Question Number 205472 by SANOGO last updated on 21/Mar/24 Answered by TheHoneyCat last updated on 01/Apr/24 $$\mathrm{This}\:\mathrm{will}\:\mathrm{be}\:\mathrm{true}\:\mathrm{if}\:\left(\mathrm{and}\:\mathrm{only}\:\mathrm{if}\right)\:\mathrm{the}\:{A}_{{n}} \:\mathrm{are}\:\mathrm{all} \\ $$$$\mathrm{disjoint}. \\ $$$$\mathrm{If}\:\mathrm{they}\:\mathrm{are}\:\mathrm{not},\:\mathrm{take}\:{x}\in{A}_{{i}} \cap{A}_{{k}} \:\left(\mathrm{with}\:{k}\neq{i}\right) \\…
Question Number 205420 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:\geqslant\:\mathrm{2} \\ $$ Answered…
Question Number 205421 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}=\mathrm{1} \\ $$$$\mathrm{Then}: \\ $$$$\frac{\mathrm{a}}{\mathrm{b}^{\mathrm{2024}} }\:+\:\frac{\mathrm{b}}{\mathrm{c}^{\mathrm{2024}} }\:+\:\frac{\mathrm{c}}{\mathrm{a}^{\mathrm{2024}} }\:\geqslant\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c} \\ $$ Terms of Service Privacy…
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