Question Number 139647 by LUFFY last updated on 30/Apr/21 Commented by LUFFY last updated on 30/Apr/21 $${which}\:{one}\:{is}\:{correct}??????\left({B}\:{or}\:{W}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 74109 by FCB last updated on 19/Nov/19 Commented by mr W last updated on 19/Nov/19 $${for}\:{a}_{{k}} >\mathrm{0}\:{and}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} =\mathrm{1} \\ $$$${when}\:{a}_{{k}} =\frac{\mathrm{1}}{{n}},…
Question Number 139641 by EnterUsername last updated on 30/Apr/21 $$\mathrm{Let}\:{a},\:{b}\:\mathrm{be}\:\mathrm{non}-\mathrm{zero}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{and}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{z}^{\mathrm{2}} +{az}+{b}=\mathrm{0}.\:\mathrm{If}\:\mathrm{there}\:\mathrm{exists} \\ $$$$\lambda\geqslant\mathrm{4}\:\mathrm{such}\:\mathrm{that}\:{a}^{\mathrm{2}} =\lambda{b},\:\mathrm{then}\:\mathrm{the}\:\mathrm{points}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{origin} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{form}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\…
Question Number 8571 by tawakalitu last updated on 16/Oct/16 Commented by sandy_suhendra last updated on 16/Oct/16 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{potensial}\:\mathrm{of}\:\mathrm{supply}\:\mathrm{1}.\mathrm{0}\:\mathrm{volt}? \\ $$ Commented by tawakalitu last updated on…
Question Number 139642 by ajfour last updated on 30/Apr/21 $${If}\:\:\mathrm{0}<{c}^{\mathrm{2}} <\frac{\mathrm{4}}{\mathrm{27}}\:\:,\:{and} \\ $$$${m}\left\{\mathrm{4}{c}^{\mathrm{2}} −{m}\left(\mathrm{1}+{m}\right)^{\mathrm{2}} \right\} \\ $$$$\:\:\:\:\:=\left\{{m}\left(\mathrm{1}+{m}\right)^{\mathrm{2}} −\mathrm{3}{c}^{\mathrm{2}} \right\}^{\mathrm{2}} \:\:{then} \\ $$$${find}\:{real}\:{values}\:{of}\:{m}\:{in}\:{terms} \\ $$$${of}\:{c}^{\mathrm{2}} .…
Question Number 139639 by bemath last updated on 30/Apr/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflection}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{point}\:\left(\mathrm{2},\mathrm{2}\right)\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}+\mathrm{2y}\:=\:\mathrm{4}? \\ $$ Commented by bramlexs22 last updated on 30/Apr/21 $$\mathrm{Let}\:\mathrm{P}\left(\mathrm{2},\mathrm{2}\right)\:\&\:\mathrm{P}'\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflectional} \\ $$$$\mathrm{image}\:\mathrm{of}\:\mathrm{P}\:\mathrm{in}\:\mathrm{L}. \\…
Question Number 8564 by tawakalitu last updated on 16/Oct/16 Commented by ridwan balatif last updated on 16/Oct/16 $$\mathrm{let}:\:\mathrm{V}'=\mathrm{V}_{\mathrm{o}} −\mathrm{4}\:,\:\:\:\mathrm{with}\:\mathrm{V}_{\mathrm{o}} \:\mathrm{is}\:\mathrm{speed}\:\mathrm{that}\:\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{count}\:\mathrm{it} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{t}^{'} \:=\mathrm{t}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:=\mathrm{240}\:\mathrm{km}…
Question Number 8560 by FilupSmith last updated on 16/Oct/16 $$\frac{{n}}{\mathrm{2}^{{k}} }={m},\:\:\:\:\:\:\:{n},{m},{k}\in\mathbb{Z} \\ $$$$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{n},\:\mathrm{how}\:\mathrm{many}\:\mathrm{times} \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{divide}\:\mathrm{it}\:\mathrm{by}\:\mathrm{2},\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{result}\:\mathrm{is}\:\mathrm{always}\:\mathrm{a}\:\mathrm{whole}\:\mathrm{number}. \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\mathrm{120} \\ $$$$\mathrm{160}/\mathrm{2}=\mathrm{80} \\ $$$$\mathrm{80}/\mathrm{2}=\mathrm{40}…
Question Number 8558 by Sopheak last updated on 16/Oct/16 Commented by FilupSmith last updated on 16/Oct/16 $${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}^{\mathrm{4}} }{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)} \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)}=\frac{{A}}{\mathrm{2}{k}−\mathrm{1}}+\frac{{B}}{\mathrm{2}{k}+\mathrm{1}} \\ $$$$\mathrm{1}={A}\left(\mathrm{2}{k}+\mathrm{1}\right)+{B}\left(\mathrm{2}{k}−\mathrm{1}\right)…
Question Number 8554 by Sopheak last updated on 16/Oct/16 $${Problem}\:.\mathrm{15} \\ $$$${Find}\:{the}\:{sum}\:{of} \\ $$$${S}=\:\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}+\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}+…+\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!} \\ $$$$\: \\ $$ Commented by Yozzias last updated on 16/Oct/16…