Question Number 185336 by Shrinava last updated on 20/Jan/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 119801 by Ar Brandon last updated on 27/Oct/20 $$\mathrm{If}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{and}\:{f}\left(\mathrm{x}+{f}\left(\mathrm{y}\right)\right)= \\ $$$${f}\left(\mathrm{x}\right)+\mathrm{y}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\:\mathrm{y}\in\mathbb{R},\:\mathrm{then} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{period}\:\mathrm{of}\:{f} \\ $$$$\left(\mathrm{B}\right)\:{f}\left({n}\right)=\mathrm{1}\:\mathrm{for}\:\mathrm{all}\:\mathrm{integers}\:{n} \\ $$$$\left(\mathrm{C}\right)\:{f}\left({n}\right)={n}\:\mathrm{for}\:\mathrm{all}\:\mathrm{integers}\:{n} \\ $$$$\left(\mathrm{D}\right)\:{f}\left(−\mathrm{1}\right)=\mathrm{0} \\ $$ Terms of…
Question Number 119800 by Ar Brandon last updated on 27/Oct/20 $$\mathrm{Examples}\:\mathrm{of}\:\mathrm{functions}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left(\mathrm{x}+\mathrm{y}\right)={f}\left(\mathrm{x}\right)+{f}\left(\mathrm{y}\right)\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\in\mathbb{R} \\ $$ Commented by mr W last updated on 27/Oct/20 $${f}\left({x}\right)={ax} \\…
Question Number 119797 by Ar Brandon last updated on 27/Oct/20 $$\mathrm{Q1} \\ $$$$\mathrm{Let}\:{M}_{\mathrm{2}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{square}\:\mathrm{matrices}\:\mathrm{of}\:\mathrm{order}\:\mathrm{2}\:\mathrm{over} \\ $$$$\mathrm{the}\:\mathrm{real}\:\mathrm{number}\:\mathrm{system}\:\mathrm{and} \\ $$$$\:\:\:\:\:\mathcal{R}=\left\{\left({A},{B}\right)\in{M}_{\mathrm{2}} ×{M}_{\mathrm{2}} \mid{A}={P}^{\:\mathrm{T}} {BP}\:\:\mathrm{for}\:\mathrm{some}\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{non}-\mathrm{singular}\:{P}\:\in{M}\right\} \\ $$$$\mathrm{Then}\:\mathcal{R}\:\mathrm{is}…
Question Number 119795 by bobhans last updated on 27/Oct/20 $${Solve}\:{in}\:{real}\:{numbers}\:{the}\:{system}\:{of} \\ $$$${equations}\:\begin{cases}{\left(\mathrm{3}{x}+{y}\right)\left({x}+\mathrm{3}{y}\right)\sqrt{{xy}}\:=\mathrm{14}}\\{\left({x}+{y}\right)\left({x}^{\mathrm{2}} +\mathrm{14}{xy}+{y}^{\mathrm{2}} \right)=\:\mathrm{36}}\end{cases}\: \\ $$ Answered by 1549442205PVT last updated on 27/Oct/20 $$\mathrm{Put}\:\mathrm{x}=\mathrm{ky}\:\mathrm{we}\:\mathrm{get} \\…
Question Number 185315 by Shrinava last updated on 20/Jan/23 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}!\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{20} \\ $$ Answered by Rasheed.Sindhi last updated on 20/Jan/23 $${f}\left({x}\right)=\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{20}−{x}! \\…
Question Number 119774 by rajesh4661kumar@gmail.com last updated on 26/Oct/20 Answered by $@y@m last updated on 27/Oct/20 $$\left(\mathrm{40}+\mathrm{50}−\mathrm{2}\right)×\mathrm{2}×\mathrm{100}={Rs}.\mathrm{17600} \\ $$ Commented by rajesh4661kumar@gmail.com last updated on…
Question Number 185310 by mathlove last updated on 20/Jan/23 Commented by HeferH last updated on 20/Jan/23 $${suma}\:{de}\:{sumas}?\: \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 119757 by Ar Brandon last updated on 26/Oct/20 $$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{n},\:\mathrm{let}\:{I}_{{n}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{interval}\:\left({n},\:{n}+\mathrm{1}\right). \\ $$$$\mathrm{Define} \\ $$$$\:\:\:\:\:\:\:\mathcal{R}=\left\{\left(\mathrm{x},\:\mathrm{y}\right)\in\mathbb{R}\mid\mathrm{both}\:\mathrm{x},\:\mathrm{y}\:\in\:{I}_{{n}} \:\mathrm{for}\:\mathrm{some}\:{n}\in\mathbb{Z}\right\} \\ $$$$\mathrm{Then}\:\mathcal{R}\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{reflexive}\:\mathrm{on}\:\mathbb{R} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{symmetric} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{transitive}…
Question Number 119713 by som(math1967) last updated on 26/Oct/20 $$\mathrm{If}\:\mathrm{3x}+\frac{\mathrm{1}}{\mathrm{2x}}=\mathrm{6}\:\mathrm{find}\:\mathrm{8x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{27x}^{\mathrm{3}} } \\ $$ Commented by bemath last updated on 26/Oct/20 $${santuyy} \\ $$ Commented…