Question Number 199309 by universe last updated on 01/Nov/23 $$\:\:\:\:{a}_{{n}+\mathrm{1}\:} =\:{a}_{{n}} \:+\:\sqrt{{a}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:\:,\:{a}_{\mathrm{0}} \:=\:\mathrm{0} \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}\:} \:=\:\:?? \\ $$ Answered by TheHoneyCat last updated…
Question Number 199310 by necx122 last updated on 01/Nov/23 $${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{a}\:{group}\:{of}\:\mathrm{3} \\ $$$${people}\:{born}\:{on}\:{the}\:{same}\:{day}\:{of}\:{the} \\ $$$${week}? \\ $$ Commented by AST last updated on 01/Nov/23…
Question Number 199311 by necx122 last updated on 01/Nov/23 $${Find}\:{the}\:{number}\:{of}\:{positive}\:{integers} \\ $$$${that}\:{are}\:{factors}\:{of}\:\mathrm{3}^{\mathrm{19}} .\mathrm{7}^{\mathrm{12}} .\mathrm{10}^{\mathrm{25}} \:{and}\:{are} \\ $$$${also}\:{multiples}\:{of}\:\mathrm{3}^{\mathrm{15}} .\mathrm{7}^{\mathrm{10}} .\mathrm{10}^{\mathrm{19}} \\ $$ Answered by AST last…
Question Number 199337 by cortano12 last updated on 01/Nov/23 Answered by mr W last updated on 01/Nov/23 $$\left.\mathrm{3}\right) \\ $$$${odd}:\:\mathrm{5}×\mathrm{6}^{\mathrm{5}} \\ $$$${even}:\:\mathrm{2}×\mathrm{6}^{\mathrm{5}} \\ $$$$\frac{{odd}}{{even}}=\frac{\mathrm{5}}{\mathrm{2}} \\…
Question Number 199338 by sonukgindia last updated on 01/Nov/23 Answered by aleks041103 last updated on 01/Nov/23 $$\mathrm{5}^{\mathrm{2}^{{M}} } −\mathrm{1}=\left(\mathrm{5}^{\mathrm{2}^{{M}−\mathrm{1}} } \right)^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} =\left(\mathrm{5}^{\mathrm{2}^{{M}−\mathrm{1}} } +\mathrm{1}\right)\left(\mathrm{5}^{\mathrm{2}^{{M}−\mathrm{1}}…
Question Number 199339 by necx122 last updated on 01/Nov/23 Commented by necx122 last updated on 01/Nov/23 $${find}\:\angle{QSR}\:{where}\:{O}\:{is}\:{the}\:{centre} \\ $$$$\angle{OTQ}\:=\mathrm{15},\:\angle{TOR}=\mathrm{110} \\ $$ Commented by AST last…
Question Number 199333 by necx122 last updated on 01/Nov/23 $${Find}\:{the}\:{number}\:{of}\:{integers}\:{greater} \\ $$$${than}\:\mathrm{6200}\:{that}\:{can}\:{be}\:{formed}\:{from} \\ $$$${the}\:{digits}\:\mathrm{1},\mathrm{3},\mathrm{6},\mathrm{8}\:{and}\:\mathrm{9},\:{where}\:{each} \\ $$$${digit}\:{is}\:{used}\:{at}\:{most}\:{once}. \\ $$ Answered by aleks041103 last updated on 01/Nov/23…
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Question Number 199331 by necx122 last updated on 01/Nov/23 $${What}\:{is}\:{the}\:{remainder}\:{when} \\ $$$$\mathrm{1}^{\mathrm{1}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +……+\mathrm{2023}^{\mathrm{2023}} \:{is}\:{divided}\:{by}\:\mathrm{7} \\ $$ Answered by AST last updated on 01/Nov/23…
Question Number 199290 by ajfour last updated on 31/Oct/23 $${If}\:{x}=\sqrt{{p}+{iq}}+\sqrt{{h}+{ik}} \\ $$$${and}\:\:\frac{{p}}{{q}}\neq\frac{{k}}{{h}}\:\:{then}\:{relate}\:{p},{q},{h},{k}\:\in\mathbb{R} \\ $$$${such}\:{that}\:{x}\in\mathbb{R}. \\ $$ Commented by Frix last updated on 31/Oct/23 $$\sqrt{{x}+{y}\mathrm{i}}={r}\mathrm{e}^{\mathrm{i}\theta} \:\mathrm{with}\:{r}>\mathrm{0}\wedge−\frac{\pi}{\mathrm{2}}<\theta\leqslant\frac{\pi}{\mathrm{2}}…