Question Number 205367 by hardmath last updated on 18/Mar/24 Answered by Ghisom last updated on 18/Mar/24 $$\left(\frac{{n}^{\mathrm{3}/\mathrm{2}} }{\mathrm{3}^{{n}} }+\frac{{n}^{\mathrm{2}} }{\mathrm{4}^{{n}} }+\frac{{n}^{\mathrm{5}/\mathrm{2}} }{\mathrm{5}^{{n}} }\right)^{\mathrm{1}/{n}} = \\…
Question Number 205353 by MATHEMATICSAM last updated on 17/Mar/24 $$\mathrm{If}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{had}\:\mathrm{two}\:\mathrm{roots}\:{p}\:\mathrm{and}\:{q} \\ $$$$\mathrm{and}\:{p}^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \:=\:{p}^{\mathrm{3}} \:+\:{q}^{\mathrm{3}} \:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${b}^{\mathrm{3}} \:−\:\mathrm{2}{a}^{\mathrm{2}} {c}\:+\:{ab}^{\mathrm{2}} \:=\:\mathrm{3}{abc}. \\ $$ Answered…
Question Number 205324 by hardmath last updated on 16/Mar/24 $$\mathrm{Compare}: \\ $$$$\mathrm{37}^{\mathrm{37}} \:\:\:\mathrm{and}\:\:\:\mathrm{36}^{\mathrm{38}} \\ $$ Answered by nikif99 last updated on 16/Mar/24 $$\mathrm{37}^{\mathrm{37}} \:\lessgtr\:\mathrm{36}^{\mathrm{38}} \:\Rightarrow…
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Question Number 205297 by mnjuly1970 last updated on 15/Mar/24 $$ \\ $$$$\:\:\:{Find}\:\:{the}''\:{range}\:''\:{of}\:\:: \\ $$$$ \\ $$$$\:\:\:{i}\::\:\:\:{f}\:\left({x}\right)\:=\lfloor\:\frac{\:{x}}{\:\lfloor\:{x}\:\rfloor}\:\rfloor \\ $$$$\:\:\:{ii}:\:{f}\left({x}\right)\:=\:\frac{\:{x}}{\lfloor\:{x}\:\rfloor\:+\:\lfloor\:−{x}\:\rfloor} \\ $$$$\:\: \\ $$ Answered by A5T…
Question Number 205273 by hardmath last updated on 14/Mar/24 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{2x}+\mathrm{2} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by Rasheed.Sindhi last updated on 14/Mar/24 $${Replace}\:\mathrm{x}\:{by}\:\mathrm{x}+\mathrm{1} \\ $$$$\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{2}=\mathrm{2x}+\mathrm{4} \\…
Question Number 205211 by cortano12 last updated on 13/Mar/24 Answered by Berbere last updated on 13/Mar/24 $$\begin{cases}{\mathrm{5}{x}^{\mathrm{2}} \left({y}^{\mathrm{2}} −\mathrm{1}\right)=\mathrm{4}{x}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}\\{\mathrm{5}{y}^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{3}{y}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}\end{cases}…
Question Number 205238 by necx122 last updated on 13/Mar/24 $$\mathrm{4}^{{x}} \:+\:{x}\:=\:\mathrm{260} \\ $$$${find}\:{the}\:{possible}\:{values}\:{of}\:{x} \\ $$$$ \\ $$ Commented by Ghisom last updated on 13/Mar/24 $$\mathrm{generally}…
Question Number 205256 by hardmath last updated on 13/Mar/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:? \\ $$ Commented by mr W last updated on 13/Mar/24 $${your}\:{earnest}? \\ $$ Commented…
Question Number 205220 by hardmath last updated on 13/Mar/24 $$\mathrm{cos}^{\mathrm{4}} \:\mathrm{x}\:−\:\mathrm{sin}^{\mathrm{4}} \:\mathrm{x}\:=\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{x} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by Sutrisno last updated on 13/Mar/24 $$\left({cos}^{\mathrm{2}}…