Question Number 181275 by Linton last updated on 23/Nov/22 $${what}\:{is}\:{the}\:{sum}\:{of}\:{all} \\ $$$${even}\:{factors}\:{of}\:\mathrm{1000}? \\ $$ Commented by Rasheed.Sindhi last updated on 24/Nov/22 ���� Commented by Linton…
Question Number 50135 by peter frank last updated on 14/Dec/18 Commented by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{solve}\:\left(\mathrm{2}{x}−\mathrm{1}\right){y}^{''} \:−{y}^{'} =\mathrm{0}\:\:\:{withy}\left(\mathrm{0}\right)=\mathrm{2}\:{and}\:{y}^{'} \left(\mathrm{0}\right)=\mathrm{3}\:\:{let}\:{use}\:{changement} \\ $$$${y}^{'}…
Question Number 181039 by depressiveshrek last updated on 20/Nov/22 $${Prove}\:{that}\:{for}\:{all}\:{a}^{\mathrm{2}} \:{divisible}\:{by}\:{b}, \\ $$$${a}\:{is}\:{also}\:{divisible}\:{by}\:{b} \\ $$$${for}\:{all}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$ Commented by mr W last updated on 20/Nov/22…
Question Number 180828 by Vynho last updated on 17/Nov/22 $${H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}} \\ $$$${H}_{\mathrm{2}{n}} =?\:{compute}\:{H}_{\mathrm{2}{n}} −{H}_{{n}} \:{and}\:{H}_{{n}+\mathrm{1}} −{H}_{{n}} \\ $$ Commented by Frix last updated on…
Question Number 49680 by peter frank last updated on 09/Dec/18 Answered by math1967 last updated on 09/Dec/18 $${Total}\:{surface}\:{area}\:=\mathrm{2}×\mathrm{6}×\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}×\mathrm{20}^{\mathrm{2}} +\mathrm{6}×\mathrm{20}×\mathrm{15} \\ $$$$=\mathrm{3878}.\mathrm{46}{cm}^{\mathrm{2}} \left({aprox}\right) \\ $$$${Volume}=\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}×\mathrm{6}×\mathrm{20}^{\mathrm{2}} ×\mathrm{15}=\mathrm{233826}.\mathrm{85}{cm}^{\mathrm{3}}…
Question Number 115194 by 1549442205PVT last updated on 24/Sep/20 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{three}−\mathrm{digits}\:\mathrm{number}\:\mathrm{whose} \\ $$$$\mathrm{digits}\:\mathrm{form}\:\mathrm{a}\:\mathrm{geometry}\:\mathrm{progression} \\ $$$$;\mathrm{if}\:\mathrm{you}\:\mathrm{known}\:\mathrm{that}\:\mathrm{after}\:\mathrm{substract}\:\mathrm{that} \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{495}\:,\mathrm{get}\:\mathrm{a}\:\mathrm{number} \\ $$$$\mathrm{written}\:\mathrm{by}\:\mathrm{the}\:\mathrm{same}\:\mathrm{digits}\:\mathrm{as}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{you}\:\mathrm{are}\:\mathrm{looking}\:\mathrm{for}\:\mathrm{but}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{reverse}\:\mathrm{order};\mathrm{if}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{obtained}\:\mathrm{after} \\…
Question Number 180695 by depressiveshrek last updated on 15/Nov/22 $${Find}\:{all}\:{k},\:{m},\:{n}\:\in\:\mathbb{N}\:{such}\:{that} \\ $$$${k}!+\mathrm{3}^{{m}} =\mathrm{3}^{{n}} \\ $$ Answered by nikif99 last updated on 16/Nov/22 $${Trying}\:{an}\:{answer}. \\ $$$${must}\:{be}\:{m}<{n}\:{and}\:\mathrm{3}^{{n}}…
Question Number 115062 by Sudip last updated on 23/Sep/20 $$\mathrm{If}\:\:\mathrm{2cos}\theta−\mathrm{sin}\theta=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\left(\mathrm{0}°<\theta<\mathrm{90}°\right) \\ $$$$\mathrm{then}\:\:\mathrm{2sin}\theta+\mathrm{cos}\theta=\:¿ \\ $$ Answered by PRITHWISH SEN 2 last updated on 23/Sep/20 $$\mathrm{let}\:\mathrm{2sin}\:\theta+\mathrm{cos}\:\theta\:=\:\mathrm{k}\:….\left(\mathrm{ii}\right) \\…
Question Number 180554 by cherokeesay last updated on 13/Nov/22 Answered by Rasheed.Sindhi last updated on 13/Nov/22 $${f}\left({x}\right)=\mathrm{2}{x}−\mathrm{5}\:\:,\:\:\:{g}\left({x}\right)={x}+\mathrm{1} \\ $$$$\left({f}\left({g}^{−\mathrm{1}} \right)\right)^{−\mathrm{1}} \left({x}\right)=? \\ $$$$\bullet{g}^{−\mathrm{1}} \left({x}\right)=? \\…
Question Number 49427 by Tawa1 last updated on 06/Dec/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}:\:\:\:\mathrm{5},\:\:\mathrm{5},\:\:\mathrm{35},\:\:\mathrm{65},\:\:\mathrm{275},\:… \\ $$ Commented by Tawa1 last updated on 07/Dec/18 $$\mathrm{Answer}:\:\:\:\:\:\mathrm{3}^{\boldsymbol{\mathrm{n}}} \:−\:\left(−\:\mathrm{2}\right)^{\boldsymbol{\mathrm{n}}} \:.\:\:\:\:\mathrm{How}\:??? \\ $$ Terms…