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Question-137893

Question Number 137893 by bemath last updated on 07/Apr/21 Answered by benjo_mathlover last updated on 08/Apr/21 $${by}\:{algebra} \\ $$$${let}\:{F}\left(\mathrm{0},\mathrm{0}\right),\:{D}\left(\mathrm{1},\mathrm{0}\right),\:{A}\left(\mathrm{0},\mathrm{1}\right),\:{C}\left(\mathrm{1},\mathrm{1}\right) \\ $$$${B}\left(\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}\right)\:,\:{E}\left(\frac{\mathrm{1}}{\mathrm{4}},\mathrm{0}\right) \\ $$$${eq}\:{of}\:{line}\:{AE}\::\:{x}+\frac{\mathrm{1}}{\mathrm{4}}{y}=\frac{\mathrm{1}}{\mathrm{4}};\: \\ $$$${eq}\:{of}\:{line}\:{FB}\::\:\:{y}=\mathrm{2}{x}\:…

The-position-vector-of-the-point-P-at-time-t-is-given-by-tant-i-sect-k-where-is-positive-constant-and-0-t-2-Show-that-the-velocity-and-acceleration-of-P-when-t-0-are-at-right-angle-

Question Number 6820 by Tawakalitu. last updated on 29/Jul/16 $${The}\:{position}\:{vector}\:{of}\:{the}\:{point}\:{P}\:\:{at}\:{time}\:{t}\:{is}\:{given}\:{by}\: \\ $$$$\left(\alpha{tant}\right){i}\:+\:\left(\alpha{sect}\right){k}\:{where}\:\alpha\:{is}\:{positive}\:{constant}\:{and} \\ $$$$\mathrm{0}\leqslant{t}\leqslant\frac{\Pi}{\mathrm{2}}.\:\:{Show}\:{that}\:{the}\:{velocity}\:{and}\:{acceleration}\:{of}\:{P}\:\:{when} \\ $$$${t}\:=\:\mathrm{0}\:{are}\:{at}\:{right}\:{angle}\:{to}\:{each}\:{other}.\:{If}\:{A}\:{is}\:{the}\:{point}\:{with}\: \\ $$$${position}\:{vector}\:\alpha{j},\:{obtain}\:{the}\:{vector}\:{equation}\:{for}\:{the}\:{straight}\: \\ $$$${line}\:{AP}\:{at}\:{time}\:{t}.\:\:{If}\:{the}\:{point}\:{Q}\:{divides}\:{AP}\:\:{internally}\:{in}\:{the} \\ $$$${ratio}\:\left({cost}\right)\::\:\left(\mathrm{1}\:−\:{cost}\right).\:{Show}\:{that}\:{the}\:{acceleration}\:{of}\:{the}\:{point} \\ $$$${Q}\:{is}\:{constant}\:{in}\:{magnitude}\:{and}\:{is}\:{always}\:{directed}\:{towards}\:{a}\: \\…

Question-72346

Question Number 72346 by aliesam last updated on 27/Oct/19 Commented by mathmax by abdo last updated on 27/Oct/19 $${I}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({x}^{\mathrm{10}} +{x}^{\mathrm{6}} \:+{x}^{\mathrm{4}} \:+\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\:\:\:{by}\:{psrts}\:{u}^{'}…

Up-to-which-prime-number-should-9-divide-9631-to-ensure-that-this-number-is-a-prime-number-or-a-composite-number-

Question Number 6810 by Tawakalitu. last updated on 28/Jul/16 $${Up}\:{to}\:{which}\:{prime}\:{number}\:{should}\:\:\:\mathrm{9}\:\:\:{divide}\:\:\:\mathrm{9631}\:\:\:{to}\:{ensure}\:{that} \\ $$$${this}\:{number}\:{is}\:{a}\:{prime}\:{number}\:{or}\:{a}\:{composite}\:{number}\:? \\ $$ Commented by Rasheed Soomro last updated on 29/Jul/16 $$\mathrm{97} \\ $$$${The}\:{largest}\:{prime}\:{number}\:{not}\:{greater}\:{than}\:\sqrt{\mathrm{9631}}…