Question Number 191631 by Spillover last updated on 27/Apr/23 $$\int_{\mathrm{0}} ^{\infty} {x}^{\frac{\mathrm{1}}{\mathrm{2}}} {e}^{−{x}^{\mathrm{2}} } {dx} \\ $$ Answered by malwan last updated on 28/Apr/23 $${put}\:{x}^{\mathrm{2}}…
Question Number 126092 by physicstutes last updated on 17/Dec/20 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{time}\:{t}\:=\:\mathrm{0}\:\mathrm{and}\:\mathrm{moves}\:\mathrm{in}\: \\ $$$$\mathrm{a}\:\mathrm{straightline}\:\mathrm{with}\:\mathrm{variable}\:\mathrm{acceleration}\:{a}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \:\mathrm{where}\: \\ $$$$\:{a}\:=\:\frac{{t}}{\mathrm{5}}\:,\:\mathrm{0}\:\leqslant\:{t}\:\leqslant\:\mathrm{5}\:,\:{a}\:=\:\frac{{t}}{\mathrm{5}}\:+\:\frac{\mathrm{10}}{{t}^{\mathrm{2}} }\:,\:{t}\:\geqslant\:\mathrm{5},\:{t}\:\mathrm{being}\:\mathrm{measured}\:\mathrm{in}\:\mathrm{seconds}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{is}\:\mathrm{22}\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{m}/\mathrm{s}\:\mathrm{when}\:{t}\:=\:\mathrm{5}\:\mathrm{and} \\ $$$$\mathrm{11}\:\mathrm{m}/\mathrm{s}\:\mathrm{when}\:{t}\:=\:\mathrm{10}. \\ $$$$\mathrm{Show}\:\mathrm{also}\:\mathrm{that}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{10}\:\mathrm{seconds}\:\mathrm{is}\:\:\left(\mathrm{43}\frac{\mathrm{1}}{\mathrm{3}}−\mathrm{10}\:\mathrm{ln}\:\mathrm{2}\right)\:\mathrm{m}. \\…
Question Number 191624 by Shrinava last updated on 27/Apr/23 Answered by ARUNG_Brandon_MBU last updated on 28/Apr/23 $$\int_{\mathrm{1}} ^{{x}} \sqrt{\frac{{t}}{\mathrm{1}+{t}^{\mathrm{3}} }}{dt} \\ $$$$=\int_{\mathrm{1}} ^{{x}} \frac{{t}^{\frac{\mathrm{1}}{\mathrm{2}}} }{\:\sqrt{\mathrm{1}+\left({t}^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 191626 by yaba1 last updated on 27/Apr/23 Answered by a.lgnaoui last updated on 28/Apr/23 $$\:\:\:\mathrm{Calcul}\:\mathrm{de}\:\mathrm{Resistance}\:\mathrm{dans}\:\mathrm{les}\:\mathrm{4}\:\mathrm{circuits} \\ $$$$\bullet\mathrm{1}\boldsymbol{\mathrm{a}}\:\:\:\boldsymbol{\mathrm{U}}=\boldsymbol{\mathrm{RI}}\:\:\:\mathrm{avec}\:\:\frac{\mathrm{1}}{\mathrm{R}}=\frac{\mathrm{1}}{\mathrm{R1}}+\frac{\mathrm{1}}{\mathrm{R2}}+\frac{\mathrm{1}}{\mathrm{R3}} \\ $$$$\:\:\:\:\:=\frac{\mathrm{R1}+\mathrm{R2}}{\mathrm{R1}×\mathrm{R2}}+\frac{\mathrm{1}}{\mathrm{R3}}=\frac{\left(\mathrm{R1}×\mathrm{R3}+\mathrm{R2}×\mathrm{R3}+\mathrm{R1}×\mathrm{R2}\right)}{\mathrm{R1}×\mathrm{R2}×\mathrm{R3}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{R}}=\frac{\mathrm{R1}×\mathrm{R2}×\mathrm{R3}}{\mathrm{R1}×\mathrm{R2}+\mathrm{R2}×\mathrm{R3}+\mathrm{R1}×\mathrm{R3}} \\ $$$$…
Question Number 191621 by Noorzai last updated on 27/Apr/23 Answered by gatocomcirrose last updated on 27/Apr/23 $$\mathrm{x}^{\mathrm{2}} =\mathrm{x}+\mathrm{1}\Rightarrow\mathrm{x}^{\mathrm{8}} =\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right)^{\mathrm{2}} =\left(\mathrm{3x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$=\mathrm{9x}^{\mathrm{2}} +\mathrm{12x}+\mathrm{4}=\mathrm{9x}+\mathrm{9}+\mathrm{12x}+\mathrm{4}=\mathrm{21x}+\mathrm{13} \\…
Question Number 191623 by Shrinava last updated on 27/Apr/23 Answered by mehdee42 last updated on 27/Apr/23 $${let}\::\:{f}\left({x}\right)={ax}+{b} \\ $$$${f}\left({f}\left({x}\right)\right)+{f}\left({x}\right)=−{x}\:\Rightarrow\left({a}^{\mathrm{2}} +{a}\right){x}+{ab}+\mathrm{2}{b}=−{x}\Rightarrow{a}=\frac{−\mathrm{1}+\sqrt{\mathrm{3}}{i}}{\mathrm{2}}={e}^{\frac{\mathrm{2}\pi}{\mathrm{3}}{i}} \:\:\&\:\:{b}=\mathrm{0}\Rightarrow{f}\left({x}\right)={e}^{\frac{\mathrm{2}\pi}{\mathrm{3}}{i}} {x} \\ $$$${f}\left({f}\left({f}\left(\frac{\mathrm{1}}{\mathrm{2}+{cosx}}\right)\right)\right)=\frac{\mathrm{1}}{\mathrm{2}+{cosx}} \\…
Question Number 126082 by amns last updated on 17/Dec/20 $$\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{only}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{three}}\:-\:\boldsymbol{\mathrm{digit}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{square}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{also}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{cube}}.\:\boldsymbol{\mathrm{Now}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{tell}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\left[{Help}\:{me}\right] \\ $$ Commented by mr…
Question Number 126080 by ajfour last updated on 17/Dec/20 Commented by ajfour last updated on 18/Dec/20 $${Cylinder}\:{and}\:{sphere}\:{have}\:{the} \\ $$$${same}\:{radius}.\:{An}\:{equilateral} \\ $$$${triangular}\:{plate}\:{rests}\:{on}\:{sphere} \\ $$$${with}\:{two}\:{vertices}\:{against}\:{curved} \\ $$$${surface}\:{of}\:{cylinder}\:{and}\:{top}\:{vertex}…
Question Number 60545 by Tawa1 last updated on 21/May/19 Answered by MJS last updated on 22/May/19 $$\mathrm{diameter}\:\mathrm{2}\:\mathrm{volume}\:\mathrm{2}^{\mathrm{3}} =\mathrm{8} \\ $$$$\mathrm{diameter}\:\mathrm{3}\:\mathrm{volume}\:\mathrm{3}^{\mathrm{3}} =\mathrm{27} \\ $$$$\mathrm{diameter}\:\mathrm{4}\:\mathrm{volume}\:\mathrm{4}^{\mathrm{3}} =\mathrm{64} \\…
Question Number 126078 by amns last updated on 17/Dec/20 $$\boldsymbol{\mathrm{Tell}}\:\boldsymbol{\mathrm{me}} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\mathrm{12}}\:−\:\frac{\mathrm{1}}{\mathrm{20}}\:−\:\frac{\mathrm{1}}{\mathrm{30}}\:−\:\frac{\mathrm{1}}{\mathrm{42}}\:−\:…..\:−\:\frac{\mathrm{1}}{\mathrm{210}}\:=\:? \\ $$ Commented by Dwaipayan Shikari last updated on 17/Dec/20 $$\frac{\mathrm{7}}{\mathrm{30}} \\ $$…