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Question Number 115294 by ZiYangLee last updated on 24/Sep/20 $$\mathrm{Given}\:\mathrm{that}\:{N}=\mathrm{1}×\mathrm{2}×\mathrm{3}×…×\mathrm{500}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{500}. \\ $$$$ \\ $$$$\mathrm{If}\:{N}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{6}^{{k}} ,\:\mathrm{find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}. \\ $$ Answered by Olaf last…
Question Number 180827 by sciencestudent last updated on 17/Nov/22 $${which}\:{is}\:{not}\:{range}\:{of}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{2}}? \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\left.\mathrm{2}\:\:\:\:\:\:\:\:\mathrm{2}\right)\:\mathrm{3}\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{10}\:\:\:\:\:\:\:\mathrm{4}\right)\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$ Commented by kaivan.ahmadi last updated on 17/Nov/22 $${we}\:{know}\:{that}\:{R}_{{f}} ={D}_{{f}^{−\mathrm{1}} } \\…
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Question Number 115250 by otchereabdullai@gmail.com last updated on 24/Sep/20 $$\mathrm{If}\:\mathrm{mr}\:\mathrm{Fosu}\:\mathrm{sells}\:\mathrm{the}\:\mathrm{car}\:\mathrm{after}\:\mathrm{covering}\: \\ $$$$\mathrm{a}\:\mathrm{mileage}\:\mathrm{of}\:\mathrm{128km}.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{i}.\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{if}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\: \\ $$$$\mathrm{depreciation}\:\mathrm{is}\:\$\:\mathrm{0}.\mathrm{03}\:\mathrm{per}\:\mathrm{km} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{for}\:\mathrm{which}\:\mathrm{Mr} \\ $$$$\mathrm{Fosu}\:\mathrm{could}\:\mathrm{sell}\:\mathrm{the}\:\mathrm{car}\:\mathrm{so}\:\mathrm{that}\:\mathrm{he}\:\mathrm{does} \\ $$$$\mathrm{not}\:\mathrm{lose}\:\mathrm{more}\:\mathrm{than}\:\$,\mathrm{2000}\:\mathrm{or}\:\mathrm{gain}\:\mathrm{more}\:\mathrm{tban}\: \\ $$$$\$\mathrm{3},\mathrm{000}\:\mathrm{on}\:\mathrm{the}\:\mathrm{depreciated}\:\mathrm{value}. \\…
Question Number 180771 by aleks041103 last updated on 17/Nov/22 $${Mr}.{W}\:{question}: \\ $$$${we}\:{have}\:{a}\:{triangle}\:{ABC}.\:{Where}\:{is}\:{point}\:{D} \\ $$$${s}.{t}.\:{AD},{BD}\:{and}\:{CD}\:{divide}\:{the}\:{triangle} \\ $$$${in}\:{equal}\:{area}\:{triangles}? \\ $$ Commented by mr W last updated on…
Question Number 115229 by mathdave last updated on 24/Sep/20 $${find}\:{the}\:{mean}\:{value}\:{of}\: \\ $$$${y}=\frac{\mathrm{5}}{\mathrm{2}−{x}−\mathrm{3}{x}^{\mathrm{2}} }\:\:{between}\:{x}=−\frac{\mathrm{1}}{\mathrm{3}}\:{and} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$ Answered by Olaf last updated on 24/Sep/20 $$…
Question Number 115224 by mohammad17 last updated on 24/Sep/20 Answered by Dwaipayan Shikari last updated on 24/Sep/20 $$\mathrm{S}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{9}}−\frac{\mathrm{1}}{\mathrm{27}}+….=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{2}} .\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }…
Question Number 115215 by mathdave last updated on 24/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$ Commented by mnjuly1970 last updated on 24/Sep/20…