Question Number 117597 by Ar Brandon last updated on 12/Oct/20 $$\mathrm{Let}\:\mathrm{A},\:\mathrm{B},\:\mathrm{and}\:\mathrm{C}\:\mathrm{be}\:\mathrm{three}\:\mathrm{sets}\:\mathrm{and}\:\mathrm{X}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all} \\ $$$$\mathrm{elements}\:\mathrm{which}\:\mathrm{belong}\:\mathrm{to}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sets}\:\mathrm{A},\mathrm{B} \\ $$$$\mathrm{and}\:\mathrm{C}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{X}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{A}\cup\mathrm{B}\cup\mathrm{C}\right)−\left[\mathrm{A}\Delta\left(\mathrm{B}\Delta\mathrm{C}\right)\right] \\ $$ Commented by prakash jain last updated…
Question Number 182718 by mnjuly1970 last updated on 13/Dec/22 $$ \\ $$$$\:\:\:\:\:\:\mathrm{If}\:,\:\:\:\:\mathrm{7}^{\:{n}} \:\overset{\mathrm{10}} {\equiv}\:\mathrm{7}^{\:\mathrm{19}} \\ $$$$\:\:\:\:\:\:\:{then}\:\:{find}\:{the}\:\:\mathrm{1}{st}\:{digit} \\ $$$$\:\:\:\:{of}\:\:{the}\:{numer}\:\:,\:\:\:\mathrm{8}^{\:{n}+\mathrm{4}} \:.\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Commented by…
Question Number 182203 by depressiveshrek last updated on 05/Dec/22 $${Let}\:{A}=\left\{\mathrm{1}^{{p}^{\mathrm{2}} −{p}} ,\:\mathrm{2}^{{p}^{\mathrm{2}} −{p}} ,…,\:\left({p}−\mathrm{1}\right)^{{p}^{\mathrm{2}} −{p}} ,\:{p}^{\mathrm{2}} −{p}+\mathrm{1}\right\} \\ $$$${where}\:{p}\:{is}\:{any}\:{prime}\:{number} \\ $$$${Prove}\:{that}\:{for}\:{any}\:{value}\:{of}\:{p}, \\ $$$${however}\:{we}\:{split}\:{this}\:{set}\:{into}\:{two} \\ $$$${disjunctive}\:{sets},\:{the}\:{arithmetic}…
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Question Number 181280 by mnjuly1970 last updated on 23/Nov/22 Answered by Frix last updated on 23/Nov/22 $$\varphi=\mathrm{1}+\frac{\mathrm{1}}{\varphi} \\ $$$$\frac{\varphi}{\mathrm{1}}=\frac{\varphi+\mathrm{1}}{\varphi} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{the}\:\mathrm{definition}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Golden}\:\mathrm{Ratio} \\ $$ Terms of…
Question Number 180299 by mnjuly1970 last updated on 10/Nov/22 Answered by som(math1967) last updated on 10/Nov/22 Commented by som(math1967) last updated on 10/Nov/22 $${let}\:{O}\:{is}\:{centre}\:{of}\:{semicircle} \\…
Question Number 179919 by mnjuly1970 last updated on 04/Nov/22 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Evaluate}\: \\ $$$$\:\:\:\:\:\:\Omega\:=\:\mathrm{lim}_{\:{n}\rightarrow\infty} \left(\:{n}−\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{cos}\:\left(\:\frac{\:\sqrt{{k}}}{\:{n}}\:\:\right)\:\right)\:=?\:\:\:\:\:\: \\ $$$$\:\:\:\:\: \\ $$ Answered by mindispower last…
Question Number 179918 by mnjuly1970 last updated on 04/Nov/22 Answered by mindispower last updated on 05/Nov/22 $$\zeta\left({t}+=−\gamma−\Sigma\zeta\left({n}+\mathrm{1}\right)\left(−{t}\right)^{{n}} \right. \\ $$$$\Psi'\left({z}+\mathrm{1}\right)=−\Sigma\frac{{n}\zeta\left({n}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{n}} {t}^{\boldsymbol{{n}}−\mathrm{1}} }{\mathrm{1}} \\ $$$${z}\Psi''\left({z}+\mathrm{1}\right)=−\Sigma{n}\left(−\mathrm{1}\right)^{{n}} {t}^{{n}}…
Question Number 114235 by Aina Samuel Temidayo last updated on 18/Sep/20 $$\mathrm{Let}\:\mathrm{A}=\left\{\left(\mathrm{n},\mathrm{2n}\right):\mathrm{n}\in\mathrm{N}\right\}\:\mathrm{and} \\ $$$$\mathrm{B}=\left\{\left(\mathrm{2n},\mathrm{3n}\right):\mathrm{n}\in\mathrm{N}\right\}.\:\mathrm{Then}\:\mathrm{A}\cap\mathrm{B}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$ Answered by 1549442205PVT last updated on 18/Sep/20…
Question Number 114236 by Aina Samuel Temidayo last updated on 18/Sep/20 $$\mathrm{70\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{employees}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{multinational}\:\mathrm{corporation}\:\mathrm{have}\:\mathrm{VCD} \\ $$$$\mathrm{players},\:\mathrm{75\%}\:\mathrm{have}\:\mathrm{microwave}\:\mathrm{ovens}, \\ $$$$\mathrm{80\%}\:\mathrm{have}\:\mathrm{ACs}\:\mathrm{and}\:\mathrm{85\%}\:\mathrm{have}\:\mathrm{washing} \\ $$$$\mathrm{machines}.\:\mathrm{At}\:\mathrm{least}\:\mathrm{what}\:\mathrm{percentage}\:\mathrm{of} \\ $$$$\mathrm{employees}\:\mathrm{has}\:\mathrm{all}\:\mathrm{four}\:\mathrm{gadgets}? \\ $$ Answered…