Question Number 155231 by mnjuly1970 last updated on 27/Sep/21 $$ \\ $$$$\:\:\:{f}\:\left({x}\right)\::=\sqrt{\frac{\mathrm{1}}{{a}}\:+{x}}\:−\sqrt{\frac{\mathrm{1}}{{a}}\:−{x}} \\ $$$$\:\:{and}\:\:\:\:\mathrm{D}_{{f}} \:\neq\:\varnothing\:, \\ $$$$\:\:\:\:\:\:\:{g}\left({x}\right)=\sqrt{\frac{{ax}−\mathrm{1}}{{f}^{\:−\mathrm{1}} \left(\:{ax}\:−{a}\:\right)}} \\ $$$$\:\:\:\:\:\:\:\:{find}\::\:\:\mathrm{D}_{\:{g}} \:=? \\ $$ Terms of…
Question Number 89687 by student work last updated on 18/Apr/20 $${x}^{\mathrm{3}} +{x}−\mathrm{16}=\mathrm{0} \\ $$ Commented by mr W last updated on 18/Apr/20 https://en.m.wikipedia.org/wiki/Cubic_equation Commented by…
Question Number 24142 by Tinkutara last updated on 13/Nov/17 $${Prove}\:{that} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{{r}} \left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}−{r}} {dx}\right) \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left[\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}} +{x}^{\mathrm{2}{n}} −\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}+\mathrm{1}}…
Question Number 155212 by ajfour last updated on 27/Sep/21 Commented by mr W last updated on 27/Sep/21 $$\mathrm{cos}\:\theta=\frac{{p}}{\mathrm{1}}\:\Rightarrow\mathrm{cos}\:\theta={p} \\ $$$$\frac{{c}}{\mathrm{sin}\:\theta}={p}\:\mathrm{sin}\:\theta\:\Rightarrow\mathrm{sin}^{\mathrm{2}} \:\theta=\frac{{c}}{{p}} \\ $$$$\frac{{c}}{{p}}+{p}^{\mathrm{2}} =\mathrm{1} \\…
Question Number 155204 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}: \\ $$$$\mathrm{abcd}\:+\:\mathrm{abc}\:=\:\left(\mathrm{a}+\mathrm{1}\right)\left(\mathrm{b}+\mathrm{1}\right)\left(\mathrm{c}+\mathrm{1}\right) \\ $$ Answered by MJS_new last updated on 27/Sep/21 $${a}\leqslant{b}\leqslant{c} \\ $$$$\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{for}\:{a}\:{b}\:{c}\:{d}\:\mathrm{are} \\…
Question Number 155207 by mathdanisur last updated on 26/Sep/21 $$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by mindispower last updated on 27/Sep/21 $$\Omega={f}'\left(\mathrm{0}\right),{f}'\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 155206 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d};\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}\:\:\mathrm{and}\:\:\mathrm{a}\neq\mathrm{b}\neq\mathrm{c}\neq\mathrm{d} \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{td}\:; \\ $$$$\mathrm{b}+\mathrm{c}+\mathrm{d}=\mathrm{xa}\:;\:\mathrm{c}+\mathrm{d}+\mathrm{a}=\mathrm{yb}\:;\:\mathrm{d}+\mathrm{a}+\mathrm{b}=\mathrm{zc} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155189 by qaz last updated on 27/Sep/21 $$\mathrm{How}\:\mathrm{to}\:\mathrm{extract}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:\mathrm{term}\:“\mathrm{x}^{\mathrm{n}} \mathrm{y}^{\mathrm{m}} \:''\:\:\mathrm{in}\:\left(\mathrm{1}+\frac{\mathrm{yx}}{\mathrm{1}−\mathrm{x}}\right)\left(\mathrm{1}−\frac{\mathrm{yx}}{\mathrm{1}−\mathrm{x}}\right)^{−\mathrm{1}} ? \\ $$ Answered by mr W last updated on 26/Sep/21 $$=\frac{\mathrm{1}−{x}+{xy}}{\mathrm{1}−{x}\left(\mathrm{1}+{y}\right)} \\…
Question Number 89653 by student work last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$\mathrm{2}^{{x}} \:=\:{p}\:\Rightarrow\:{p}^{\mathrm{3}} \:+\:{p}\:=\:\mathrm{16}\: \\ $$$${use}\:{Cardano}\:{method}\: \\ $$…
Question Number 155180 by mathdanisur last updated on 26/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com