Question Number 200004 by Mingma last updated on 12/Nov/23 Answered by aleks041103 last updated on 12/Nov/23 $$−\mathrm{1}<{x}<\mathrm{1} \\ $$$${f}\left({x}\right)=\frac{{x}+\mathrm{2}^{{k}} }{\mathrm{2}^{{k}+\mathrm{1}} }=\frac{{x}}{\mathrm{2}^{{k}+\mathrm{1}} }+\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}^{{k}+\mathrm{1}} }<{f}\left({x}\right)<\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{{k}+\mathrm{1}} } \\…
Question Number 199913 by WaqasShabbir last updated on 11/Nov/23 $$ \\ $$To calculate the mean and median of the distribution, you can follow these steps:…
Question Number 199863 by Karanji last updated on 10/Nov/23 $$−\mathrm{5}+\left(−\mathrm{8}\right)+\left(−\mathrm{11}\right)+…+\left(−\mathrm{230}\right) \\ $$ Answered by som(math1967) last updated on 10/Nov/23 $$\:{c}.{d}=\left(−\mathrm{8}\right)−\left(−\mathrm{5}\right)=−\mathrm{3} \\ $$$$−\mathrm{230}=−\mathrm{5}\:+\left({n}−\mathrm{1}\right)×−\mathrm{3} \\ $$$$\Rightarrow\left({n}−\mathrm{1}\right)=\mathrm{75} \\…
Question Number 199771 by Rupesh123 last updated on 09/Nov/23 Answered by AST last updated on 09/Nov/23 $$\frac{{sin}\left(\mathrm{4}{x}\right)=\mathrm{2}{sin}\left(\mathrm{2}{x}\right){cos}\left(\mathrm{2}{x}\right)}{{a}}=\frac{{sin}\left(\mathrm{2}{x}\right)}{{b}} \\ $$$$\Rightarrow{cos}\left(\mathrm{2}{x}\right)=\frac{{a}}{\mathrm{2}{b}}=\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}\Rightarrow{cos}^{\mathrm{2}} {x}=\frac{{a}+\mathrm{2}{b}}{\mathrm{4}{b}} \\ $$$$\frac{{sin}\left(\mathrm{2}{x}\right)=\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right)}{{b}}=\frac{{sin}\left({x}\right)}{{c}}\Rightarrow{cos}\left({x}\right)=\frac{{b}}{\mathrm{2}{c}} \\ $$$$\Rightarrow\frac{{a}+\mathrm{2}{b}}{{b}}=\frac{{b}^{\mathrm{2}}…
Question Number 199729 by Mingma last updated on 08/Nov/23 Answered by mathfreak01 last updated on 08/Nov/23 $${N}\:=\:\underset{{n}\:=\:\mathrm{1}} {\overset{\mathrm{450}} {\sum}}\left(\mathrm{10}^{{n}} \:−\:\mathrm{1}\right) \\ $$$${N}\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{450}} {\sum}}\mathrm{10}^{{n}} \:−\:\mathrm{450}…
Question Number 199659 by cherokeesay last updated on 06/Nov/23 Answered by Frix last updated on 07/Nov/23 $$\mathrm{If}\:\mathrm{we}\:\mathrm{stay}\:\mathrm{in}\:\mathbb{R}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{−{r}}=−\sqrt[{\mathrm{3}}]{{r}} \\ $$$$\mathrm{Obvious}\:\mathrm{solutions} \\ $$$${x}=−\mathrm{1}\vee{x}=\mathrm{0} \\ $$$$\mathrm{Not}\:\mathrm{so}\:\mathrm{obvious}\:\mathrm{solutions} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}…
Question Number 199621 by Mingma last updated on 06/Nov/23 Answered by AST last updated on 06/Nov/23 $${x}+{y}\overset{\mathrm{3}} {\equiv}\mathrm{2}…\left({i}\right) \\ $$$$\left(\mathrm{6}+\mathrm{6}+{y}\right)−\left(\mathrm{7}+{x}\right)=\mathrm{5}+{y}−{x}\overset{\mathrm{11}} {\equiv}\mathrm{0}\Rightarrow{x}−{y}\overset{\mathrm{11}} {\equiv}\mathrm{5}…\left({ii}\right) \\ $$$$\left({i}\right)\wedge\left({ii}\right)\Rightarrow\left({x},{y}\right)=\left(\mathrm{8},\mathrm{3}\right);\left(\mathrm{5},\mathrm{0}\right);\left(\mathrm{1},\mathrm{7}\right) \\…
Question Number 199405 by mnjuly1970 last updated on 03/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}\:… \\ $$$$\:\:\mathrm{Q}:\:\:\:\:\:\:\mathrm{I}{f}\:\:,\:\:\:{f}\left({x}\right)\:=\mathrm{2}\:{e}^{{x}} \:−\mathrm{1}\:+\:\lfloor{e}^{{x}} +\:\frac{\mathrm{3}}{\mathrm{2}}\:+\lfloor{e}^{{x}} \rfloor\:\rfloor \\ $$$$\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{f}\:^{−\mathrm{1}} \:\left(\:\frac{\pi}{\mathrm{4}}\:\right)\:=? \\ $$$$\:\:\:\:\: \\ $$ Answered…
Question Number 199399 by Calculusboy last updated on 03/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{log}}_{\mathrm{2}} \boldsymbol{{r}}+\boldsymbol{{log}}_{\mathrm{3}} \boldsymbol{{p}}=\mathrm{3} \\ $$$$\boldsymbol{{p}}+\boldsymbol{{r}}=\mathrm{11}\:\:\:\boldsymbol{{fund}}\:\boldsymbol{{p}}\:\boldsymbol{{and}}\:\boldsymbol{{r}}. \\ $$ Answered by mr W last updated on 03/Nov/23 $${one}\:{solution}\:\left({p}=\mathrm{9},\:{r}=\mathrm{2}\right)\:{can}\:{be}\:“{seen}'',…
Question Number 198949 by ArifinTanjung last updated on 26/Oct/23 $$\:\:\frac{\mathrm{5}!×\mathrm{4}!}{\mathrm{3}!×\mathrm{2}!}\:=\:….\:\: \\ $$ Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\:\:\frac{\mathrm{5}!×\mathrm{4}!}{\mathrm{3}!×\mathrm{2}!}\:=\:\frac{\mathrm{5}!×\cancel{\overset{\mathrm{2}} {\mathrm{4}}}×\cancel{\mathrm{3}!}}{\cancel{\mathrm{3}!}×\cancel{\underset{\mathrm{1}} {\mathrm{2}}}×\mathrm{1}}=\mathrm{2}×\mathrm{5}! \\ $$$$ \\…