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Question Number 70742 by Joel122 last updated on 07/Oct/19 $$\mathrm{Prove}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{x}\:−\:{a}\:\mathrm{cos}\:\left({x}\right)\:−\:{b} \\ $$$$\mathrm{has}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\mathrm{for}\:\forall{a},{b}\:\in\:\mathbb{R} \\ $$ Commented by kaivan.ahmadi last updated on 07/Oct/19 $${x}−{acosx}−{b}=\mathrm{0}\Rightarrow{x}−{b}={acosx} \\ $$$${y}_{\mathrm{1}} ={x}−{b}…
Question Number 4790 by Dnilka228 last updated on 10/Mar/16 $${Function}\:\Gamma\:{is}\:{a}+{b} \\ $$$${a}+{b}={AB} \\ $$$${a}\neq{b}−\mathrm{4} \\ $$$${b}−\mathrm{4}=\mathrm{4}+{b} \\ $$$${b}={a}−\mathrm{1} \\ $$$${a}−\mathrm{1}=\mathrm{2} \\ $$$${b}=\mathrm{2} \\ $$$${a}=\mathrm{3} \\…
Question Number 70168 by Askash last updated on 01/Oct/19 Commented by Askash last updated on 01/Oct/19 Please solve ���� Commented by MJS last updated on 01/Oct/19 $$\mathrm{zillions}\:\mathrm{of}\:\mathrm{possibilities}…
Question Number 4621 by Yozzii last updated on 14/Feb/16 $${Prove}\:{or}\:{disprove}\:{that}\:,\:{as}\:{time}\:{goes}\:{by}, \\ $$$${the}\:{influence}\:{of}\:{the}\:{past}\:{on}\:{the}\: \\ $$$${present}\:{diminishes}.\: \\ $$$$\left({I}\:{met}\:{this}\:{idea}\:{in}\:{an}\:{informal}\right. \\ $$$${analysis}\:{of}\:{the}\:{origins}\:{of}\:{equilibrium}\: \\ $$$${probabilities}\:{found}\:{for}\:{the}\:{transition} \\ $$$$\left.{matrix}\:{of}\:{a}\:{Markov}\:{chain}\:{scenario}.\right) \\ $$ Commented…
Question Number 135348 by nadovic last updated on 12/Mar/21 $$\mathrm{An}\:\mathrm{online}\:\mathrm{trading}\:\mathrm{company}\:\mathrm{wants}\:\mathrm{to} \\ $$$$\mathrm{offer}\:\mathrm{discounts}\:\mathrm{to}\:\mathrm{customers}.\:\mathrm{The}\: \\ $$$$\mathrm{company}\:\mathrm{has}\:\mathrm{recently}\:\mathrm{emailed}\:\mathrm{the} \\ $$$$\mathrm{discount}\:\mathrm{codes}\:\mathrm{to}\:\mathrm{customers}.\:\mathrm{New}\: \\ $$$$\mathrm{customers}\:\mathrm{must}\:\mathrm{have}\:\mathrm{the}\:\mathrm{code}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{eligible}\:\mathrm{but}\:\mathrm{returning}\:\mathrm{customers}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{eligible}\:\mathrm{for}\:\mathrm{the}\:\mathrm{discount}. \\ $$$$\:\:\:\:\:\:{Let}\:\:\:{A}\:−\:{Returning}\:{Customer} \\…
Question Number 4196 by Rasheed Soomro last updated on 31/Dec/15 $$\:\:\mathrm{Q}#\mathrm{4140}\:\mathrm{is}\:\mathrm{again}\:\mathrm{asked}\:\mathrm{with}\:\mathrm{following}\:\mathrm{changes}: \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{b}}\right), \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{c}}\right), \\ $$$$\boldsymbol{\mathrm{c}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{d}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{d}}\right),\: \\ $$$$\boldsymbol{\mathrm{d}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{a}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{a}}\right), \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{a}}',\boldsymbol{\mathrm{b}}',\boldsymbol{\mathrm{c}}'\:\mathrm{and}\:\boldsymbol{\mathrm{d}}'\:\mathrm{are}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{line} \\ $$$$\mathrm{segments}\:\boldsymbol{\mathrm{ab}},\:\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cd}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{da}}\:\mathrm{respectively}. \\ $$…
Question Number 134948 by rexford last updated on 08/Mar/21 Commented by bobhans last updated on 09/Mar/21 $$\mathrm{what}\:\mathrm{definition}\:\overset{\rightarrow} {\mathrm{a}}\wedge\overset{\rightarrow} {\mathrm{b}}\:? \\ $$ Commented by rexford last…
Question Number 134689 by benjo_mathlover last updated on 06/Mar/21 $$\:\frac{\mathrm{2}^{\mathrm{289}} +\mathrm{1}}{\mathrm{2}^{\mathrm{17}} +\mathrm{1}}\:=\:\mathrm{2}^{{a}_{\mathrm{1}} } \:+\:\mathrm{2}^{{a}_{\mathrm{2}} } \:+\:\mathrm{2}^{{a}_{\mathrm{3}} } \:+\:…\:+\:\mathrm{2}^{{a}_{{k}} } \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}. \\ $$ Answered by…
Question Number 69116 by ~ À ® @ 237 ~ last updated on 20/Sep/19 $$\:{Here}\:\:{are}\:{three}\:{propositions}:\: \\ $$$$−\:{This}\:{sentence}\:{has}\:{exactly}\:{six}\:{words} \\ $$$$−{There}\:{are}\:{two}\:{wrong}\:{propositions} \\ $$$$−{The}\:{two}\:{previous}\:{sentences}\:{are}\:{correct} \\ $$$$ \\ $$$${Among}\:{that}\:{propositions}\:,{how}\:{many}\:{are}\:{wrong}?\:{list}\:{them}!…