Question Number 205422 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\left(\mathrm{a}\:+\:\mathrm{1}\right)\left(\mathrm{b}\:+\:\mathrm{1}\right)\left(\mathrm{c}\:+\:\mathrm{1}\right)\:=\:\mathrm{8} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\geqslant\:\mathrm{3} \\ $$ Answered by A5T last…
Question Number 205406 by mr W last updated on 20/Mar/24 Commented by lepuissantcedricjunior last updated on 21/Mar/24 $$\boldsymbol{{d}}'\boldsymbol{{apre}}'\boldsymbol{{s}}\:\boldsymbol{{pythagore}}\: \\ $$$$\boldsymbol{{d}}^{\mathrm{2}} =\mathrm{7}^{\mathrm{2}} +\boldsymbol{{k}}^{\mathrm{2}} \:\left(\mathrm{1}\right) \\ $$$$\boldsymbol{{d}}'\boldsymbol{{apres}}\:\boldsymbol{{alkashil}}…
Question Number 205423 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\mathrm{a}\:,\:\mathrm{b}\:\in\:\mathbb{R} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:\geqslant\:\mathrm{ab}\:+\:\sqrt{\frac{\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} }{\mathrm{2}}} \\ $$ Answered by Berbere…
Question Number 205403 by BaliramKumar last updated on 20/Mar/24 Answered by Rajpurohith last updated on 20/Mar/24 $${Clearly}\:\mathrm{cot}^{\mathrm{2}} \left({A}\right)\left(\mathrm{1}+\mathrm{cot}^{\mathrm{2}} \left({A}\right)\right)=\mathrm{1} \\ $$$${i}.{e},\mathrm{cot}^{\mathrm{2}} \left({A}\right)\left(\mathrm{cosec}^{\mathrm{2}} \left({A}\right)\right)=\mathrm{1} \\ $$$$\Rightarrow\frac{\mathrm{cos}^{\mathrm{2}}…
Question Number 205396 by MathedUp last updated on 20/Mar/24 $$\mathrm{Can}'\mathrm{t}\:\mathrm{understand}\:\mathrm{why} \\ $$$$\int_{\mathrm{0}} ^{\infty} \left[{e}_{\:} ^{\mathrm{sin}\left({z}\right)} −{e}^{\mathrm{cos}\left({z}\right)} \right]\mathrm{d}{z}\:\mathrm{isn}'{t}\:\frac{\mathrm{1}}{\mathrm{2}}\pi\left(\boldsymbol{\mathrm{I}}_{\mathrm{0}} ^{\:} \left(\mathrm{1}\right)−\boldsymbol{\mathrm{L}}_{\mathrm{0}} \left(\mathrm{1}\right)\right)\approx\mathrm{3}.\mathrm{104}… \\ $$$$\mathrm{I}\:\mathrm{Just}\:\mathrm{guessing}\:{f}\left(\mathrm{0}\right)=\:\frac{\mathrm{1}}{\mathrm{2}}\pi\boldsymbol{\mathrm{I}}_{\mathrm{0}} \left(\mathrm{1}\right)−\boldsymbol{\mathrm{L}}_{\mathrm{0}} \left(\mathrm{1}\right) \\…
Question Number 205409 by Red1ight last updated on 20/Mar/24 $$\mathrm{let}\:{x},\:{y},\:{z}\:\mathrm{be}\:\mathrm{random}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$$$\mathrm{where}\:{x},{y},{z}\in\mathbb{R} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\left.{a}\right)\:\mathrm{all}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{satisfied} \\ $$$$\mid{x}−{y}\mid\geqslant\mathrm{2} \\ $$$$\mid{x}−{z}\mid\geqslant\mathrm{2} \\ $$$$\mid{y}−{z}\mid\geqslant\mathrm{2} \\ $$$$\left.{b}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\…
Question Number 205372 by gth last updated on 19/Mar/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205373 by gth last updated on 19/Mar/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205371 by 073 last updated on 19/Mar/24 Commented by lepuissantcedricjunior last updated on 19/Mar/24 $$\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\mathrm{2}} \boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{8}\right)\boldsymbol{\mathrm{dx}} \\ $$$$\boldsymbol{\mathrm{posons}}\:\begin{cases}{\boldsymbol{\mathrm{u}}=\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{8}\right)}\\{\boldsymbol{\mathrm{v}}'=\mathrm{1}}\end{cases}\Leftrightarrow\begin{cases}{\boldsymbol{\mathrm{u}}'=\frac{\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} }{\left(\boldsymbol{{x}}^{\mathrm{3}} +\mathrm{8}\right)\boldsymbol{\mathrm{ln}}\mathrm{10}}}\\{\boldsymbol{\mathrm{v}}=\boldsymbol{\mathrm{x}}}\end{cases}…
Question Number 205380 by cortano12 last updated on 19/Mar/24 Commented by Rasheed.Sindhi last updated on 19/Mar/24 $$\boldsymbol{{please}}\:{don}'{t}\:{write}\:{your}\:{solution} \\ $$$${as}\:{a}\:{comment}!\:{Instead}\:{write}\:{it}\:{as} \\ $$$${answer}\:\boldsymbol{{in}}\:\boldsymbol{{order}}\:\boldsymbol{{to}}\:\boldsymbol{{prserve}}\:\boldsymbol{{chronological}} \\ $$$$\boldsymbol{{order}}\:\boldsymbol{{of}}\:\boldsymbol{{answers}}! \\ $$…