Question Number 138123 by Caroline last updated on 10/Apr/21 Answered by Dwaipayan Shikari last updated on 10/Apr/21 $${Det}\left({M}\right)=\mathrm{0} \\ $$$$\Rightarrow−\mathrm{1}\left(\mathrm{8}−\mathrm{20}\right)−\mathrm{4}\left(\mathrm{8}+\mathrm{60}+\mathrm{4}{k}\right)−\mathrm{4}\left(−\mathrm{4}−\mathrm{75}−\mathrm{5}{k}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{12}−\mathrm{272}−\mathrm{16}{k}+\mathrm{316}+\mathrm{20}{k}=\mathrm{0}\Rightarrow\mathrm{4}{k}=−\mathrm{56}\Rightarrow{k}=−\mathrm{14} \\ $$ Commented…
Question Number 7043 by Tawakalitu. last updated on 07/Aug/16 $${Resolve}\:{into}\:{factors} \\ $$$$ \\ $$$${x}^{\mathrm{35}} \:+\:{x}^{\mathrm{19}} \:+\:{x}^{\mathrm{17}} \:+\:{x}^{\mathrm{2}} \:−\:\mathrm{1} \\ $$$$ \\ $$$$ \\ $$ Commented…
Question Number 138112 by 676597498 last updated on 10/Apr/21 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left({sin}^{\mathrm{2}{k}} \left({x}\right){dx}\right)=\frac{\left(\mathrm{2}{k}\right)!\mathrm{2}^{−\mathrm{2}{k}−\mathrm{1}} }{\left({k}!\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 72579 by TawaTawa last updated on 30/Oct/19 Answered by mind is power last updated on 30/Oct/19 $$\mathrm{CF}.\mathrm{AD}=\mathrm{DC}.\mathrm{AE}=\mathrm{AB}.\mathrm{AE} \\ $$$$\Rightarrow\mathrm{AD}=\frac{\mathrm{16}.\mathrm{8}}{\mathrm{10}}=\frac{\mathrm{64}}{\mathrm{5}}=\mathrm{12}.\mathrm{8cm} \\ $$$$\left.\mathrm{2}\right)\mathrm{ar}\left(\mathrm{ABCD}\right)=\mathrm{DC}.\mathrm{AD}.\mathrm{sin}\left(\angle\mathrm{CDA}\right) \\ $$$$\mathrm{ar}\left(\mathrm{EFGH}\right)=\mathrm{ar}\left(\mathrm{ABCD}\right)−\mathrm{ar}\left(\mathrm{EBF}\right)−\mathrm{ar}\left(\mathrm{FCG}\right)−\mathrm{ar}\left(\mathrm{GDH}\right)−\mathrm{ar}\left(\mathrm{DHE}\right)…
Question Number 138114 by mnjuly1970 last updated on 10/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:……\:{calculus}…..\left({III}\right)…… \\ $$$$\:\:\:\:\:\:\:\:\:{evaluate}::\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\overset{???} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\:{x}} \frac{{cos}\left({y}\right)}{\:\sqrt{\left(\frac{\pi}{\mathrm{2}}−{x}\right)\left(\frac{\pi}{\mathrm{2}}−{y}\right)}}{dydx} \\ $$$$ \\ $$ Commented by…
Question Number 72577 by aliesam last updated on 30/Oct/19 $${solve}\:{the}\:{equation} \\ $$$$ \\ $$$${z}\left({x}+{z}\right)\frac{\partial{z}}{\partial{x}}\:−\:{y}\left({y}+{z}\right)\frac{\partial{z}}{\partial{y}}\:=\:\mathrm{0} \\ $$$$ \\ $$$${where}\:{z}=\sqrt{{y}}\:{when}\:{x}=\mathrm{1} \\ $$ Commented by mind is power…
Question Number 7040 by FilupSmith last updated on 07/Aug/16 $${f}\left({x},{y}\right)={ax}^{\mathrm{2}} +{by}^{\mathrm{2}} \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{where}\:\mathrm{the}\:\mathrm{gradient} \\ $$$$\mathrm{is}\:\mathrm{zero}\:\mathrm{for}\:\mathrm{multivariable}\:\mathrm{funtions}? \\ $$ Commented by Yozzii last updated on 07/Aug/16 $$\bigtriangledown{f}={grad}\:{f}=\begin{pmatrix}{\frac{\partial{f}}{\partial{x}}}\\{\frac{\partial{f}}{\partial{y}}}\end{pmatrix}…
Question Number 7039 by Rasheed Soomro last updated on 07/Aug/16 $${Show}\:{without}\:{using}\:{calculator}\:{that} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}\:\mathrm{20sin}\:\mathrm{150sin}\:\mathrm{160}}{\mathrm{sin}\:\mathrm{10}\:\mathrm{sin}\:\mathrm{140}+\mathrm{sin}\:\mathrm{20}\:\mathrm{sin}\:\mathrm{150}\:\mathrm{cos}\:\mathrm{160}}\right)=\mathrm{130} \\ $$ Commented by Yozzii last updated on 08/Aug/16 $${All}\:{figures}\:{are}\:{assumed}\:{to}\:{be}\:{in}\:{degrees}. \\…
Question Number 72569 by otchereabdullai@gmail.com last updated on 30/Oct/19 $$\mathrm{2x}−\mathrm{y}+\mathrm{3z}\:=\mathrm{1} \\ $$$$\mathrm{4x}+\mathrm{2y}−\mathrm{z}\:=\:−\mathrm{8} \\ $$$$\mathrm{3x}+\mathrm{y}+\mathrm{2z}\:=\:−\mathrm{1} \\ $$ Answered by MJS last updated on 30/Oct/19 $$\left(\mathrm{2}\right)\:\:{z}=\mathrm{4}{x}+\mathrm{2}{y}+\mathrm{8} \\…
Question Number 7031 by Tawakalitu. last updated on 07/Aug/16 Commented by FilupSmith last updated on 07/Aug/16 $${my}\:{attempt} \\ $$$$\mathrm{0}<{x},{y}<\frac{\pi}{\mathrm{2}} \\ $$$${x}<{y} \\ $$$${x}−\mathrm{sin}\left({x}\right)<{y}−\mathrm{sin}\left({y}\right) \\ $$$$\:…