Question Number 10694 by ABD last updated on 23/Feb/17 Answered by mrW1 last updated on 23/Feb/17 $${f}\left(\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{3}} \right)=\mathrm{6}{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}=\mathrm{2}\left(\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{3}} \right)−\mathrm{3} \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}…
Question Number 76228 by arkanmath7@gmail.com last updated on 25/Dec/19 $${prove}\:{that}\:\mathrm{6}^{{n}} \:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{10}\right),\:{for}\:{any}\:{n}\:\in\:{Z}^{\:+} \\ $$ Commented by turbo msup by abdo last updated on 25/Dec/19 $$\Leftrightarrow\mathrm{6}^{{n}} −\mathrm{6}\:\equiv\mathrm{0}\left[\mathrm{10}\right]\:\Leftrightarrow\:\mathrm{10}\:{divide}\:\mathrm{6}^{{n}}…
Question Number 10693 by ABD last updated on 23/Feb/17 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{1}}{\mathrm{4}}\:\:,\:{f}\left({a}\right)+{f}\left({b}\right)=\frac{\mathrm{9}}{\mathrm{2}} \\ $$$$\Rightarrow{a}+{b}=? \\ $$ Answered by nume1114 last updated on 23/Feb/17 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{1}}{\mathrm{4}} \\ $$$$\Rightarrow{f}\left({a}\right)=\frac{\mathrm{5}{a}−\mathrm{1}}{\mathrm{4}},{f}\left({b}\right)=\frac{\mathrm{5}{b}−\mathrm{1}}{\mathrm{4}} \\…
Question Number 76229 by arkanmath7@gmail.com last updated on 25/Dec/19 $${Let}\:{P}\left({x}\right)\:{be}\:{polynomial}\:{in}\:{x}\:{with}\:{integral} \\ $$$${coefficients}.\:{If}\:{n}\:{is}\:{a}\:{solution}\:{of}\: \\ $$$${P}\left({x}\right)\equiv\mathrm{0}\left({mod}\:{n}\right)\:,\:{and}\:{a}\equiv{b}\left({mod}\:{n}\right), \\ $$$${prove}\:{that}\:{b}\:{is}\:{also}\:{a}\:{solution}. \\ $$ Answered by Rio Michael last updated on…
Question Number 10692 by ABD last updated on 23/Feb/17 $${f}\left({x}+{y}\right)={f}\left({x}\right)×{f}\left({y}\right) \\ $$$${f}\left(\mathrm{16}\right)=\mathrm{8}\:\Rightarrow{f}\left(\mathrm{64}\right) \\ $$ Answered by nume1114 last updated on 23/Feb/17 $${f}\left(\mathrm{64}\right)={f}\left(\left(\mathrm{16}+\mathrm{16}\right)+\left(\mathrm{16}+\mathrm{16}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{16}+\mathrm{16}\right)×{f}\left(\mathrm{16}+\mathrm{16}\right) \\…
Question Number 10690 by Saham last updated on 22/Feb/17 Answered by sandy_suhendra last updated on 23/Feb/17 Commented by sandy_suhendra last updated on 23/Feb/17 $$\Delta\mathrm{TCB}\Rightarrow\mathrm{tan}\:\mathrm{30}°=\frac{\mathrm{x}}{\mathrm{TC}} \\…
Question Number 141757 by Ndala last updated on 23/May/21 $$\Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}\centerdot\Gamma\left(\mathrm{2n}+\mathrm{1}\right)}{\mathrm{2}^{\mathrm{2n}} \Gamma\left(\mathrm{n}+\mathrm{1}\right)} \\ $$ Commented by Ndala last updated on 23/May/21 $$\mathrm{someone}\:\mathrm{to}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{the}\:\mathrm{proof}.\:\mathrm{Please} \\ $$ Terms of…
Question Number 10687 by Saham last updated on 22/Feb/17 $$\mathrm{Abbey}\:\mathrm{and}\:\mathrm{mary}\:\mathrm{carry}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{log}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10m}\:\mathrm{and}\:\mathrm{weight}\:\mathrm{100N}. \\ $$$$\mathrm{Abbey}\:\mathrm{is}\:\mathrm{1m}\:\mathrm{from}\:\mathrm{one}\:\mathrm{end}\:\mathrm{and}\:\mathrm{mary}\:\mathrm{is}\:\mathrm{2m}\:\mathrm{from}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}.\:\mathrm{what} \\ $$$$\mathrm{weight}\:\mathrm{does}\:\mathrm{abbey}\:\mathrm{and}\:\mathrm{mary}\:\mathrm{support}. \\ $$ Answered by mrW1 last updated on 22/Feb/17 $${weight}\:{is}\:{in}\:{the}\:{middle}\:{of}\:{log}. \\…
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Question Number 76220 by Master last updated on 25/Dec/19 Commented by benjo last updated on 25/Dec/19 $$\mathrm{waw}..\mathrm{this}\:\mathrm{problem}\:\mathrm{very}\:\mathrm{nice} \\ $$ Answered by MJS last updated on…