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Question-40173

Question Number 40173 by scientist last updated on 16/Jul/18 Commented by math khazana by abdo last updated on 17/Jul/18 $${let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:\:\Rightarrow{ln}\left({f}\left({x}\right)\right)=\frac{\mathrm{1}}{\mathrm{2}}\left\{{ln}\left(\mathrm{1}+{x}\right)−{ln}\left(\mathrm{1}−{x}\right)\right\} \\ $$$${but}\:{ln}^{'} \left(\mathrm{1}+{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}}\:=\mathrm{1}−{x}\:+{x}^{\mathrm{2}} \:+{o}\left({x}^{\mathrm{3}}…

Question-171179

Question Number 171179 by Mastermind last updated on 09/Jun/22 Answered by aleks041103 last updated on 09/Jun/22 $$\sqrt[{\mathrm{1}/\mathrm{4}}]{{tg}^{{n}^{\mathrm{2}} −{n}+\frac{\mathrm{1}}{\mathrm{4}}} \left({x}\right)}={tg}^{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{4}{n}+\mathrm{1}} \left({x}\right)= \\ $$$$={tg}^{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} } \left({x}\right)…

An-aeroplane-covers-a-certain-distance-at-a-speed-of-240kmph-in-5-hours-to-cover-the-same-distance-in-1-2-3-hrs-it-must-travel-at-a-speed-of-A-300kmph-B-360kmph-C-600kmph-D-700kmph-Mastermind

Question Number 171153 by Mastermind last updated on 08/Jun/22 $${An}\:{aeroplane}\:{covers}\:{a}\:{certain}\:{distance} \\ $$$${at}\:{a}\:{speed}\:{of}\:\mathrm{240}{kmph}\:{in}\:\mathrm{5}\:{hours}. \\ $$$${to}\:{cover}\:{the}\:{same}\:{distance}\:{in}\:\mathrm{1}\frac{\mathrm{2}}{\mathrm{3}}\:{hrs}, \\ $$$${it}\:{must}\:{travel}\:{at}\:{a}\:{speed}\:{of}: \\ $$$$\left.{A}\right)\:\mathrm{300}{kmph} \\ $$$$\left.{B}\right)\:\mathrm{360}{kmph} \\ $$$$\left.{C}\right)\:\mathrm{600}{kmph} \\ $$$$\left.{D}\right)\:\mathrm{700}{kmph} \\…

The-average-ages-of-three-person-is-27-years-Their-ages-are-in-the-propor-tion-of-1-3-5-What-is-the-age-in-years-of-the-youngest-one-among-them-Mastermind-

Question Number 171152 by Mastermind last updated on 08/Jun/22 $${The}\:{average}\:{ages}\:{of}\:{three}\:{person}\:{is} \\ $$$$\mathrm{27}\:{years}.\:{Their}\:{ages}\:{are}\:{in}\:{the}\:{propor} \\ $$$${tion}\:{of}\:\mathrm{1}:\mathrm{3}:\mathrm{5}.\:{What}\:{is}\:{the}\:{age}\:{in}\:{years} \\ $$$${of}\:{the}\:{youngest}\:{one}\:{among}\:{them}? \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by Rasheed.Sindhi…

solve-for-x-5-x-5x-140-

Question Number 40083 by tawa tawa last updated on 15/Jul/18 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\mathrm{5}^{\mathrm{x}} \:+\:\mathrm{5x}\:=\:\mathrm{140} \\ $$ Commented by MrW3 last updated on 16/Jul/18 $$\mathrm{5}^{{x}} =\left(\mathrm{28}−{x}\right)×\mathrm{5} \\ $$$$\mathrm{5}^{{x}−\mathrm{28}}…

Mr-John-bought-a-four-roomed-house-for-2520000bucks-these-rooms-are-rented-out-to-four-students-at-9000-buck-per-month-for-each-room-a-find-the-rents-collected-at-the-end-of-each-year-if-each-year

Question Number 40060 by Rio Mike last updated on 15/Jul/18 $${Mr}\:{John}\:{bought}\:{a}\:{four}\:{roomed} \\ $$$${house}\:{for}\:\mathrm{2520000}{bucks}. \\ $$$${these}\:{rooms}\:{are}\:{rented}\:{out} \\ $$$${to}\:{four}\:{students}\:,{at}\:\mathrm{9000}\:{buck} \\ $$$${per}\:{month}\:{for}\:{each}\:{room}. \\ $$$$\left.{a}\right)\:{find}\:{the}\:{rents}\:{collected}\:{at}\:{the}\:{end} \\ $$$${of}\:{each}\:{year}.{if}\:{each}\:{year}\:\mathrm{72000}\:{bucks} \\ $$$${is}\:{spent}\:{on}\:{repairs}.…