Question Number 192924 by a.lgnaoui last updated on 31/May/23 $$\mathrm{1}\bullet\mathrm{determiner}:\:\mathrm{tan}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{tan}\:\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{2}\bullet\mathrm{on}\:\mathrm{donne}\:\:\mathrm{tan}\:\boldsymbol{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{8}}\:\:\:\:\mathrm{tan}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}=? \\ $$$$\mathrm{3}\bullet\:\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{proche}\:\mathrm{de}\:\boldsymbol{\mathrm{x}}? \\ $$ Answered by a.lgnaoui last updated on 31/May/23 $$\mathrm{1}\bullet\mathrm{tan}\:\mathrm{x}=\frac{\mathrm{2t}}{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }\:\:\:\:\mathrm{t}=\mathrm{tan}\left(\:\frac{\mathrm{x}}{\mathrm{2}}\right)…
Question Number 192927 by 073 last updated on 31/May/23 Answered by aba last updated on 31/May/23 $$\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{m}} \approx\sqrt{\mathrm{2}\pi\mathrm{n}}\left(\frac{\mathrm{n}}{\mathrm{e}}\right)^{\mathrm{n}} ×\mathrm{n}^{\mathrm{m}} \:\:\wedge\:\left(\mathrm{n}+\mathrm{m}\right)!\approx\sqrt{\mathrm{2}\pi\left(\mathrm{n}+\mathrm{m}\right)}\left(\frac{\mathrm{n}+\mathrm{m}}{\mathrm{e}}\right)^{\mathrm{n}+\mathrm{m}} \\ $$$$\Rightarrow\frac{\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{m}} }{\left(\mathrm{n}+\mathrm{m}\right)!}\approx\frac{\sqrt{\mathrm{2}\pi\mathrm{n}}}{\:\sqrt{\mathrm{2}\pi\left(\mathrm{n}+\mathrm{m}\right)}}×\frac{\mathrm{n}^{\mathrm{n}+\mathrm{m}} }{\mathrm{e}^{\mathrm{n}} }×\frac{\mathrm{e}^{\mathrm{n}+\mathrm{m}}…
Question Number 192926 by Shrinava last updated on 31/May/23 $$\mathrm{1}.\:\mathrm{7}^{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{1}} \:\geqslant\:\mathrm{21} \\ $$$$\mathrm{2}.\:\mathrm{6},\mathrm{5}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \:\geqslant\:\mathrm{200} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61850 by mr W last updated on 10/Jun/19 $${Find}\:{all}\:{integer}\:{solution}\left({s}\right): \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{615}+\boldsymbol{{x}}^{\mathrm{2}} =\mathrm{2}^{\boldsymbol{{y}}} \\ $$ Commented by Rasheed.Sindhi last updated on 10/Jun/19 $${One}\:{solution}:\:\:{x}=\mathrm{59}\:,\:{y}=\mathrm{12} \\…
Question Number 192917 by BaliramKumar last updated on 31/May/23 Answered by AST last updated on 31/May/23 $${Let}\:{tan}\theta={t},{cot}\theta={c};\:{tc}=\mathrm{1} \\ $$$${t}^{\mathrm{2}} +{c}^{\mathrm{2}} =\left({t}+{c}\right)^{\mathrm{2}} −\mathrm{2}{tc}=\left({t}+{c}\right)^{\mathrm{2}} −\mathrm{2} \\ $$$${t}^{\mathrm{5}}…
Question Number 127382 by I want to learn more last updated on 29/Dec/20 Answered by mr W last updated on 29/Dec/20 Commented by mr W…
Question Number 192916 by Mingma last updated on 31/May/23 Answered by ARUNG_Brandon_MBU last updated on 31/May/23 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}−\mathrm{sin2}{x}}{\mathrm{1}+\mathrm{cos}{x}}+\frac{\mathrm{1}−\mathrm{cos2}{x}}{\mathrm{1}+\mathrm{sin}{x}}\right){dx} \\ $$$$\:\:\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+\mathrm{cos}{x}}+\mathrm{2}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}{x}}{\mathrm{1}+\mathrm{cos}{x}}\left(\mathrm{sin}{xdx}\right)+\mathrm{2}\int_{\mathrm{0}}…
Question Number 127383 by Lordose last updated on 29/Dec/20 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{analytic}\:\mathrm{proof}\:\mathrm{of}\:\mathrm{the}\:\mathrm{result} \\ $$$$\mathrm{sin}\left(\mathrm{x}+\mathrm{y}\right)\:=\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{y}\right)\:+\:\mathrm{sin}\left(\mathrm{y}\right)\mathrm{cos}\left(\mathrm{x}\right) \\ $$ Answered by bemath last updated on 29/Dec/20 Answered by liberty last…
Question Number 192918 by MATHEMATICSAM last updated on 31/May/23 Answered by aba last updated on 31/May/23 $$\mathrm{x}+\mathrm{1}=\mathrm{log}_{\mathrm{2a}} \left(\frac{\mathrm{bcd}}{\mathrm{2}}\right)+\mathrm{1}=\mathrm{log}_{\mathrm{2a}} \left(\frac{\mathrm{bcd}}{\mathrm{2}}\right)+\mathrm{log}_{\mathrm{2a}} \left(\mathrm{2a}\right)=\mathrm{log}_{\mathrm{2a}} \left(\mathrm{abcd}\right)\:\Rightarrow\frac{\mathrm{1}}{\mathrm{x}+\mathrm{1}}=\mathrm{log}_{\mathrm{abcd}} \left(\mathrm{2a}\right) \\ $$$$\mathrm{y}+\mathrm{1}=\mathrm{log}_{\mathrm{3b}} \left(\frac{\mathrm{acd}}{\mathrm{3}}\right)+\mathrm{1}=\mathrm{log}_{\mathrm{3b}}…
Question Number 61843 by psyche last updated on 10/Jun/19 $$\boldsymbol{{let}}\:\boldsymbol{{V}}\:\:\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{vector}}\:\boldsymbol{{space}}\:\boldsymbol{{and}}\:\boldsymbol{{let}}\:\boldsymbol{{H}}\:\boldsymbol{{and}}\:\boldsymbol{{K}}\:\boldsymbol{{be}}\: \\ $$$$\boldsymbol{{subspace}}\:\boldsymbol{{of}}\:\boldsymbol{{V}}.\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:, \\ $$$${H}+{K}=\left\{\boldsymbol{{x}}:\boldsymbol{{x}}=\boldsymbol{{h}}+\boldsymbol{{k}},\:\boldsymbol{{where}}\:\boldsymbol{{h}}\in{H}\:\boldsymbol{{and}}\:\:\boldsymbol{{k}}\in{K}\right\}\:\boldsymbol{{is}}\:\:\boldsymbol{{a}}\:\boldsymbol{{subspace}}\:\boldsymbol{{of}}\:\boldsymbol{{V}}.\: \\ $$ Commented by arcana last updated on 10/Jun/19 $$\mathrm{if}\:\mathrm{V}\:\mathrm{is}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{over}\:\mathrm{a}\:\mathrm{field}\:\mathrm{K}. \\…