Question Number 202100 by sonukgindia last updated on 20/Dec/23 Answered by mr W last updated on 21/Dec/23 $${f}'={g} \\ $$$${f}''={g}'={f} \\ $$$${f}''−{f}=\mathrm{0} \\ $$$${r}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:\Rightarrow{r}=\pm\mathrm{1}…
Question Number 202102 by MATHEMATICSAM last updated on 20/Dec/23 $$\mathrm{If}\:{x}\:=\:\mathrm{3}\:+\:\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{then}\:\frac{{x}^{\mathrm{6}} \:+\:{x}^{\mathrm{4}} \:+\:{x}^{\mathrm{2}} \:+\:\mathrm{1}}{{x}^{\mathrm{3}} }\:=\:? \\ $$ Answered by AST last updated on 20/Dec/23 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}=\mathrm{6} \\…
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Question Number 202093 by sonukgindia last updated on 20/Dec/23 Commented by a.lgnaoui last updated on 22/Dec/23 Commented by a.lgnaoui last updated on 22/Dec/23 $$\Delta\mathrm{AMN}\:\:\measuredangle\:\mathrm{MNA}=\frac{\mathrm{3}\pi}{\mathrm{4}}−\alpha \\…
Question Number 202094 by otchereabdullai@gmail.com last updated on 20/Dec/23 $$\:{A}\:{computer}\:{systerm}\:{has}\:{a}\:{memory}\: \\ $$$$\:\:{leak}\:{issue}\:{causing}\:{its}\:{usage}\:{to} \\ $$$$\:\:{increase}\:{over}\:{time}.\:{the}\:{rate}\:{of}\: \\ $$$$\:\:{memory}\:{usage}\:{growth}\:{is}\:{directly}\: \\ $$$$\:\:{proportional}\:{to}\:{the}\:{difference}\: \\ $$$$\:\:{between}\:{the}\:{current}\:{memory}\:{usage}\: \\ $$$$\:{and}\:{the}\:{systerms}\:{maximum}\:{memory} \\ $$$$\:\:{capacity}.\:{Write}\:{one}\:{ODE}\:{and}\:{one}\: \\…
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Question Number 202086 by necx122 last updated on 20/Dec/23 $${There}\:{are}\:{two}\:{possible}\:{routes}\:{from} \\ $$$${Zindhi}\:{to}\:{Katifa}.\:{One}\:{route}\:{is}\:{through} \\ $$$${Zindhi}/{Chadler}\:{expressway}\:{which}\:{is} \\ $$$$\mathrm{100}{km}\:{and}\:{the}\:{other}\:{is}\:{through}\:{Adfeti}\:{and} \\ $$$${Ngonu}\:{covering}\:{a}\:{distance}\:{of}\:\mathrm{80}{km}.\:{A} \\ $$$${motorist}\:{going}\:{through}\:{the}\:{expressway} \\ $$$${can}\:{travel}\:\mathrm{10}{km}/{h}\:{faster}\:{than}\:{the}\:{one} \\ $$$${going}\:{through}\:{Adfeti}\:{and}\:{Ngonu},\:{and} \\…
Question Number 202044 by hardmath last updated on 19/Dec/23 $$\mathrm{If} \\ $$$$\mathrm{a}\:=\:\mathrm{9999999998000000001} \\ $$$$\mathrm{Find} \\ $$$$\mathrm{A}\:=\:\sqrt[{\mathrm{9}}]{\sqrt{\mathrm{a}}\:+\:\mathrm{1}}\:\:\:\rightarrow\:\:\:\mathrm{A}\:=\:? \\ $$ Commented by mr W last updated on…
Question Number 202079 by necx122 last updated on 19/Dec/23 $${A}\:{man}\:{travelled}\:{from}\:{town}\:{A}\:{to}\:{B},\:{a} \\ $$$${distance}\:{of}\:\mathrm{360}{km}.\:{He}\:{left}\:{A}\:{one}\:{hour} \\ $$$${later}\:{than}\:{he}\:{had}\:{planned}\:{so}\:{he}\:{decided} \\ $$$${to}\:{drive}\:{at}\:\mathrm{5}{km}/{h}\:{faster}\:{than}\:{his} \\ $$$${normal}\:{speed},\:{in}\:{order}\:{to}\:{reach}\:{B}\:{on} \\ $$$${schedule}.\:{If}\:{he}\:{arrived}\:{B}\:{at}\:{exactly}\:{the} \\ $$$${scheduled}\:{time},\:{find}\:{the}\:{normal}\:{speed}. \\ $$ Answered…
Question Number 202041 by hardmath last updated on 19/Dec/23 $$\mathrm{Simplify}:\:\:\:\frac{\sqrt{\mathrm{2}}\:−\:\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha}{\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha} \\ $$ Answered by cortano12 last updated on 19/Dec/23 $$\:=\:\frac{\sqrt{\mathrm{2}}−\sqrt{\mathrm{2}}\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\mathrm{sin}\:\alpha+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\mathrm{cos}\:\alpha\right)}{\:\sqrt{\mathrm{2}}\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\mathrm{sin}\:\alpha−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\mathrm{cos}\:\alpha\right)} \\ $$$$\:=\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\alpha−\mathrm{45}°\right)}{\mathrm{sin}\:\:\left(\alpha−\mathrm{45}°\right)} \\ $$$$\:=\:\mathrm{csc}\:\left(\alpha−\mathrm{45}°\right)−\mathrm{cot}\:\left(\alpha−\mathrm{45}°\right) \\…