Question Number 19167 by Tinkutara last updated on 06/Aug/17 $$\mathrm{Two}\:\mathrm{particles}\:{A}\:\mathrm{and}\:{B}\:\mathrm{move}\:\mathrm{with} \\ $$$$\mathrm{constant}\:\mathrm{velocities}\:{v}_{\mathrm{1}} \:\mathrm{and}\:{v}_{\mathrm{2}} \:\mathrm{along}\:\mathrm{two} \\ $$$$\mathrm{mutually}\:\mathrm{perpendicular}\:\mathrm{straight}\:\mathrm{lines} \\ $$$$\mathrm{towards}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{point}\:{O}.\:\mathrm{At} \\ $$$$\mathrm{moment}\:{t}\:=\:\mathrm{0},\:\mathrm{the}\:\mathrm{particles}\:\mathrm{were} \\ $$$$\mathrm{located}\:\mathrm{at}\:\mathrm{distances}\:{d}_{\mathrm{1}} \:\mathrm{and}\:{d}_{\mathrm{2}} \:\mathrm{from}\:{O} \\…
Question Number 84680 by M±th+et£s last updated on 15/Mar/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({xyz}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{z}^{\mathrm{2}} \right)}\:{dx}\:{dy}\:{dz}=\frac{−\mathrm{3}\pi^{\mathrm{2}} {G}}{\mathrm{16}} \\ $$ Answered…
Question Number 19140 by Tinkutara last updated on 05/Aug/17 $$\mathrm{A}\:\mathrm{racing}\:\mathrm{car}\:\mathrm{travels}\:\mathrm{on}\:\mathrm{a}\:\mathrm{track}\:\left(\mathrm{without}\right. \\ $$$$\left.\mathrm{banking}\right)\:{ABCDEFA}.\:{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circular} \\ $$$$\mathrm{arc}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{2}{R}.\:{CD}\:\mathrm{and}\:{FA}\:\mathrm{are} \\ $$$$\mathrm{straight}\:\mathrm{paths}\:\mathrm{of}\:\mathrm{length}\:{R}\:\mathrm{and}\:{DEF}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{circular}\:\mathrm{arc}\:\mathrm{of}\:\mathrm{radius}\:{R}\:=\:\mathrm{100}\:\mathrm{m}.\:\mathrm{The} \\ $$$$\mathrm{co}-\mathrm{efficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{on}\:\mathrm{the}\:\mathrm{road}\:\mathrm{is}\:\mu\:= \\ $$$$\mathrm{0}.\mathrm{1}.\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{is} \\ $$$$\mathrm{50}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{time}\:\mathrm{for}…
Question Number 19137 by Tinkutara last updated on 05/Aug/17 $$\mathrm{Figure}\:\mathrm{shows}\:\left({x},\:{t}\right),\:\left({y},\:{t}\right)\:\mathrm{diagram}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{particle}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{2}-\mathrm{dimensions}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{has}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{500}\:\mathrm{g},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{force}\:\left(\mathrm{direction}\:\mathrm{and}\:\mathrm{magnitude}\right)\:\mathrm{acting} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{particle}. \\ $$ Commented by Tinkutara last updated…
Question Number 84637 by Rio Michael last updated on 14/Mar/20 $$\mathrm{prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\right)^{{x}} \:={e} \\ $$ Commented by ajfour last updated on 14/Mar/20 $${prove}\:{that}\:\:\mathrm{sin}\:\theta=\frac{{p}}{{h}}\:. \\ $$…
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Question Number 150156 by Lekhraj last updated on 09/Aug/21 Answered by Ar Brandon last updated on 10/Aug/21 $${u}_{{n}} =−\mathrm{4},\:\mathrm{1},\:\mathrm{12},\:\mathrm{29},\:\mathrm{52},\:\mathrm{81},\:\mathrm{116},…\:{u}_{\mathrm{1}} =−\mathrm{4} \\ $$$$\Delta{u}_{{n}} =\mathrm{5},\:\mathrm{11},\:\mathrm{17},\:\mathrm{23},\:\mathrm{29},…\:\:{d}_{\mathrm{1}} =\mathrm{5} \\…
Question Number 84607 by M±th+et£s last updated on 14/Mar/20 $$\left.\mathrm{1}\right)\int\sqrt{{sin}\left({x}\right)}\:{dx} \\ $$$$\left.\mathrm{2}\right)\int{cos}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$ \\ $$ Commented by john santu last updated on 14/Mar/20…
Question Number 84510 by 698148290 last updated on 13/Mar/20 Answered by jagoll last updated on 14/Mar/20 $$\mathrm{equation}\:\mathrm{of}\:\mathrm{tangent} \\ $$$$\Rightarrow\:\frac{\mathrm{x}_{\mathrm{1}} \mathrm{x}}{\mathrm{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}_{\mathrm{1}} \mathrm{y}}{\mathrm{b}^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\frac{\mathrm{cos}\:\theta\:\mathrm{x}}{\mathrm{a}}\:+\:\frac{\mathrm{sin}\:\theta\:\mathrm{y}}{\mathrm{b}}\:=\:\mathrm{1}\:…
Question Number 18965 by Tinkutara last updated on 02/Aug/17 $$\mathrm{Two}\:\mathrm{blocks}\:\mathrm{of}\:\mathrm{masses}\:{M}\:\mathrm{and}\:\mathrm{2}{M}\:\mathrm{are} \\ $$$$\mathrm{connected}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}\:\mathrm{through}\:\mathrm{a}\:\mathrm{light} \\ $$$$\mathrm{spring}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{If}\:\mathrm{we}\:\mathrm{push}\:\mathrm{the} \\ $$$$\mathrm{mass}\:{M}\:\mathrm{with}\:\mathrm{a}\:\mathrm{force}\:{F}\:\mathrm{which}\:\mathrm{cause} \\ $$$$\mathrm{acceleration}\:\mathrm{a}\:\mathrm{in}\:\mathrm{mass}\:{M},\:\mathrm{what}\:\mathrm{will}\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{in}\:\mathrm{2}{M}? \\ $$ Commented by Tinkutara…