Question Number 33146 by Ahmad Hajjaj last updated on 11/Apr/18 $$\mathrm{If}\:\mathrm{the}\:\mathrm{expression}\: \\ $$$${exp}\left\{\left(\mathrm{1}+\mid\mathrm{cos}\:{x}\mid+\mathrm{cos}^{\mathrm{2}} {x}+\mid\mathrm{cos}^{\mathrm{3}} {x}\mid+\mathrm{cos}^{\mathrm{4}} {x}\right.\right. \\ $$$$\left.\:\left.\:\:\:\:\:\:\:\:\:\:\:+….\infty\right)\mathrm{log}_{{e}} \mathrm{4}\right\}\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation} \\ $$$${y}^{\mathrm{2}} −\mathrm{20}{y}+\mathrm{64}=\mathrm{0}\:\mathrm{for}\:\mathrm{0}<\:{x}\:<\pi,\:\mathrm{then}\:\mathrm{the}\:\mathrm{set} \\ $$$$\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{is} \\…
Question Number 33145 by Ahmad Hajjaj last updated on 11/Apr/18 $$\underset{\:\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}+\mathrm{1}}\:+\:\sqrt{\mathrm{5}{x}+\mathrm{1}}}\:= \\ $$ Commented by prof Abdo imad last updated on 11/Apr/18 $${I}\:=\:\int_{\mathrm{0}}…
Question Number 98464 by Vishal Sharma last updated on 14/Jun/20 $$\mathrm{Working}\:\mathrm{individually},\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{can} \\ $$$$\mathrm{finish}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}\:\mathrm{in}\:\mathrm{16}\:\mathrm{days},\:\mathrm{20}\:\mathrm{days} \\ $$$$\mathrm{and}\:\mathrm{30}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many} \\ $$$$\mathrm{days}\:\mathrm{can}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{together}\:\mathrm{complete} \\ $$$$\mathrm{a}\:\mathrm{work}\:\mathrm{which}\:\mathrm{is}\:\mathrm{3}\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{times}\:\mathrm{the}\:\mathrm{previous} \\ $$$$\mathrm{work}? \\ $$ Answered by…
Question Number 98368 by nesreen last updated on 13/Jun/20 $$\mathrm{If}\:\overset{\rightarrow} {{G}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{then} \\ $$$$\overset{\rightarrow} {{GA}}+\overset{\rightarrow} {{GB}}+\overset{\rightarrow} {{GC}}\:= \\ $$ Answered by abdomathmax last updated on 13/Jun/20…
Question Number 98369 by nesreen last updated on 13/Jun/20 $$\mathrm{If}\:{A},\:{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{square}\:\mathrm{matrices}\:\mathrm{such} \\ $$$$\mathrm{that}\:{AB}\:=\:{A}\:\mathrm{and}\:{BA}\:=\:{B},\:\mathrm{then} \\ $$ Answered by bobhans last updated on 13/Jun/20 $$\mathrm{A}^{−\mathrm{1}} \mathrm{AB}=\mathrm{A}^{−\mathrm{1}} \mathrm{A}\:\Rightarrow\:\mathrm{B}\:=\:\mathrm{I} \\…
Question Number 32745 by vakil vishaWakrma last updated on 01/Apr/18 $$\mathrm{The}\:\mathrm{first},\:\mathrm{second}\:\mathrm{and}\:\mathrm{middle}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{AP}\:\mathrm{are}\:{a},\:{b},\:{c}\:\mathrm{respectively}.\:\mathrm{Their}\:\mathrm{sum}\:\mathrm{is} \\ $$ Answered by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{AP}\:\mathrm{has}\:\mathrm{n}\:\left(\mathrm{odd}\right)\:\mathrm{terms}\:\mathrm{and}\:\mathrm{common} \\ $$$$\mathrm{difference}\:\mathrm{d}.…
Question Number 98058 by PengagumRahasiamu last updated on 11/Jun/20 $$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} −{cx}+{d}=\mathrm{0}\:\mathrm{has}\:\mathrm{roots} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{powers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots} \\ $$$$\mathrm{of}\:{x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0},\:\mathrm{where}\:{a}^{\mathrm{2}} >\mathrm{4}{b}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\mathrm{of}\:{x}^{\mathrm{2}} −\mathrm{4}{bx}+\mathrm{2}{b}^{\mathrm{2}} −{c}=\mathrm{0}\:\mathrm{will}\:\mathrm{be} \\ $$ Answered by…
Question Number 98056 by PengagumRahasiamu last updated on 11/Jun/20 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic} \\ $$$$\mathrm{equation}\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} +\left({x}−\mathrm{5}\right)^{\mathrm{2}} +\left({x}−\mathrm{6}\right)^{\mathrm{2}} =\mathrm{0}\:\mathrm{is} \\ $$ Commented by som(math1967) last updated on 11/Jun/20 $$\mathrm{4},\mathrm{5},\mathrm{6}…
Question Number 98057 by PengagumRahasiamu last updated on 11/Jun/20 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \:\mathrm{is}\:\_\_\_\_. \\ $$ Answered by Rio Michael last updated on 11/Jun/20…
Question Number 32418 by hizmzm1 last updated on 24/Mar/18 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{or} \\ $$$${x}^{\mathrm{8}} −\:{x}^{\mathrm{5}} −\:{x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by hizmzm1 last updated on 27/Mar/18 $$\mathrm{1}^{\mathrm{8}} −\mathrm{1}^{\mathrm{5}}…