Question Number 58176 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{If}\:\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} ,\:{x}_{\mathrm{4}} \:\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{4}} −{x}^{\mathrm{3}} \mathrm{sin}\:\mathrm{2}\beta+{x}^{\mathrm{2}} \mathrm{cos}\:\mathrm{2}\beta−{x}\:\mathrm{cos}\:\beta−\mathrm{sin}\:\beta=\mathrm{0}, \\ $$$$\mathrm{then} \\ $$$$\mathrm{tan}^{−\mathrm{1}} {x}_{\mathrm{1}}…
Question Number 58175 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\left(\pi+\theta\right)\:\mathrm{sin}\left(\pi−\theta\right)\:\mathrm{cosec}^{\mathrm{2}} \theta \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by math1967 last updated on 19/Apr/19 $$−{sin}\theta×{sin}\theta×{cosec}^{\mathrm{2}} \theta=−\mathrm{1}…
Question Number 58174 by mamah Fousséni last updated on 19/Apr/19 $$\mathrm{Four}\:\mathrm{digit}\:\mathrm{integers}\:\mathrm{are}\:\mathrm{taken}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{and}\:\mathrm{are}\:\mathrm{multiplied}\:\mathrm{together}.\:\mathrm{Then}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{them}\:\mathrm{will} \\ $$$$\mathrm{be}\:\mathrm{alive}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{year}\:\mathrm{is} \\ $$ Commented by mr W last updated…
Question Number 58056 by Salomon M. last updated on 17/Apr/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{forces}\:\mathrm{2}\boldsymbol{\mathrm{i}}−\mathrm{5}\boldsymbol{\mathrm{j}}+\mathrm{6}\boldsymbol{\mathrm{k}}\:\mathrm{and} \\ $$$$−\boldsymbol{\mathrm{i}}+\mathrm{2}\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}}\:\mathrm{act}\:\mathrm{on}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{due}\:\mathrm{to}\:\mathrm{which} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{displaced}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:{A}\left(\mathrm{4},−\mathrm{3},−\mathrm{2}\right) \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{point}\:{B}\left(\mathrm{6},\:\mathrm{1},−\mathrm{3}\right),\:\mathrm{then}\:\mathrm{the}\:\mathrm{work}\: \\ $$$$\mathrm{done}\:\mathrm{by}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{is} \\ $$ Answered by tanmay last…
Question Number 58055 by Salomon M. last updated on 17/Apr/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{forces}\:\mathrm{2}\boldsymbol{\mathrm{i}}−\mathrm{5}\boldsymbol{\mathrm{j}}+\mathrm{6}\boldsymbol{\mathrm{k}}\:\mathrm{and} \\ $$$$−\boldsymbol{\mathrm{i}}+\mathrm{2}\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}}\:\mathrm{act}\:\mathrm{on}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{due}\:\mathrm{to}\:\mathrm{which} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{displaced}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:{A}\left(\mathrm{4},−\mathrm{3},−\mathrm{2}\right) \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{point}\:{B}\left(\mathrm{6},\:\mathrm{1},−\mathrm{3}\right),\:\mathrm{then}\:\mathrm{the}\:\mathrm{work}\: \\ $$$$\mathrm{done}\:\mathrm{by}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{is} \\ $$ Answered by Kunal12588 last…
Question Number 57822 by 1103264451 last updated on 12/Apr/19 $$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{non}\:\mathrm{empty}\: \\ $$$$\mathrm{equivalent}\:\mathrm{sets},\:\mathrm{then}\:\mathrm{a}\:\mathrm{possible}\:\mathrm{value} \\ $$$$\mathrm{of}\:{n}\left(\mathrm{A}×\mathrm{B}\right)\:\mathrm{is} \\ $$ Commented by Rasheed.Sindhi last updated on 13/Apr/19 $${n}\left(\mathrm{A}×\mathrm{B}\right)={n}\left(\mathrm{A}\right)×{n}\left(\mathrm{B}\right) \\…
Question Number 57448 by Pk1167156@gmail.com last updated on 04/Apr/19 $$\mathrm{If}\:\:\:\mathrm{sin}\:{x}+\mathrm{cosec}\:{x}=\mathrm{2},\:\mathrm{then}\:\mathrm{sin}^{{n}} {x}+\mathrm{cosec}^{{n}} {x} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Apr/19 $${a}+\frac{\mathrm{1}}{{a}}=\mathrm{2} \\…
Question Number 57140 by mustakim420 last updated on 30/Mar/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}\:{dx}\:\leqslant\:\frac{\mathrm{15}}{\mathrm{8}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19 $$\frac{\mathrm{1}+{x}}{\mathrm{2}}\geqslant\sqrt{{x}}\: \\ $$$$\frac{\mathrm{1}+{x}^{\mathrm{3}}…
Question Number 57138 by mustakim420 last updated on 30/Mar/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\:\mathrm{cos}\:{x}+\mathrm{1}}\:{dx}\:\:\left({a}\:>\mathrm{1}\right)\:\:\mathrm{is} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 57136 by mustakim420 last updated on 30/Mar/19 $$\underset{{a}} {\overset{{b}} {\int}}\:\:\frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19 $${I}=\int_{{a}} ^{{b}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx} \\…