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Category: Logic

eqution-

Question Number 5450 by 3 last updated on 15/May/16 $${eqution} \\ $$ Answered by FilupSmith last updated on 15/May/16 $${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{with}\:\mathrm{solution}: \\ $$$${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}}…

Prove-that-f-x-x-a-cos-x-b-has-at-least-one-real-root-for-a-b-R-

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}…

Function-is-a-b-a-b-AB-a-b-4-b-4-4-b-b-a-1-a-1-2-b-2-a-3-Function-is-a-b-sin-a-b-a-b-sin-a-b-a-b-1-b-5-a-4-9-a-b-9-b-a-Funcion-is-sin-a-sin-b-sin-1-a-sin-1-b-a-b-sin-a-sin-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} \\…

Prove-or-disprove-that-as-time-goes-by-the-influence-of-the-past-on-the-present-diminishes-I-met-this-idea-in-an-informal-analysis-of-the-origins-of-equilibrium-probabilities-found-for-the-tra

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…

An-online-trading-company-wants-to-offer-discounts-to-customers-The-company-has-recently-emailed-the-discount-codes-to-customers-New-customers-must-have-the-code-to-be-eligible-but-returning-cust

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} \\…

Q-4140-is-again-asked-with-following-changes-a-always-moves-towards-b-instead-of-b-b-always-moves-towards-c-instead-of-c-c-always-moves-towards-d-instead-of-d-d-always-moves-towards-

Question Number 4196 by Rasheed Soomro last updated on 31/Dec/15 $$\:\:\mathrm{Q}#\mathrm{4140}\:\mathrm{is}\:\mathrm{again}\:\mathrm{asked}\:\mathrm{with}\:\mathrm{following}\:\mathrm{changes}: \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{b}}\right), \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{c}}\right), \\ $$$$\boldsymbol{\mathrm{c}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{d}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{d}}\right),\: \\ $$$$\boldsymbol{\mathrm{d}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{a}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{a}}\right), \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{a}}',\boldsymbol{\mathrm{b}}',\boldsymbol{\mathrm{c}}'\:\mathrm{and}\:\boldsymbol{\mathrm{d}}'\:\mathrm{are}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{line} \\ $$$$\mathrm{segments}\:\boldsymbol{\mathrm{ab}},\:\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cd}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{da}}\:\mathrm{respectively}. \\ $$…