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Author: Tinku Tara

Show-that-t-0-x-1-where-x-e-t-2-t-2-2t-2-t-R-

Question Number 915 by 112358 last updated on 24/Apr/15 $${Show}\:{that}\:\forall{t}\geqslant\mathrm{0}\:,\:{x}\leqslant\mathrm{1}\:{where} \\ $$$${x}=\frac{{e}^{−{t}} }{\mathrm{2}}\left({t}^{\mathrm{2}} +\mathrm{2}{t}+\mathrm{2}\right)\:\:,\:{t}\in\mathbb{R}.\: \\ $$ Commented by 123456 last updated on 24/Apr/15 $${t}\geqslant\mathrm{0}\Leftrightarrow−{t}\leqslant\mathrm{0}\Leftrightarrow{e}^{−{t}} \leqslant{e}^{\mathrm{0}}…

Eight-people-are-seated-around-a-circular-table-Each-person-must-shake-everyone-s-hand-but-they-must-not-shake-hands-with-the-two-persons-seated-at-their-sides-How-many-handshakes-occur-

Question Number 911 by 112358 last updated on 22/Apr/15 $${Eight}\:{people}\:{are}\:{seated}\:{around} \\ $$$${a}\:{circular}\:{table}.\:{Each}\:{person} \\ $$$${must}\:{shake}\:{everyone}'{s}\:{hand}\:{but} \\ $$$${they}\:{must}\:{not}\:{shake}\:{hands}\:{with} \\ $$$${the}\:{two}\:{persons}\:{seated}\:{at}\:{their}\:{sides}. \\ $$$${How}\:{many}\:{handshakes}\:{occur}? \\ $$ Answered by prakash…

Show-that-for-the-system-of-equations-x-y-z-3-2x-2y-2z-6-3x-3y-3z-9-the-general-solution-is-given-by-x-1-

Question Number 908 by 112358 last updated on 20/Apr/15 $${Show}\:{that}\:{for}\:{the}\:{system}\:{of}\: \\ $$$${equations} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}+{y}+{z}=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}=\mathrm{6} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}{x}+\mathrm{3}{y}+\mathrm{3}{z}=\mathrm{9} \\ $$$${the}\:{general}\:{solution}\:{is}\:{given}\:{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\lambda+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}=\mu+\mathrm{1} \\…

Determine-the-results-of-the-following-I-1-a-e-x-a-e-x-dx-I-2-tanx-tanx-1-tan-2-x-dx-

Question Number 907 by Yugi last updated on 19/Apr/15 $${Determine}\:{the}\:{results}\:{of}\:{the}\:{following}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}_{\mathrm{1}} =\int\sqrt{\frac{{a}+{e}^{{x}} }{{a}−{e}^{{x}} }}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}_{\mathrm{2}} =\int\frac{\left({tanx}\right)\mid{tanx}\mid}{\mathrm{1}−{tan}^{\mathrm{2}} {x}}{dx} \\ $$ Commented by prakash jain…

for-a-geometric-series-can-the-sun-to-infinty-use-the-two-formulas-S-a-1-r-r-lt-1-and-S-a-r-1-r-gt-1-please-i-am-getting-confused-on-this-

Question Number 66439 by Rio Michael last updated on 15/Aug/19 $${for}\:{a}\:{geometric}\:{series}. \\ $$$${can}\:{the}\:{sun}\:{to}\:{infinty}\:{use}\:{the}\:{two}\:{formulas} \\ $$$${S}_{\infty} =\:\frac{{a}}{\mathrm{1}−{r}}\:\:\mid{r}\mid\:\:<\mathrm{1}\:\:{and}\:{S}_{\infty} \:=\:\frac{{a}}{{r}−\mathrm{1}}\:\mid{r}\mid\:>\:\mathrm{1}\:??\:{please}\:{i}\:{am}\:{getting}\:{confused}\:{on}\:{this}. \\ $$ Commented by JDamian last updated on…

X-is-a-person-that-can-only-one-of-these-a-only-tell-truth-b-only-tell-lie-using-a-minimal-number-of-question-how-to-discover-what-type-of-people-are-X-

Question Number 902 by 123456 last updated on 18/Apr/15 $$\mathrm{X}\:\mathrm{is}\:\mathrm{a}\:\mathrm{person}\:\mathrm{that}\:\mathrm{can}\:\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{these} \\ $$$$\mathrm{a}.\mathrm{only}\:\mathrm{tell}\:\mathrm{truth} \\ $$$$\mathrm{b}.\mathrm{only}\:\mathrm{tell}\:\mathrm{lie} \\ $$$$\mathrm{using}\:\mathrm{a}\:\mathrm{minimal}\:\mathrm{number}\:\mathrm{of}\:\mathrm{question} \\ $$$$\mathrm{how}\:\mathrm{to}\:\mathrm{discover}\:\mathrm{what}\:\mathrm{type}\:\mathrm{of}\:\mathrm{people} \\ $$$$\mathrm{are}\:\mathrm{X}? \\ $$ Answered by prakash…

Ninety-students-including-Joe-and-Jane-are-to-be-split-into-three-classes-of-equal-size-and-is-to-be-done-at-random-What-is-the-probability-that-Joe-and-Jane-end-up-in-the-same-class-

Question Number 131975 by liberty last updated on 10/Feb/21 $$\:\mathrm{Ninety}\:\mathrm{students}\:,\:\mathrm{including}\:\mathrm{Joe} \\ $$$$\mathrm{and}\:\mathrm{Jane}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{split}\:\mathrm{into}\: \\ $$$$\mathrm{three}\:\mathrm{classes}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{size}\:\mathrm{and}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{done}\:\mathrm{at}\:\mathrm{random}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{Joe}\:\mathrm{and}\:\mathrm{Jane} \\ $$$$\mathrm{end}\:\mathrm{up}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{class}\:? \\ $$ Commented by liberty…