Question Number 47476 by hassentimol last updated on 10/Nov/18 $$\mathrm{How}\:\mathrm{may}\:\mathrm{I}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{theorem}\:? \\ $$$$ \\ $$$$\:\:\:\frac{\boldsymbol{{a}}\:+\:\boldsymbol{{b}}}{\mathrm{2}}\:\:\:\geqslant\:\:\sqrt{\:\boldsymbol{{ab}}\:\:} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$ Commented by prakash jain last…
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Question Number 178508 by yaslm last updated on 17/Oct/22 Commented by MJS_new last updated on 17/Oct/22 $$\mathrm{obviously}\:{x}={y}=\mathrm{0} \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{choose}\:{x}\in\mathbb{R}\backslash\left\{\mathrm{log}_{\mathrm{6}} \:\mathrm{48}\right\}\:\mathrm{to}\:\mathrm{get} \\ $$$${y}=\frac{{x}\mathrm{ln}\:\mathrm{72}}{{x}\mathrm{ln}\:\mathrm{6}\:−\mathrm{ln}\:\mathrm{48}} \\ $$$$ \\…
Question Number 112962 by mohammad17 last updated on 10/Sep/20 Commented by john santu last updated on 10/Sep/20 $${i}\:{think}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:{t}^{\mathrm{8}} \:{e}^{−\mathrm{4}{t}} \:{dt} \\ $$ Commented…
Question Number 47421 by 143jesus last updated on 09/Nov/18 $$\sqrt{\mathrm{400}^{\mathrm{2}} +\mathrm{100}^{\mathrm{2}} =} \\ $$ Answered by MJS last updated on 09/Nov/18 $$=\sqrt{\mathrm{100}^{\mathrm{2}} ×\mathrm{4}^{\mathrm{2}} +\mathrm{100}^{\mathrm{2}} ×\mathrm{1}^{\mathrm{2}}…
Question Number 178468 by Huy last updated on 16/Oct/22 $${For}\:{the}\:{sequence}\:\left\{{u}_{{n}} \right\}\:{if}\:{u}_{\mathrm{1}} =\mathrm{1},\:{u}_{\mathrm{2}} =\mathrm{2}\:{and}\:{u}_{{n}+\mathrm{2}} ^{\mathrm{2}} ={u}_{{n}} ^{\mathrm{2}} +{u}_{{n}+\mathrm{1}} ^{\mathrm{2}} −{u}_{{n}} {u}_{{n}+\mathrm{1}} ,\:{for}\:{all}\:{natural}\:{number}\:{n}. \\ $$$${Find}\:{lim}\:{u}_{{n}} ? \\…
Question Number 178467 by mokys last updated on 16/Oct/22 $${find}\:{n}^{{th}\:} {terms}\:{of}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{11},\mathrm{13},\mathrm{15},\mathrm{17},. \\ $$ Answered by Frix last updated on 16/Oct/22 $${a}_{{n}} =−\frac{\mathrm{41}{n}^{\mathrm{7}} }{\mathrm{5040}}+\frac{\mathrm{37}{n}^{\mathrm{6}} }{\mathrm{144}}−\frac{\mathrm{2381}{n}^{\mathrm{5}} }{\mathrm{720}}+\frac{\mathrm{3211}{n}^{\mathrm{4}}…
Question Number 112908 by mohammad17 last updated on 10/Sep/20 $${if}\:{the}\:{angle}\:{between}\left(\:{kx}+\mathrm{5}{y}=\mathrm{1}\:,\:{kx}−\mathrm{2}{y}=\mathrm{2}\right){equal}\:\mathrm{60}^{°} {then}\:{k}=? \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\ $$ Commented by mohammad17 last updated on 10/Sep/20 $${please}\:{sir}\:{im}\:{very}\:{need}\:{this}…
Question Number 112904 by mohammad17 last updated on 10/Sep/20 $${solve}\:{the}\:{equation}\:{y}+{x}=\mathrm{3},\:\mathrm{2}{y}+{x}=\mathrm{5}\:{by}\:{ussing}\:{matrixis}\:{method} \\ $$$${help}\:{me}\:{sir}\:{please}\:? \\ $$ Answered by bemath last updated on 10/Sep/20 $$\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\mathrm{2}}\end{pmatrix}\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\end{pmatrix}=\begin{pmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\mathrm{2}}\end{pmatrix}^{−\mathrm{1}} \begin{pmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{pmatrix}…
Question Number 112906 by mohammad17 last updated on 10/Sep/20 $${prove}\:{that}\:\left({B}^{−\mathrm{1}} \right)\left({A}^{−\mathrm{1}} \right)=\left({AB}\right)^{−\mathrm{1}} \:{if}\:{A}=\left(\mathrm{34},\mathrm{12}\right),{B}=\left(\mathrm{12},−\mathrm{13}\right) \\ $$$${please}\:{sir}\:{help}\:{me} \\ $$ Commented by mohammad17 last updated on 10/Sep/20 $${help}\:{me}\:{sir}…