Question Number 213031 by ChantalYah last updated on 29/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212991 by efronzo1 last updated on 28/Oct/24 $$\:\:\:\:\:\underbrace{\downharpoonleft\underline{}\:} \\ $$ Answered by Frix last updated on 28/Oct/24 $${H}\left({n}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:{k}!\left({k}^{\mathrm{2}} +{k}+\mathrm{1}\right) \\ $$$$\frac{{H}\left({n}\right)+\mathrm{1}}{\left({n}+\mathrm{1}\right)!}={n}+\mathrm{1}\:\:\:\:\:\left[\mathrm{test}\:\mathrm{it}\:\mathrm{for}\:{n}=\mathrm{1},\:\mathrm{2},\:\mathrm{3},…\right]…
Question Number 213002 by efronzo1 last updated on 28/Oct/24 $$\:\:\frac{\left(\mathrm{52}+\mathrm{6}\sqrt{\mathrm{43}}\:\right)^{\mathrm{3}/\mathrm{2}} −\left(\mathrm{52}−\mathrm{6}\sqrt{\mathrm{43}}\right)^{\mathrm{3}/\mathrm{2}} }{\mathrm{18}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 28/Oct/24 $$\:\:\frac{\left(\mathrm{52}+\mathrm{6}\sqrt{\mathrm{43}}\:\right)^{\mathrm{3}/\mathrm{2}} −\left(\mathrm{52}−\mathrm{6}\sqrt{\mathrm{43}}\right)^{\mathrm{3}/\mathrm{2}} }{\mathrm{18}}=? \\…
Question Number 212976 by hardmath last updated on 27/Oct/24 $$\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{125}\:\:\:\mathrm{and}\:\:\:\mathrm{8}^{\boldsymbol{\mathrm{y}}} \:=\:\mathrm{5} \\ $$$$\mathrm{find}:\:\:\:\frac{\mathrm{2x}\:−\:\mathrm{y}}{\mathrm{y}}\:=\:? \\ $$ Answered by Amiltonsad last updated on 27/Oct/24 $$ \\…
Question Number 212834 by efronzo1 last updated on 25/Oct/24 $$\:\:\:\:\underbrace{\:} \\ $$ Answered by golsendro last updated on 25/Oct/24 $$\:\:\mathrm{let}\:\begin{cases}{\mathrm{a}=\mathrm{sin}\:\mathrm{x}\:,\:\mathrm{b}=\mathrm{cos}\:\mathrm{x}}\\{\mathrm{c}=\mathrm{sin}\:\mathrm{y}\:,\:\mathrm{d}=\mathrm{cos}\:\mathrm{y}}\end{cases} \\ $$$$\:\:\mathrm{ac}\:+\:\mathrm{bd}\:=\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{y}\right) \\ $$$$\:\:\mid\mathrm{ac}+\mathrm{bd}\mid\:\leqslant\:\mathrm{1}\: \\…
Question Number 212790 by RojaTaniya last updated on 24/Oct/24 Answered by A5T last updated on 24/Oct/24 $${x}−{y}=\left({y}−\mathrm{1}+{x}−\mathrm{1}\right)\left({y}−\mathrm{1}−{x}+\mathrm{1}\right) \\ $$$$\Rightarrow{x}={y}\:{or}\:−\mathrm{1}={x}+{y}−\mathrm{2}\Rightarrow{x}+{y}=\mathrm{1} \\ $$$$\Rightarrow{x}+\mathrm{1}={x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\:{or}\:{x}+\mathrm{1}={x}^{\mathrm{2}} \Rightarrow{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={x}+{y}+\mathrm{2}=\mathrm{3}…
Question Number 212736 by RojaTaniya last updated on 22/Oct/24 Answered by efronzo1 last updated on 22/Oct/24 $$\:\:\:\:\frac{\mathrm{x}}{\mathrm{4}}\:=\:\frac{\mathrm{9}}{\mathrm{15}}\:\Rightarrow\mathrm{x}=\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\:\:\:\:\frac{\mathrm{y}}{\mathrm{5}}=\:\frac{\mathrm{9}}{\mathrm{15}}\Rightarrow\mathrm{y}=\:\mathrm{3} \\ $$$$\:\:\:\:\:\frac{\mathrm{z}}{\mathrm{6}}=\:\frac{\mathrm{9}}{\mathrm{15}}\:\Rightarrow\mathrm{z}=\frac{\mathrm{18}}{\mathrm{5}} \\ $$ Commented by…
Question Number 212711 by RojaTaniya last updated on 21/Oct/24 $$\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$$\:{y}={f}\left({x}\right),\:{z}={f}\left({y}\right),\:{f}\left({z}\right)=? \\ $$ Answered by MATHEMATICSAM last updated on 21/Oct/24 $${y}\:=\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}} \\ $$$${f}\left({y}\right)\:=\:{f}\left(\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}}}\:=\:\frac{\mathrm{1}\:−\:{x}}{−\:{x}}\:=\:\frac{{x}\:−\:\mathrm{1}}{{x}} \\…
Question Number 212673 by golsendro last updated on 21/Oct/24 $$\:\:\:\: \\ $$ Answered by Frix last updated on 21/Oct/24 $$\sqrt{\mathrm{2}{x}+\mathrm{3}}={x}^{\mathrm{2}} −{x}−\mathrm{3} \\ $$$$\mathrm{Squaring}\:\&\:\mathrm{transforming} \\ $$$$\:\:\:\:\:\left[\mathrm{introduces}\:\mathrm{false}\:\mathrm{solutions}!\right]…
Question Number 212654 by Spillover last updated on 20/Oct/24 Answered by mr W last updated on 20/Oct/24 Commented by mr W last updated on 20/Oct/24…