Question Number 139319 by mathsuji last updated on 25/Apr/21 $${prove}\:{that}\:{are}\:{axactly}\:\mathrm{1729}\:{positive} \\ $$$${integer}\:{solutions}\:{to}\:{the}\:{below}\:{equation} \\ $$$$\mathrm{4}{x}^{\mathrm{4}} +\mathrm{3}{y}^{\mathrm{3}} +\mathrm{2}{z}^{\mathrm{2}} +{t}=\mathrm{4311} \\ $$ Commented by Rasheed.Sindhi last updated on…
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Question Number 8236 by Yozzias last updated on 03/Oct/16 $$\mathrm{Define}\:\mathrm{a}\:\mathrm{3}×\mathrm{3}\:\mathrm{matrix}\:\mathrm{whose}\:\mathrm{entries} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{first}\:\mathrm{9}\:\mathrm{positive}\:\mathrm{integers}. \\ $$$$\mathrm{Let}\:\mathrm{s}_{\mathrm{k}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements} \\ $$$$\mathrm{across}\:\mathrm{the}\:\mathrm{kth}\:\mathrm{row}.\:\mathrm{Is}\:\mathrm{there}\:\mathrm{such}\:\mathrm{a}\: \\ $$$$\mathrm{matrix}\:\mathrm{where}\:\mathrm{s}_{\mathrm{1}} \::\:\mathrm{s}_{\mathrm{2}} \::\:\mathrm{s}_{\mathrm{3}} \:=\:\mathrm{1}\::\:\mathrm{2}\::\:\mathrm{3}\:? \\ $$$$−−−−−−−−−−−−−−−−−−−− \\…
Question Number 73766 by mathocean1 last updated on 15/Nov/19 $$\begin{cases}{\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{y}−\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{z}−\mathrm{3}}}\\{\mathrm{x}+\mathrm{2y}+\mathrm{3z}=\mathrm{56}}\end{cases} \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \\ $$ Answered by MJS last updated on 15/Nov/19 $$ \\…
Question Number 139290 by mathdanisur last updated on 25/Apr/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{{sin}\left({x}^{\mathrm{2}} −{arctan}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\right)}{\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx} \\ $$ Answered by Ar Brandon last updated on 25/Apr/21…
Question Number 8217 by tawakalitu last updated on 02/Oct/16 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{x}^{\mathrm{5}} \right)^{\mathrm{6}} \\ $$ Commented by 123456 last updated on…
Question Number 8148 by Rasheed Soomro last updated on 02/Oct/16 $$\mathrm{Determine}\:\mathrm{x}^{\mathrm{4}} −\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }\:,\:\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{34}\:. \\ $$ Commented by sou1618 last updated on 02/Oct/16 $${set}\:{X}={x}^{\mathrm{2}}…
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Question Number 73679 by Tinku Tara last updated on 14/Nov/19 $$\mathrm{We}\:\mathrm{have}\:\mathrm{updated}\:\mathrm{backend}\:\mathrm{code}\:\mathrm{to}\: \\ $$$$\mathrm{disallow}\:\mathrm{delete}\:\mathrm{of}\:\mathrm{question}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{already}\:\mathrm{answered}\:\mathrm{or}\:\mathrm{commented}. \\ $$$$ \\ $$ Commented by malwaan last updated on…
Question Number 8134 by 314159 last updated on 01/Oct/16 Answered by prakash jain last updated on 01/Oct/16 $$\mathrm{See}\:\mathrm{question}\:\mathrm{8025}. \\ $$ Terms of Service Privacy Policy…
Question Number 73665 by aliesam last updated on 14/Nov/19 $${if} \\ $$$$ \\ $$$${cos}^{\mathrm{2}} \left(\theta\right)=\frac{{m}^{\mathrm{2}} −\mathrm{1}}{\mathrm{3}}\:\:,\:\:{tan}^{\mathrm{3}} \left(\frac{\theta}{\mathrm{2}}\right)={tan}\left({a}\right) \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{cos}^{\mathrm{2}}…