Question Number 16645 by Tinkutara last updated on 24/Jun/17 $$\mathrm{A}\:\mathrm{body}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{at}\:{x}\:=\:\mathrm{0}.\:\mathrm{At}\:{t}\:=\:\mathrm{0},\:\mathrm{it} \\ $$$$\mathrm{starts}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{the}\:\mathrm{positive}\:{x}-\mathrm{direction} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{acceleration}.\:\mathrm{At}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{instant}\:\mathrm{another}\:\mathrm{body}\:\mathrm{passes} \\ $$$$\mathrm{through}\:{x}\:=\:\mathrm{0}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{the}\:\mathrm{positive} \\ $$$${x}-\mathrm{direction}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{speed}.\:\mathrm{The} \\ $$$$\mathrm{position}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{body}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${x}_{\mathrm{1}} \left({t}\right)\:\mathrm{after}\:\mathrm{time}\:'{t}'\:\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}…
Question Number 147713 by Odhiambojr last updated on 22/Jul/21 $${Find}\:{a}\:{point}\:{on}\:{the}\:{curve}\:{y}=\sqrt{{x}} \\ $$$${where}\:{the}\:{tangent}\:{makes}\:{an}\:{angle}\: \\ $$$$\mathrm{45}°\:{with}\:{the}\:{positive}\:{x}-{axis} \\ $$ Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\frac{{dy}}{{dx}}\:=\:\mathrm{tan}\left(\theta\left({x}\right)\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}} \\…
Question Number 82176 by oyemi kemewari last updated on 19/Feb/20 Commented by jagoll last updated on 19/Feb/20 $$\left(\mathrm{1}{b}\right)\:\sqrt{\mathrm{32}−\mathrm{2}\sqrt{\mathrm{135}}}\:=\:\sqrt{\mathrm{27}+\mathrm{5}−\mathrm{2}\sqrt{\mathrm{27}×\mathrm{5}}} \\ $$$$=\:\sqrt{\mathrm{27}}−\sqrt{\mathrm{5}}\:=\:\mathrm{3}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}} \\ $$ Commented by jagoll…
Question Number 16641 by Tinkutara last updated on 24/Jun/17 $$\mathrm{Prove}\:\mathrm{that}\:{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{if}\:\mathrm{and} \\ $$$$\mathrm{only}\:\mathrm{if}\:\mathrm{every}\:\mathrm{equiangular}\:\mathrm{polygon}\:\mathrm{with} \\ $$$${p}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{lengths}\:\mathrm{is}\:\mathrm{regular}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 147714 by puissant last updated on 22/Jul/21 $$\mathrm{Resoudre} \\ $$$$\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} \right)\:>\:\mathrm{log}_{\mathrm{a}^{\mathrm{2}} } \left(\mathrm{3x}−\mathrm{2}\right) \\ $$$$\mathrm{avec}\:\:\mathrm{a}\in\mathbb{R}_{+} \backslash\left\{\mathrm{1}\right\} \\ $$$$\mathrm{NB}:\:\mathrm{a}\:\mathrm{et}\:\mathrm{a}^{\mathrm{2}} \:\mathrm{sont}\:\mathrm{les}\:\mathrm{bases}\:\mathrm{des}\:\mathrm{logarithmes} \\ $$$$\mathrm{des}\:\mathrm{nombres}\:\mathrm{de}\:\mathrm{l}'\mathrm{in}\acute {\mathrm{e}galite}..…
Question Number 82174 by jagoll last updated on 18/Feb/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:{x}\:{ln}\left(\mathrm{sin}\:{x}\right)\:{dx}\:=\:?\: \\ $$ Commented by mathmax by abdo last updated on 19/Feb/20 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\pi}…
Question Number 82175 by jagoll last updated on 19/Feb/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{8}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}−\sqrt[{\mathrm{3}\:}]{\mathrm{8}{x}^{\mathrm{3}} +\mid{px}\mid^{\mathrm{2}} −\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${find}\:{p}\: \\ $$ Commented by mr W last updated…
Question Number 16638 by tawa tawa last updated on 24/Jun/17 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\mathrm{tan}^{\mathrm{2}} \left(\mathrm{3x}\right)\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 24/Jun/17 $$\:\int_{\mathrm{0}} ^{\:\:\pi/\mathrm{4}}…
Question Number 147711 by lapache last updated on 22/Jul/21 $${Determiner}\:{l}'{original}\:{de}\:{laplace} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$\mathrm{G}\left({x}\right)\:=\:{F}\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}}…
Question Number 16635 by tawa tawa last updated on 24/Jun/17 $$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y},\:\mathrm{z} \\ $$$$\sqrt{\mathrm{x}}\:+\:\sqrt{\mathrm{y}}\:+\:\sqrt{\mathrm{z}}\:=\:\mathrm{4} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{40}.\mathrm{125} \\ $$$$\mathrm{e}^{\mathrm{xyz}} \:=\:\mathrm{4}.\mathrm{771} \\ $$ Terms of…