Question Number 190882 by mathlove last updated on 13/Apr/23 Commented by Tinku Tara last updated on 14/Apr/23 $$\mathrm{Where}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{these}\:\mathrm{questions}? \\ $$ Commented by mathlove last updated…
Question Number 125288 by Mathgreat last updated on 09/Dec/20 Commented by Mathgreat last updated on 09/Dec/20 $$\boldsymbol{{Prove}} \\ $$ Commented by mr W last updated…
Question Number 190820 by Rupesh123 last updated on 12/Apr/23 Answered by Rasheed.Sindhi last updated on 12/Apr/23 $$\frac{\mathrm{3}^{\mathrm{3}{x}} −\mathrm{2}^{\mathrm{3}{x}} }{\mathrm{2}^{{x}} \centerdot\mathrm{3}^{\mathrm{2}{x}} −\mathrm{3}^{{x}} \centerdot\mathrm{2}^{\mathrm{2}{x}} }=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$\frac{\left(\mathrm{3}^{{x}}…
Question Number 125262 by physicstutes last updated on 09/Dec/20 $$\mathrm{Find}\:{GP}\:\mathrm{the}\:\mathrm{matrix}\:\mathrm{permutation}\:\mathrm{where} \\ $$$$\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{c}}&{{a}}&{{d}}\end{pmatrix}\:\mathrm{and}\:{G}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{a}}&{{c}}&{{d}}&{{b}}\end{pmatrix} \\ $$$$\mathrm{explain} \\ $$ Commented by kaivan.ahmadi last updated on 09/Dec/20 $${GP}=\begin{pmatrix}{{a}\:\:\:\:\:\:{b}\:\:\:\:\:\:\:{c}\:\:\:\:\:\:{d}}\\{{c}\:\:\:\:\:\:\:{d}\:\:\:\:\:\:\:{a}\:\:\:\:\:{b}}\end{pmatrix} \\…
Question Number 190802 by mathlove last updated on 12/Apr/23 $${log}_{{x}} {x}={x}^{\mathrm{5}{x}−\mathrm{10}} \:\:\:\:\:{x}=? \\ $$ Answered by gungun last updated on 12/Apr/23 $$\mathrm{log}_{{a}} {a}=\mathrm{1} \\ $$$${a}^{\mathrm{5}{a}−\mathrm{10}}…
Question Number 125258 by Mathgreat last updated on 09/Dec/20 $${a},{b},{c}\:\:=>\:\:\blacktriangle\:\boldsymbol{{tomonlari}} \\ $$$$\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)+\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)+\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)\geqslant\sqrt{\mathrm{3}}\:\boldsymbol{{S}} \\ $$ Commented by Mathgreat last updated on 09/Dec/20 $$\:\boldsymbol{{S}}\:=>\:\boldsymbol{{uchburchak}}\:\:\boldsymbol{{yuzi}} \\ $$ Terms…
Question Number 190784 by mnjuly1970 last updated on 11/Apr/23 $$ \\ $$$$\:\:\mathrm{If}\:,\:\mathrm{0}\:\dashrightarrow\:\mathrm{M}'\:\overset{{f}} {\dashrightarrow}\mathrm{M}\overset{{g}} {\dashrightarrow}\mathrm{M}''\dashrightarrow\mathrm{0}\:\mathrm{is} \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{short}\:\mathrm{exact}\:\mathrm{sequence}\:\:\mathrm{and}\:\:\mathrm{M}'\:,\:\mathrm{M}''\:\mathrm{are} \\ $$$$\:\:\:\mathrm{two}\:\:\mathrm{finitely}\:\mathrm{generated}\:\:\mathrm{R}\:−\mathrm{modules} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{prove}\:\:\:\mathrm{M}\:\:\mathrm{is}\:\:\mathrm{finitely}\:\mathrm{generated}.\: \\ $$$$\:\:\:\mathrm{Hint}:\:\:{f}\:\:,\:\:{g}\:\:\:{are}\:\:{two}\:\:\:{R}\:−\:{homomorphism}. \\ $$ Terms…
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Question Number 190765 by mustafazaheen last updated on 10/Apr/23 Answered by qaz last updated on 11/Apr/23 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{−{e}^{\mathrm{2}} +\left(\mathrm{1}+\mathrm{2}{x}\right)^{\frac{\mathrm{1}}{{x}}} }{\mathrm{sin}\:{x}}=\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{−{e}^{\mathrm{2}} +{e}^{\frac{\mathrm{1}}{{x}}{ln}\left(\mathrm{1}+\mathrm{2}{x}\right)} }{{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 125226 by Mathgreat last updated on 09/Dec/20 Commented by Mathgreat last updated on 09/Dec/20 $${O}_{\mathrm{1}} {A}=\boldsymbol{{r}} \\ $$$${O}_{\mathrm{2}} {B}=\boldsymbol{{R}} \\ $$$$ \\ $$…