Question Number 216164 by BaliramKumar last updated on 29/Jan/25 Answered by AntonCWX last updated on 29/Jan/25 $${The}\:{smallest}\:{distance}\:{between}\:{two}\:{sides}\:{is}\:\mathrm{2}−\mathrm{1}=\mathrm{1} \\ $$$${The}\:{sum}\:{of}\:{three}\:{sides}\:{is}\:\mathrm{1}+\mathrm{2}+\mathrm{4}=\mathrm{7} \\ $$$${Let}\:{the}\:{fourth}\:{side}\:{be}\:{d} \\ $$$$\mathrm{1}<{d}<\mathrm{7} \\ $$$${possible}\:{values}:\:\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}…
Question Number 216183 by MATHEMATICSAM last updated on 29/Jan/25 Answered by A5T last updated on 29/Jan/25 $$=\mathrm{a}^{\mathrm{3}} −\mathrm{a}^{\mathrm{2}} \left(\mathrm{b}+\mathrm{c}\right)+\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} +\mathrm{2abc}−\mathrm{b}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{c}\right)−\mathrm{c}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{b}\right) \\ $$$$=\mathrm{a}^{\mathrm{2}}…
Question Number 216178 by hardmath last updated on 29/Jan/25 $$\mathrm{B}\:=\:\frac{\mathrm{3}^{\mathrm{4}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{3}^{\mathrm{7}} \:-\:\mathrm{3}}\:+\:\frac{\mathrm{4}^{\mathrm{4}} \:+\:\mathrm{4}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{4}^{\mathrm{7}} \:-\:\mathrm{4}}\:+\:…\:+\:\frac{\mathrm{10}^{\mathrm{4}} \:+\:\mathrm{10}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{10}^{\mathrm{7}} \:-\:\mathrm{1}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{B}\:+\:\frac{\mathrm{1}}{\mathrm{220}}\:=\:? \\ $$ Answered by…
Question Number 216153 by Tawa11 last updated on 28/Jan/25 Answered by AntonCWX last updated on 29/Jan/25 $${i}={i}_{{L}} =\frac{\mathrm{12}{V}}{\mathrm{1}\Omega+\mathrm{5}\Omega}=\mathrm{2}{A} \\ $$$${v}_{{C}} =\left(\mathrm{1}\Omega+\mathrm{4}\Omega\right)\left(\mathrm{2}{A}\right)=\mathrm{10}{V} \\ $$$$ \\ $$$${W}_{{C}}…
Question Number 216139 by mr W last updated on 28/Jan/25 Commented by mr W last updated on 28/Jan/25 $${find}\:\left({AP}+{PQ}\right)_{{min}} =? \\ $$ Commented by Ghisom…
Question Number 216123 by a.lgnaoui last updated on 28/Jan/25 $$\mathrm{determiner}\:\mathrm{la}\:\mathrm{surface}\:\mathrm{de} \\ $$$$\:\left[\mathrm{ADCMNFEB}\right]\:\: \\ $$ Commented by a.lgnaoui last updated on 28/Jan/25 Terms of Service Privacy…
Question Number 216144 by klipto last updated on 28/Jan/25 $$\mathrm{1}.\:\boldsymbol{\mathrm{Lim}}_{\mathrm{n}\rightarrow\infty} \left[\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+\frac{\mathrm{2}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+\frac{\mathrm{3}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+…+\frac{\boldsymbol{\mathrm{n}}+\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right] \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} \left(\frac{\mathrm{3}\boldsymbol{\mathrm{sin}}\mathrm{5}\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}\right)^{\frac{\mathrm{1}−\boldsymbol{\mathrm{cos}}\mathrm{4}\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }} \\ $$ Answered by Ghisom last…
Question Number 216161 by Spillover last updated on 28/Jan/25 Answered by MrGaster last updated on 15/Feb/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left({xy}\right)}{\mathrm{1}+{xy}}{xydxdy}=\int_{\mathrm{0}} ^{\mathrm{1}} {xdx}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left({xy}\right)}{\mathrm{1}+{xy}}{dy}…
Question Number 216162 by Spillover last updated on 28/Jan/25 Answered by MrGaster last updated on 02/Feb/25 $$\mathrm{Let}\:{x}=\frac{\pi}{\mathrm{3}}−{t}\Rightarrow{dx}=−{dt} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \sqrt{\mathrm{sin}^{\mathrm{3}} {x}\mathrm{sin}\left(\frac{\pi}{\mathrm{3}}−{x}\right)}{dx}\int_{\frac{\pi}{\mathrm{3}}} ^{\mathrm{0}} \sqrt{\mathrm{sin}^{\mathrm{3}} \left(\frac{\pi}{\mathrm{3}}−{t}\right)\mathrm{sin}\:{t}}\left(−{dt}\right)=\int_{\mathrm{0}}…
Question Number 216093 by mnjuly1970 last updated on 27/Jan/25 Answered by mahdipoor last updated on 27/Jan/25 $${note}\::\:\mathrm{0}\leqslant{x}<\mathrm{1}\:\:,\:\:{y}^{\mathrm{2}} =\left(\mathrm{1}+{y}^{\mathrm{2}} \right){x} \\ $$$${get}\:\:{f}={ln}\left({y}\right)+{ln}\left({y}'\right) \\ $$$$\Rightarrow\frac{{df}}{{dx}}=\frac{{y}^{'} }{{y}}+\frac{{y}^{''} }{{y}'}=\mathrm{2}\varphi…