Question Number 196277 by cortano12 last updated on 21/Aug/23 $$\:\:\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$ Answered by mr W last updated on 21/Aug/23 $${say}\:{z}=\mathrm{sin}^{\mathrm{3}} \:{x} \\ $$$$\frac{{dz}}{{dy}}=\frac{{dz}}{{dx}}×\frac{{dx}}{{dy}}=\mathrm{3}\:\mathrm{sin}^{\mathrm{2}}…
Question Number 196276 by SaRahAli last updated on 21/Aug/23 Answered by MM42 last updated on 21/Aug/23 $$\int\:\frac{{dx}}{\mathrm{1}+{sin}\mathrm{2}{x}}\:=\int\:\frac{\mathrm{1}+{tan}^{\mathrm{2}} {x}}{\left(\mathrm{1}+{tanx}\right)^{\mathrm{2}} }\:{dx} \\ $$$$\overset{\mathrm{1}+{tanx}={u}} {=}\:\int\:\frac{{du}}{{u}}\:={lnu}+{c} \\ $$$$={ln}\left(\mathrm{1}+{tanx}\right)+{c}\:\checkmark \\…
Question Number 196275 by AROUNAMoussa last updated on 21/Aug/23 Answered by MM42 last updated on 21/Aug/23 $$\langle{ABD}=\mathrm{35}\Rightarrow{AD}={AB} \\ $$$$\langle{BCD}=\mathrm{55} \\ $$$$\frac{{AB}}{{AC}}=\frac{{sinx}}{{sin}\mathrm{130}}\:\:\:\&\:\:\frac{{AD}}{{AC}}=\frac{{sin}\left(\mathrm{55}−{x}\right)}{{sin}\mathrm{65}} \\ $$$$\Rightarrow{sinx}×{sin}\mathrm{65}=\mathrm{2}{sin}\mathrm{65}×{cos}\mathrm{65}×{sin}\left(\mathrm{55}−{x}\right) \\ $$$$\Rightarrow{sinx}=\mathrm{2}{cos}\mathrm{65}{sin}\left(\mathrm{55}−{x}\right)={sin}\left(\mathrm{55}−{x}+\mathrm{65}\right)+{sin}\left(\mathrm{55}−{x}−\mathrm{65}\right)…
Question Number 196265 by KRIMO last updated on 21/Aug/23 Answered by a.lgnaoui last updated on 21/Aug/23 $$\mathrm{posons}\:\mathrm{z}=\mathrm{a}+\mathrm{ib}\:\Leftrightarrow\mathrm{z}=\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:}\:\left(\frac{\mathrm{a}}{\:\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }}+\mathrm{i}\frac{\mathrm{b}}{\:\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }}\right) \\ $$$$\mathrm{avec}\:\:\frac{\mathrm{a}}{\:\sqrt{\mathrm{a}^{\mathrm{2}}…
Question Number 196267 by Rodier97 last updated on 21/Aug/23 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:{if}\:\:\:{lim}_{{n}\rightarrow+\infty} \:\left(\mathrm{1}+\:\frac{{x}}{\mathrm{7}{n}}\right)^{\mathrm{29}{n}} =\mathrm{2023} \\ $$$$\:\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{{x}}\:?? \\ $$$$ \\…
Question Number 196261 by sonukgindia last updated on 21/Aug/23 Answered by mr W last updated on 22/Aug/23 Commented by mr W last updated on 22/Aug/23…
Question Number 196257 by mathlove last updated on 21/Aug/23 Answered by cortano12 last updated on 21/Aug/23 $$\:\:\mathrm{g}\left(\mathrm{x}\right)\:\Rightarrow\mathrm{m}\:=\:\mathrm{2}+\mathrm{b}\:\mathrm{and}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\:\mathrm{1}+\mathrm{b}+\mathrm{c}\right) \\ $$$$\:\Rightarrow\mathrm{y}−\left(\mathrm{1}+\mathrm{b}+\mathrm{c}\right)=\:\left(\mathrm{2}+\mathrm{b}\right)\left(\mathrm{x}−\mathrm{1}\right) \\ $$$$\:\Rightarrow\mathrm{y}=\:\left(\mathrm{2}+\mathrm{b}\right)\mathrm{x}−\mathrm{2}−\mathrm{b}+\mathrm{1}+\mathrm{b}+\mathrm{c} \\ $$$$\:\Rightarrow\mathrm{y}=\:\left(\mathrm{2}+\mathrm{b}\right)\mathrm{x}+\mathrm{c}−\mathrm{1}…
Question Number 196258 by York12 last updated on 21/Aug/23 $${If}\left({x}_{{m}} +{iy}_{{m}} \right)^{\mathrm{2}{n}+\mathrm{1}} =\mathrm{1}\:,\:{such}\:{that} \\ $$$${m}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},….,\mathrm{2}{n}\right\}\:\wedge\:{x}_{{m}} ,{y}_{{m}} \in\mathbb{R} \\ $$$${p}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2020}} {\sum}}\left[\frac{\mathrm{1}−{x}_{{k}} +{iy}_{{k}} }{\mathrm{1}+{x}_{{k}} +{iy}_{{k}} }\right]\:,\:{Find}\:\left(\frac{{p}}{\mathrm{43}}\right)…
Question Number 196221 by liuxinnan last updated on 20/Aug/23 $${there}\:{is}\:{a}\:{cylinder}\:{on}\:{the}\:{horizontal}\:{plane} \\ $$$${and}\:{there}\:{is}\:{a}\:{little}\:{ball}\:{with}\:{mass}\:{m} \\ $$$${at}\:{the}\:{center}\:{of}\:{a}\:{circle}\:{on}\:{the}\:{vertical}\:{plane} \\ $$$${and}\:{there}\:{is}\:{a}\:{little}\:{hole}\:{in}\:{the}\:{wall}\:{of} \\ $$$${the}\:{cylinder}\:{on}\:{the}\:{lift}\:{of}\:{the}\:{ball}\:{which} \\ $$$${just}\:{enough}\:{for}\:{the}\:{ball}\:{to}\:{pass}\:{through} \\ $$$${the}\:{gravitational}\:{acceleration}\:{is}\:{g} \\ $$$${the}\:{collision}\:{between}\:{the}\:{ball}\:{and} \\…
Question Number 196249 by mathlove last updated on 20/Aug/23 $${log}_{{a}} {x}=\mathrm{30} \\ $$$${log}_{{b}} {x}=\mathrm{70} \\ $$$${log}_{{ab}} {x}=? \\ $$ Answered by AST last updated on…