Question Number 18384 by Tinkutara last updated on 19/Jul/17 $$\mathrm{Let}\:{a},\:{b},\:{c}\:\in\:{R},\:{a}\:\neq\:\mathrm{0},\:\mathrm{such}\:\mathrm{that}\:{a}\:\mathrm{and} \\ $$$$\mathrm{4}{a}\:+\:\mathrm{3}{b}\:+\:\mathrm{2}{c}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{sign}.\:\mathrm{Show} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{can} \\ $$$$\mathrm{not}\:\mathrm{have}\:\mathrm{both}\:\mathrm{roots}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{1},\:\mathrm{2}\right). \\ $$ Answered by Tinkutara last…
Question Number 83919 by john santu last updated on 08/Mar/20 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{3}}{\pi}\mathrm{arc}\:\mathrm{tan}\:{x}\right)^{\mathrm{2}{x}} \:=\:? \\ $$ Commented by john santu last updated on 08/Mar/20 $$=\:\mathrm{e}\:^{\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\left(\mathrm{ln}\left(\frac{\mathrm{3}}{\pi}\mathrm{tan}^{−\mathrm{1}}…
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Question Number 83917 by turbo msup by abdo last updated on 07/Mar/20 $${find}\:\int\:\:\:\frac{{dx}}{\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} } \\ $$ Answered by redmiiuser last updated on 08/Mar/20 Answered…
Question Number 18379 by virus last updated on 19/Jul/17 Answered by mrW1 last updated on 19/Jul/17 $$\mathrm{T}=\mathrm{tension}\:\mathrm{in}\:\mathrm{rope} \\ $$$$\mathrm{4T}=\mathrm{m}_{\mathrm{A}} \mathrm{a}_{\mathrm{A}} \:\:\:…\left(\mathrm{i}\right) \\ $$$$\mathrm{F}−\mathrm{5T}=\mathrm{m}_{\mathrm{B}} \mathrm{a}_{\mathrm{B}} \:\:\:…\left(\mathrm{ii}\right)…
Question Number 18377 by tawa tawa last updated on 19/Jul/17 $$\mathrm{Suppose}\:\mathrm{one}\:\mathrm{is}\:\mathrm{given}\:\mathrm{two}\:\mathrm{vector}\:\mathrm{field}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{in}\:\mathrm{region}\:\mathrm{of}\:\mathrm{space}\:\mathrm{such}\:\mathrm{that}, \\ $$$$\mathrm{A}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\:\mathrm{4xi}\:+\:\mathrm{zj}\:+\:\mathrm{y}^{\mathrm{2}} \mathrm{z}^{\mathrm{2}} \mathrm{k} \\ $$$$\mathrm{B}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\:\mathrm{yi}\:+\mathrm{3j}\:−\:\mathrm{yzk} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{C}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:\mathrm{if}\:\mathrm{C}\:=\:\mathrm{A}\:\wedge\:\mathrm{B} \\ $$$$\mathrm{Also}\:\mathrm{prove}\:\mathrm{that},\:\:\mathrm{C}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{A}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right) \\ $$ Terms of…
Question Number 83910 by redmiiuser last updated on 07/Mar/20 $$\mathrm{find}\:\mathrm{all}\:\mathrm{6}\:\mathrm{digit}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{only}\:\mathrm{palindrome}\:\mathrm{but}\:\mathrm{also}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{495}. \\ $$ Commented by redmiiuser last updated on 08/Mar/20 $$\mathrm{CAN}\:\mathrm{ANYONE}\: \\ $$$$\mathrm{ANSWER}\:\mathrm{THIS} \\…
Question Number 149447 by liberty last updated on 05/Aug/21 $$\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\: \\ $$$$\:\begin{cases}{\mathrm{sin}\:\mathrm{2x}+\mathrm{cos}\:\mathrm{3y}=−\mathrm{1}}\\{\sqrt{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{y}}\:+\sqrt{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{y}}\:=\mathrm{1}+\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)}\end{cases} \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 149440 by nadovic last updated on 05/Aug/21 Answered by Olaf_Thorendsen last updated on 07/Aug/21 $$\left(\mathrm{a}\right)\:\mathrm{A}_{\mathrm{1}} =\:“\mathrm{persons}\:\mathrm{from}\:\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{three} \\ $$$$\mathrm{groups}''. \\ $$$$\mathrm{That}\:\mathrm{means}\:\mathrm{3}\:\mathrm{volleyball}\:\mathrm{players}\:\mathrm{or} \\ $$$$\mathrm{3}\:\mathrm{hockey}\:\mathrm{players}. \\…
Question Number 18369 by Tinkutara last updated on 19/Jul/17 $$\mathrm{Prove}\:\mathrm{that}\:{a}^{\mathrm{4}} \:+\:{b}^{\mathrm{4}} \:+\:{c}^{\mathrm{4}} \:\geqslant\:{abc}\left({a}\:+\:{b}\:+\:{c}\right) \\ $$ Answered by mrW1 last updated on 19/Jul/17 $$\mathrm{a}^{\mathrm{4}} +\mathrm{b}^{\mathrm{4}} \geqslant\mathrm{2a}^{\mathrm{2}}…