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Author: Tinku Tara

Let-a-b-be-non-zero-complex-numbers-and-z-1-z-2-be-the-roots-of-the-equation-z-2-az-b-0-If-there-exists-4-such-that-a-2-b-then-the-points-z-1-z-2-and-the-origin-A-form-an-equilateral-t

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-8571

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…

If-0-lt-c-2-lt-4-27-and-m-4c-2-m-1-m-2-m-1-m-2-3c-2-2-then-find-real-values-of-m-in-terms-of-c-2-

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}} .…

What-is-the-reflection-of-the-point-2-2-in-the-line-x-2y-4-

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-8564

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}…

n-2-k-m-n-m-k-Z-For-any-integer-n-how-many-times-can-you-divide-it-by-2-such-that-the-result-is-always-a-whole-number-e-g-120-160-2-80-80-2-40-40-2-20-20-2-10-10-2-5-5-2-Z-divides-5-t

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-8558

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)…

Problem-15-Find-the-sum-of-S-3-1-2-3-4-2-3-4-5-3-4-5-2016-2014-2015-2016-

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…