 last updated on 11/Feb/25 Commented by Tawa11 last updated on 11/Feb/25 In the mechanical system represented in Figure 16, the…
Question Number 216582 by klipto last updated on 11/Feb/25 $$ \\ $$$$\mathrm{using}\:\mathrm{first}\:\mathrm{principle}\:\mathrm{solve} \\ $$$$\mathrm{y}=\frac{\mathrm{x}+\mathrm{2}}{\:\sqrt{\mathrm{x}}+\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{with}\:\mathrm{first}\:\mathrm{principle} \\ $$ Commented by Rasheed.Sindhi last updated on 12/Feb/25…
Question Number 216592 by Davidtim last updated on 11/Feb/25 $${if}\:{we}\:{have}\:{the}\:{following}\:{system}: \\ $$$$\frac{{tanx}}{{tany}}={a} \\ $$$${x}\pm{y}=\alpha \\ $$$${we}\:{have}\:{the}\:{general}\:{candition}: \\ $$$$−\mathrm{1}\leqslant\left(\frac{{a}−\mathrm{1}}{{a}+\mathrm{1}}\right){sin}\alpha\leqslant\mathrm{1} \\ $$$${if}\:{you}\:{apply}\:{the}\:{general}\:{candition}\:{by} \\ $$$${the}\:{following}\:{system}\:{it}\:{does}\:{not}\:{give} \\ $$$${us}\:{the}\:{reality},\:{despite}\:{this}\:{system}\:{have} \\…
Question Number 216593 by Tawa11 last updated on 11/Feb/25 Answered by A5T last updated on 11/Feb/25 $$\mathrm{At}\:\mathrm{vertex},\:\:\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{2ax}+\mathrm{b}=\mathrm{0}\Rightarrow\mathrm{18a}+\mathrm{b}=\mathrm{0}\Rightarrow\mathrm{b}=−\mathrm{18a} \\ $$$$−\mathrm{14}=\mathrm{81a}+\mathrm{9b}+\mathrm{c} \\ $$$$\Rightarrow\mathrm{c}=−\mathrm{14}+\mathrm{81a} \\ $$$$\Rightarrow\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{a}−\mathrm{18a}−\mathrm{14}+\mathrm{81a}=\mathrm{64a}−\mathrm{14} \\ $$$$\frac{\mathrm{d}^{\mathrm{2}}…
Question Number 216579 by MrGaster last updated on 11/Feb/25 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{tan}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+\mathrm{sin}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}{\mathrm{tan}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+\mathrm{cos}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}{dxdy} \\ $$ Terms…
Question Number 216572 by Samuel12 last updated on 10/Feb/25 Answered by maths2 last updated on 11/Feb/25 $${si}\:\alpha\notin{I}\Rightarrow\alpha=\frac{{a}}{{b}}\in{IQ}\:\:{b} {a}=\mathrm{1}\:{on}\:{va}\:{montrer}\:{Que}\:{b}\mid{a} \\ $$$$\Rightarrow{a}^{{n}} −\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}{c}_{{k}} {a}^{{k}} {b}^{{n}−{k}}…
Question Number 216542 by Davidtim last updated on 10/Feb/25 $${if}\:{y}={cosu}\:{then}\:{prove}\:{that}\:{y}'={sinu}\centerdot{u}' \\ $$$${by}\:{newton}'{s}\:{formula}. \\ $$ Commented by Davidtim last updated on 11/Feb/25 $${please}\:{solve}\:{the}\:{problem}. \\ $$ Terms…