Question Number 147137 by mathdanisur last updated on 18/Jul/21 Answered by bramlexs22 last updated on 18/Jul/21 $$\mathrm{AB}\:=\:\mathrm{DC} \\ $$$$\Rightarrow\begin{pmatrix}{\:\:−\mathrm{4}}\\{\mathrm{m}−\mathrm{7}}\\{\:\:\:\:\:\mathrm{16}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{3}−\mathrm{n}}\\{−\mathrm{10}}\\{\mathrm{p}−\mathrm{10}}\end{pmatrix} \\ $$$$\:\blacktriangle\begin{cases}{\mathrm{n}=\mathrm{7}}\\{\mathrm{m}=−\mathrm{3}}\\{\mathrm{p}=\mathrm{26}}\end{cases}\:\:\Rightarrow\mathrm{m}+\mathrm{n}+\mathrm{p}\:=\:\mathrm{30} \\ $$ Commented by…
Question Number 16067 by Tinkutara last updated on 21/Jun/17 $$\mathrm{Let}\:{d},\:{d}'\:\mathrm{be}\:\mathrm{two}\:\mathrm{nonparallel}\:\mathrm{lines}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{plane}\:\mathrm{and}\:\mathrm{let}\:{k}\:>\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of} \\ $$$$\mathrm{points},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{whose}\:\mathrm{distances}\:\mathrm{to} \\ $$$${d}\:\mathrm{and}\:{d}'\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:{k}. \\ $$ Commented by mrW1 last updated on 29/Jun/17…
Question Number 16066 by Tinkutara last updated on 21/Jun/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{and}\:\mathrm{let}\:{k}\:>\:\mathrm{0}\:\mathrm{be}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{points}\:{M}\:\mathrm{in}\:\mathrm{its}\:\mathrm{interior} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\left[{MAB}\right]\:+\:\mathrm{2}\left[{MCD}\right]\:=\:{k}. \\ $$ Answered by mrW1 last updated…
Question Number 16065 by Tinkutara last updated on 21/Jun/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{points}\:{M}\:\mathrm{in}\:\mathrm{its}\:\mathrm{interior} \\ $$$$\mathrm{such}\:\mathrm{that}\:\left[{MAB}\right]\:=\:\mathrm{2}\left[{MCD}\right]. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 16064 by Tinkutara last updated on 21/Jun/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{and}\:\mathrm{M}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{its}\:\mathrm{interior}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left[{MAB}\right]\:=\:\left[{MBC}\right]\:=\:\left[{MCD}\right]\:=\:\left[{MDA}\right]. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagonals}\:\mathrm{of} \\ $$$${ABCD}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{diagonal}. \\ $$ Commented by Tinkutara…
Question Number 81598 by zainal tanjung last updated on 03/Mar/20 $$\mathrm{fog}\left(\mathrm{x}\right)=\mathrm{8x}+\mathrm{3} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=…..? \\ $$$$ \\ $$$$\mathrm{gof}\left(\mathrm{x}\right)=\mathrm{6x}+\mathrm{1} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{5x}+\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=…..? \\ $$$$…
Question Number 147135 by puissant last updated on 18/Jul/21 Answered by gsk2684 last updated on 18/Jul/21 $${let}\:{y}={x}^{{x}^{{x}^{.} } } \:{then}\:{y}={x}^{{y}} \\ $$$$\mathrm{ln}\:{y}\:=\:{y}\:\mathrm{ln}\:{x} \\ $$$$\frac{\mathrm{1}}{{y}}\:\frac{{dy}}{{dx}}={y}\:\frac{\mathrm{1}}{{x}}\:+\:\frac{{dy}}{{dx}}\:\mathrm{ln}\:{x} \\…
Question Number 81596 by zainal tanjung last updated on 14/Feb/20 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1}\:,\:\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{3} \\ $$$$\left.\mathrm{a}\right).\:\mathrm{fog}\left(\mathrm{x}\right)=…. \\ $$$$\left.\mathrm{b}\right).\:\mathrm{gof}\left(\mathrm{x}\right)=…. \\ $$ Commented by Tony Lin last updated on 14/Feb/20…
Question Number 16061 by Joel577 last updated on 17/Jun/17 $$\int\:{x}^{\mathrm{5}} \sqrt{\mathrm{2}\:−\:{x}^{\mathrm{3}} }\:{dx} \\ $$ Answered by Tinkutara last updated on 17/Jun/17 $$\mathrm{Let}\:\mathrm{2}\:−\:{x}^{\mathrm{3}} \:=\:{t} \\ $$$$\mathrm{Then}\:−\mathrm{3}{x}^{\mathrm{2}}…
Question Number 147134 by mathdanisur last updated on 18/Jul/21 $$\sqrt{\mathrm{2}{sin}\left({x}\right)−\mathrm{1}}\:\centerdot\:{sin}\left({x}\right)\:>\:\mathrm{0} \\ $$ Commented by hknkrc46 last updated on 18/Jul/21 $$\blacktriangleright\:\mathrm{2sin}\:\boldsymbol{{x}}\:−\:\mathrm{1}\:>\:\mathrm{0}\:\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0}\:\equiv\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\blacktriangleright\:\frac{\boldsymbol{\pi}}{\mathrm{6}}\:<\:\boldsymbol{{x}}\:<\:\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{6}}\:\: \\…