Question Number 204158 by siyathokoza last updated on 07/Feb/24 Commented by siyathokoza last updated on 07/Feb/24 $$\boldsymbol{\mathrm{HI}}\:\boldsymbol{\mathrm{PROF}}… \\ $$$$\boldsymbol{\mathrm{Please}}\:\boldsymbol{\mathrm{explain}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{word}}\:\boldsymbol{\mathrm{problem}} \\ $$ Commented by siyathokoza last…
Question Number 204152 by universe last updated on 07/Feb/24 $$\:\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{xy}−\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{2}} \\ $$$$\:\mathrm{attained}\:\mathrm{over}\:\mathrm{the}\:\mathrm{square}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{1};\mathrm{0}\leqslant\mathrm{y}\leqslant\mathrm{1}\:\mathrm{is} \\ $$ Answered by ajfour last updated on 08/Feb/24 $${f}\left({x},{y}\right)={z}={t}−{t}^{\mathrm{3}} \\ $$$$\frac{{dz}}{{dt}}=\mathrm{1}−\mathrm{3}{t}^{\mathrm{2}}…
Question Number 204123 by Ari last updated on 06/Feb/24 Commented by Rasheed.Sindhi last updated on 06/Feb/24 $$\mathrm{0}\:{is}\:{even}\:{because}\:{it}'{s}\:{divisible}\:{by}\:\mathrm{2} \\ $$ Answered by Frix last updated on…
Question Number 204129 by hardmath last updated on 06/Feb/24 $$\mathrm{a}\:,\:\mathrm{b}\:,\:\mathrm{x}\:,\:\mathrm{y}\:\in\:\mathbb{R} \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{23} \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{79} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{217} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{661} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{by}^{\mathrm{4}}…
Question Number 204056 by hardmath last updated on 05/Feb/24 $$\begin{cases}{\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{8}}\\{\mathrm{3x}\:+\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{10}}\\{\mathrm{4x}\:+\:\mathrm{3y}\:−\:\mathrm{2z}\:=\:\mathrm{4}}\end{cases} \\ $$$$\mathrm{Solve}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{matrix} \\ $$ Answered by AST last updated on 05/Feb/24 $$\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{3}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{4}}&{\mathrm{3}}&{−\mathrm{2}}\end{bmatrix}\begin{bmatrix}{{x}}\\{{y}}\\{{z}}\end{bmatrix}=\begin{bmatrix}{\mathrm{8}}\\{\mathrm{10}}\\{\mathrm{4}}\end{bmatrix}\underset{{R}_{\mathrm{3}} −\mathrm{4}{R}_{\mathrm{1}} } {\overset{{R}_{\mathrm{2}}…
Question Number 204054 by hardmath last updated on 05/Feb/24 $$\mathrm{y}\:=\:\sqrt{\mathrm{sinx}}\:+\:\mathrm{cos}^{\mathrm{3}} \mathrm{x} \\ $$$$\mathrm{find}:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Answered by AST last updated on 05/Feb/24 $${y}'=\frac{{cos}\left({x}\right)}{\:\mathrm{2}\sqrt{{sinx}}}−\mathrm{3}{sin}\left({x}\right){cos}^{\mathrm{2}} {x}…
Question Number 204055 by hardmath last updated on 05/Feb/24 $$\mathrm{y}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{arctg}\:\left(\mathrm{x}^{\mathrm{4}} \right) \\ $$$$\mathrm{find}:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Answered by AST last updated on 05/Feb/24 $${y}^{'} =\frac{\mathrm{2}}{\mathrm{3}}\left[\frac{{d}}{{dx}}{tan}^{−\mathrm{1}}…
Question Number 204082 by depressiveshrek last updated on 05/Feb/24 $$\sqrt{\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }+{x}}{{x}}}−\sqrt{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }−{x}^{\mathrm{2}} }=\mathrm{5} \\ $$ Commented by Frix last updated on 05/Feb/24 $${x}=\frac{\mathrm{6}}{\:\sqrt{\mathrm{119}}}…
Question Number 204041 by hardmath last updated on 04/Feb/24 $$\mathrm{Find}:\:\:\:\begin{vmatrix}{\mathrm{1}}&{\mathrm{7}}&{−\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{3}}&{\mathrm{5}}\\{−\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}=\:? \\ $$ Answered by AST last updated on 04/Feb/24 $$=\mathrm{1}\begin{vmatrix}{−\mathrm{3}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}−\mathrm{7}\begin{vmatrix}{\mathrm{9}}&{\mathrm{5}}\\{−\mathrm{1}}&{\mathrm{3}}\end{vmatrix}−\mathrm{1}\begin{vmatrix}{\mathrm{9}}&{−\mathrm{3}}\\{−\mathrm{1}}&{\mathrm{5}}\end{vmatrix} \\ $$$$=−\mathrm{9}−\mathrm{25}−\mathrm{7}\left(\mathrm{27}+\mathrm{5}\right)−\mathrm{1}\left(\mathrm{45}−\mathrm{3}\right)=−\mathrm{300} \\ $$ Answered…
Question Number 204039 by hardmath last updated on 04/Feb/24 $$\begin{vmatrix}{\mathrm{1}}&{\mathrm{7}}&{−\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{3}}&{\boldsymbol{\mathrm{x}}}\\{−\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}=\:\mathrm{0}\:\:\:\Rightarrow\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by AST last updated on 04/Feb/24 $$\mathrm{1}\left(−\mathrm{9}−\mathrm{5}{x}\right)−\mathrm{7}\left(\mathrm{27}+{x}\right)−\mathrm{1}\left(\mathrm{45}−\mathrm{3}\right)=\mathrm{0} \\ $$$$\Rightarrow−\mathrm{9}−\mathrm{5}{x}−\mathrm{189}−\mathrm{7}{x}−\mathrm{42}=\mathrm{0}\Rightarrow\mathrm{12}{x}=−\mathrm{240} \\ $$$$\Rightarrow{x}=−\mathrm{20} \\…