Question Number 200321 by mr W last updated on 17/Nov/23 $${for}\:{x},{y},{z}\:\in{N},\:{if} \\ $$$$\mathrm{38}{x}+\mathrm{40}{y}+\mathrm{41}{z}=\mathrm{520} \\ $$$${find}\:{x}+{y}+{z}=? \\ $$ Answered by Rasheed.Sindhi last updated on 17/Nov/23 $$\mathrm{520}−\mathrm{38}{x}−\mathrm{40}{y}=\mathrm{41}{z}…
Question Number 200236 by mr W last updated on 16/Nov/23 $${what}\:{is}\:{the}\:{smallest}\:{natural}\:{number} \\ $$$${which}\:{has}\:{at}\:{least}\:\mathrm{100}\:{divisors}? \\ $$ Answered by MM42 last updated on 16/Nov/23 $$\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{4}} ×\mathrm{5}×\mathrm{7}=\mathrm{45360}\:\checkmark…
Question Number 200265 by cherokeesay last updated on 16/Nov/23 Answered by witcher3 last updated on 16/Nov/23 $$\begin{cases}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{2}.\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)=\mathrm{0}}\\{\left(\mathrm{2}\right)\Leftrightarrow\left(\mathrm{2}\right)}\end{cases} \\ $$$$\Leftrightarrow\begin{cases}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}−\mathrm{5}\right)^{\mathrm{2}} =\mathrm{0}}\\{\sqrt{\left(\mathrm{x}^{\mathrm{2}}…
Question Number 200205 by cherokeesay last updated on 15/Nov/23 Commented by Frix last updated on 15/Nov/23 $$\mathrm{min}\:=\mathrm{4} \\ $$$$\mathrm{max}=+\infty \\ $$ Terms of Service Privacy…
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Question Number 200005 by Mingma last updated on 12/Nov/23 Answered by AST last updated on 12/Nov/23 $$\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \geqslant\left(\frac{{a}+{b}+{c}}{\mathrm{3}}\right)\Rightarrow{a}+{b}+{c}\leqslant\mathrm{3} \\ $$$$\Sigma\frac{\mathrm{1}}{\mathrm{2}{a}+{b}}\geqslant\frac{\mathrm{9}}{\mathrm{3}\left({a}+{b}+{c}\right)}\geqslant\frac{\mathrm{9}}{\mathrm{3}×\mathrm{3}}=\mathrm{1} \\ $$$${Equality}\:{holds}\:{when}\:{a}={b}={c}=\mathrm{1}…
Question Number 200004 by Mingma last updated on 12/Nov/23 Answered by aleks041103 last updated on 12/Nov/23 $$−\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}}…