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 $${I}=\int_{{a}} ^{{b}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx} \\…
Question Number 56886 by gunawan last updated on 25/Mar/19 $$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{r}} \frac{\mathrm{1}+{r}\:\mathrm{log}_{{e}} \mathrm{10}}{\left(\mathrm{1}+\mathrm{log}_{{e}} \mathrm{10}^{{n}} \right)^{{r}} }\:\:\mathrm{equals} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 56424 by gunawan last updated on 16/Mar/19 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{10}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\left({x}+\:\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} \:+\:\left({x}^{\mathrm{2}} +\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}} \:+\:\left({x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\mathrm{2}} +…\:\mathrm{is} \\ $$ Answered by mr W…
Question Number 56423 by gunawan last updated on 16/Mar/19 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{15}}\:+\:\frac{\mathrm{1}}{\mathrm{35}}\:+\:….\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{2}}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19 $${T}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{3}−\mathrm{1}}{\mathrm{3}×\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$${T}_{\mathrm{2}}…
Question Number 56422 by gunawan last updated on 16/Mar/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$${ax}\:+\:{by}\:+\:\left({a}\lambda+{b}\right){z}\:=\:\mathrm{0} \\ $$$${bx}\:+\:{cy}\:+\:\left({b}\lambda+{c}\right){z}\:=\:\mathrm{0} \\ $$$$\left({a}\lambda\:+\:{b}\right){x}\:+\:\left({b}\lambda+{c}\right){y}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{non}−\mathrm{trivial}\:\mathrm{solution},\:\mathrm{then} \\ $$ Answered by MJS last updated…
Question Number 56421 by gunawan last updated on 16/Mar/19 $$\mathrm{Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} \:,\:…,\:{a}_{\mathrm{10}} \:\mathrm{be}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{and}\:{h}_{\mathrm{1}} ,\:{h}_{\mathrm{2}} ,…,\:{h}_{\mathrm{10}} \\ $$$$\mathrm{be}\:\mathrm{in}\:\mathrm{HP}.\:\mathrm{If}\:\:{a}_{\mathrm{1}} =\:{h}_{\mathrm{1}} =\mathrm{2}\:\:\mathrm{and}\:\:{a}_{\mathrm{10}} =\:{h}_{\mathrm{10}} =\mathrm{3}, \\ $$$$\mathrm{then}\:{a}_{\mathrm{4}} {h}_{\mathrm{7}} \:\:\mathrm{is}…