Question Number 45830 by jashim last updated on 17/Oct/18 $$\mathrm{Given}\:{A}=\:\mathrm{sin}^{\mathrm{2}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta,\:\mathrm{then}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\theta \\ $$ Commented by maxmathsup by imad last updated on 17/Oct/18…
Question Number 45829 by jashim last updated on 17/Oct/18 $$\mathrm{Given}\:{A}=\:\mathrm{sin}^{\mathrm{2}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta,\:\mathrm{then}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\theta \\ $$ Commented by MJS last updated on 17/Oct/18 $$\mathrm{this}\:\mathrm{isn}'\mathrm{t}\:\mathrm{a}\:\mathrm{clear}\:\mathrm{question}. \\…
Question Number 111001 by ZiYangLee last updated on 01/Sep/20 $$\mathrm{Two}\:\mathrm{numbers}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at} \\ $$$$\mathrm{random}\:\mathrm{from}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{first}\:\mathrm{30}\:\mathrm{natural} \\ $$$$\mathrm{numbers}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:{a}^{\mathrm{2}} −{b}^{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{is} \\ $$ Commented by bemath last updated on…
Question Number 44612 by rahul 19 last updated on 02/Oct/18 $${Prove}\:{that}\:\mathrm{One}\:\mathrm{factor}\:\mathrm{of}\begin{vmatrix}{{a}^{\mathrm{2}} +{x}}&{\:\:{ab}}&{\:\:{ac}}\\{\:\:{ab}}&{{b}^{\mathrm{2}} +{x}}&{\:\:{cb}}\\{\:\:{ca}}&{\:\:{cb}}&{{c}^{\mathrm{2}} +{x}}\end{vmatrix}\:\mathrm{is}\:{x}^{\mathrm{2}} . \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 Commented…
Question Number 44541 by Yadavsantosh37941@gmail.com last updated on 01/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{the} \\ $$$$\mathrm{polynomial}\:{p}\left({y}\right)={y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{1}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:{y}−\mathrm{1}. \\ $$ Commented by $@ty@m last updated on 01/Oct/18…
Question Number 110016 by ZiYangLee last updated on 26/Aug/20 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left({x}+\mathrm{1}\right)+\left({x}+\mathrm{4}\right)+\left({x}+\mathrm{7}\right)+…+\left({x}+\mathrm{28}\right)=\mathrm{155} \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{x}\:=\:\_\_\_\_\_. \\ $$ Answered by Aziztisffola last updated on 26/Aug/20 $$\:\mathrm{10}{x}+\mathrm{1}+\mathrm{4}+\mathrm{7}+…+\mathrm{28}=\mathrm{155} \\…
Question Number 110015 by ZiYangLee last updated on 26/Aug/20 $$\mathrm{The}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{are} \\ $$$$\mathrm{grouped}\:\mathrm{as}\:\mathrm{1}^{\mathrm{3}} ,\:\left(\mathrm{2}^{\mathrm{3}} ,\:\mathrm{3}^{\mathrm{3}} \right),\:\left(\mathrm{4}^{\mathrm{3}} ,\:\mathrm{5}^{\mathrm{3}} ,\:\mathrm{6}^{\mathrm{3}} \right),\:…., \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{the}\:{n}\mathrm{th} \\ $$$$\mathrm{group}\:\mathrm{is} \\ $$ Commented…
Question Number 44315 by Tip Top last updated on 26/Sep/18 $$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{{n}} \:\mathrm{is}\:\mathrm{6561},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{is} \\ $$ Answered by MrW3 last updated on 27/Sep/18…
Question Number 44231 by Mawitea Cck last updated on 24/Sep/18 $$\mathrm{The}\:\mathrm{square}\:\mathrm{root}\:\mathrm{of}\:\:{x}^{{m}^{\mathrm{2}} −{n}^{\mathrm{2}} } \centerdot\:{x}^{{n}^{\mathrm{2}} +\mathrm{2}{mn}} \centerdot\:{x}^{{n}^{\mathrm{2}} } \:\mathrm{is} \\ $$ Answered by Joel578 last updated…
Question Number 44128 by gunawan last updated on 22/Sep/18 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{5}−\mathrm{tuples} \\ $$$$\left({a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:{a}_{\mathrm{4}} ,\:{a}_{\mathrm{5}} \right)\:\mathrm{such}\:\mathrm{that}\: \\ $$$${a}_{\mathrm{1}} +{a}_{\mathrm{2}} \mathrm{sin}\:{x}+{a}_{\mathrm{3}} \mathrm{cos}\:{x}+{a}_{\mathrm{4}} \mathrm{sin}\:\mathrm{2}{x}+{a}_{\mathrm{5}} \mathrm{cos}\:\mathrm{2}{x}=\mathrm{0} \\…