Question Number 73775 by FCB last updated on 15/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8236 by Yozzias last updated on 03/Oct/16 $$\mathrm{Define}\:\mathrm{a}\:\mathrm{3}×\mathrm{3}\:\mathrm{matrix}\:\mathrm{whose}\:\mathrm{entries} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{first}\:\mathrm{9}\:\mathrm{positive}\:\mathrm{integers}. \\ $$$$\mathrm{Let}\:\mathrm{s}_{\mathrm{k}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements} \\ $$$$\mathrm{across}\:\mathrm{the}\:\mathrm{kth}\:\mathrm{row}.\:\mathrm{Is}\:\mathrm{there}\:\mathrm{such}\:\mathrm{a}\: \\ $$$$\mathrm{matrix}\:\mathrm{where}\:\mathrm{s}_{\mathrm{1}} \::\:\mathrm{s}_{\mathrm{2}} \::\:\mathrm{s}_{\mathrm{3}} \:=\:\mathrm{1}\::\:\mathrm{2}\::\:\mathrm{3}\:? \\ $$$$−−−−−−−−−−−−−−−−−−−− \\…
Question Number 8234 by sandy_suhendra last updated on 03/Oct/16 $$\mathrm{Question}\::\:\mathrm{figure}\:\mathrm{x}\:\mathrm{for} \\ $$$$\sqrt{\mathrm{x}−\mathrm{4}}\:>\:\mathrm{6}−\mathrm{x} \\ $$$$\mathrm{my}\:\mathrm{answer}\:: \\ $$$$\left(\mathrm{1}\right)\:\:\:\mathrm{x}−\mathrm{4}\:>\:\left(\mathrm{6}−\mathrm{x}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\left(\mathrm{x}−\mathrm{5}\right)\left(\mathrm{x}−\mathrm{8}\right)\:<\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}<\mathrm{x}<\mathrm{8} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\:\:\mathrm{x}−\mathrm{4}\:\geqslant\:\mathrm{0} \\…
Question Number 8232 by FilupSmith last updated on 03/Oct/16 $$\mathrm{Every}\:\mathrm{day},\:\mathrm{for}\:{n}\:\mathrm{days},\:\mathrm{you}\:\mathrm{put}\:\mathrm{either} \\ $$$$\$\mathrm{1},\:\$\mathrm{2},\:\mathrm{or}\:\$\mathrm{3}\:\mathrm{into}\:\mathrm{a}\:\mathrm{saving}\:\mathrm{account}. \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{random}\:\mathrm{as}\:\mathrm{to}\:\mathrm{how}\:\mathrm{much}\:\mathrm{you}\:\mathrm{save} \\ $$$$\mathrm{each}\:\mathrm{day}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:{average}\:\mathrm{amount} \\ $$$$\mathrm{you}\:\mathrm{will}\:\mathrm{have}\:\mathrm{saved}\:\mathrm{in}\:{n}\:\mathrm{days}? \\ $$ Answered by prakash jain last…
Question Number 73766 by mathocean1 last updated on 15/Nov/19 $$\begin{cases}{\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{y}−\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{z}−\mathrm{3}}}\\{\mathrm{x}+\mathrm{2y}+\mathrm{3z}=\mathrm{56}}\end{cases} \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \\ $$ Answered by MJS last updated on 15/Nov/19 $$ \\…
Question Number 139296 by mohammad17 last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}+\sqrt{{x}}}{dx} \\ $$ Answered by qaz last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}+\sqrt{{x}}}{dx}=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 8224 by trapti rathaur@ gmail.com last updated on 03/Oct/16 $${if}\:\:\varnothing\:{lies}\:{between}\:\:\:−\frac{\pi}{\mathrm{4}}\:{and}\:\:\frac{\pi}{\mathrm{4}}\:\:\:{then}\:\:{prove}\:{that} \\ $$$$\varnothing^{\mathrm{2}} =\mathrm{tan}\:^{\mathrm{2}} \varnothing\:−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)\frac{\mathrm{tan}\:^{\mathrm{4}} \varnothing}{\mathrm{2}}\:+\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}\right)\frac{\mathrm{tan}\:^{\mathrm{6}} \varnothing}{\mathrm{3}}\:+−−−−− \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−{to}\:\infty\:{terms} \\ $$$$ \\ $$ Commented…
Question Number 73757 by Maclaurin Stickker last updated on 15/Nov/19 $$\mathrm{cos}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{200}°=? \\ $$ Commented by mathmax by abdo last updated on 15/Nov/19 $$\mathrm{70}^{{o}} =\frac{\mathrm{70}\pi}{\mathrm{180}}\:=\frac{\mathrm{7}\pi}{\mathrm{18}}\:\:\:{and}\:\mathrm{200}^{{o}} =\frac{\mathrm{200}\pi}{\mathrm{180}}\:=\frac{\mathrm{20}\pi}{\mathrm{18}}\:\Rightarrow…
Question Number 139288 by 7770 last updated on 25/Apr/21 $$\boldsymbol{{IF}}\:\frac{\boldsymbol{{x}}^{\mathrm{3}} +\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1}}=\boldsymbol{{x}}+\sqrt{\frac{\mathrm{6}}{\boldsymbol{{x}}}} \\ $$$$\mathrm{6}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{{x}}+\mathrm{4}=?? \\ $$ Answered by MJS_new last updated on 25/Apr/21 $$\frac{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 73755 by ~blr237~ last updated on 15/Nov/19 $${show}\:{that}\:\:\:{for}\:{all}\:{integer}\:\:{n}\:,\:\:{n}+\mathrm{1}\:{divides}\:\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix} \\ $$ Answered by mind is power last updated on 15/Nov/19 $$\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\left(\mathrm{2}{n}\right)!}{{n}!{n}!}\in\mathbb{N} \\ $$$$\frac{{n}}{{n}+\mathrm{1}}\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\mathrm{2}{n}!}{{n}!.\left({n}\right)!}.\frac{{n}}{{n}+\mathrm{1}}=\frac{\mathrm{2}{n}!}{\left({n}−\mathrm{1}\right)!.\left({n}+\mathrm{1}\right)!}=\begin{pmatrix}{\mathrm{2}{n}}\\{{n}+\mathrm{1}}\end{pmatrix} \\…