Question Number 151513 by pete last updated on 21/Aug/21 $$\mathrm{Find}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{p}\:\mathrm{if}\:\mathrm{the}\:\mathrm{lines} \\ $$$${px}−{y}=\mathrm{0}\:\mathrm{and}\:\mathrm{3}{x}+{y}+\mathrm{1}=\mathrm{0}\:\mathrm{intersect}\:\mathrm{at}\:\mathrm{45}° \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\Delta_{\mathrm{1}} \::\:{px}−{y}\:=\:\mathrm{0} \\ $$$$\Delta_{\mathrm{2}}…
Question Number 151504 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{ln}\:{x}}{\:\sqrt{{x}}\:\sqrt{{x}+\mathrm{1}}\:\sqrt{\mathrm{2}{x}+\mathrm{1}}}\:{dx} \\ $$$$\: \\ $$ Answered by Kamel last updated on 21/Aug/21…
Question Number 151501 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\left(\mathrm{log}\:{x}\:+\:\mathrm{1}\right){x}^{{x}} \:{dx} \\ $$$$\: \\ $$ Answered by puissant last updated on 21/Aug/21 $${K}=\int\left(\mathrm{1}+{lnx}\right){x}^{{x}}…
Question Number 20430 by Tinkutara last updated on 26/Aug/17 $$\mathrm{Let}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{be}\:\mathrm{such}\:\mathrm{that}\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{0} \\ $$$$\mathrm{and} \\ $$$${P}\:=\:\frac{{a}^{\mathrm{2}} }{\mathrm{2}{a}^{\mathrm{2}} \:+\:{bc}}\:+\:\frac{{b}^{\mathrm{2}} }{\mathrm{2}{b}^{\mathrm{2}} \:+\:{ca}}\:+\:\frac{{c}^{\mathrm{2}} }{\mathrm{2}{c}^{\mathrm{2}} \:+\:{ab}} \\ $$$$\mathrm{is}\:\mathrm{defined}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{P}? \\ $$ Commented…
Question Number 151503 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}−\mathrm{1}}{\:\sqrt{\mathrm{2}^{{x}} −\mathrm{1}}\:\mathrm{ln}\left(\mathrm{2}^{{x}} −\mathrm{1}\right)}\:{dx} \\ $$$$\: \\ $$ Answered by Kamel last updated…
Question Number 151496 by puissant last updated on 21/Aug/21 $$\forall{x},{y}\in\mathbb{R}_{+} ^{\ast} ,\:{show}\:{that}\:\frac{{x}}{{x}^{\mathrm{4}} +{y}^{\mathrm{2}} }+\frac{{y}}{{y}^{\mathrm{4}} +{x}^{\mathrm{2}} }\leqslant\frac{\mathrm{1}}{{xy}} \\ $$ Answered by dumitrel last updated on 21/Aug/21…
Question Number 20425 by Tinkutara last updated on 27/Aug/17 $$\mathrm{On}\:\mathrm{a}\:\mathrm{frictionless}\:\mathrm{horizontal}\:\mathrm{surface}, \\ $$$$\mathrm{assumed}\:\mathrm{to}\:\mathrm{be}\:\mathrm{the}\:{x}-{y}\:\mathrm{plane},\:\mathrm{a}\:\mathrm{small} \\ $$$$\mathrm{trolley}\:{A}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:{y}-\mathrm{axis}\:\left(\mathrm{see}\:\mathrm{figure}\right) \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{velocity}\:\mathrm{of}\:\left(\sqrt{\mathrm{3}}\:−\:\mathrm{1}\right)\:\mathrm{m}/\mathrm{s}. \\ $$$$\mathrm{At}\:\mathrm{a}\:\mathrm{particular}\:\mathrm{instant},\:\mathrm{when}\:\mathrm{the}\:\mathrm{line} \\ $$$${OA}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}°\:\mathrm{with}\:\mathrm{the} \\ $$$${x}-\mathrm{axis},\:\mathrm{a}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{along}\:\mathrm{the} \\…
Question Number 85961 by A8;15: last updated on 26/Mar/20 Commented by MJS last updated on 26/Mar/20 $$\mathrm{we}\:\mathrm{still}\:\mathrm{do}\:\mathrm{not}\:\mathrm{know}\:\mathrm{what}\:{V}_{{a}} ^{{b}} \:\mathrm{is} \\ $$ Commented by jagoll last…
Question Number 151493 by iloveisrael last updated on 21/Aug/21 $$\:\:\:\frac{\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{2}}−\mathrm{6}{x}\right)+\mathrm{sin}\:\left(\pi+\mathrm{4}{x}\right)+\mathrm{sin}\:\left(\mathrm{3}\pi−{x}\right)}{\mathrm{sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{2}}+\mathrm{6}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}−\mathrm{2}\pi\right)+\mathrm{cos}\:\left({x}+\mathrm{2}\pi\right)}\:=? \\ $$ Commented by MJS_new last updated on 21/Aug/21 $$\mathrm{tan}\:{x} \\ $$ Commented by liberty…
Question Number 151492 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{tan}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$ Terms of Service Privacy Policy…