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Author: Tinku Tara

2x-3y-z-7-4x-y-2z-1-x-5y-3z-14-find-x-y-z-

Question Number 212479 by hardmath last updated on 14/Oct/24 $$\begin{cases}{\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{z}\:=\:\mathrm{7}}\\{\mathrm{4x}\:−\:\mathrm{y}\:+\:\mathrm{2z}\:=\:\mathrm{1}}\\{−\mathrm{x}\:+\:\mathrm{5y}\:+\:\mathrm{3z}\:=\:\mathrm{14}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{x},\mathrm{y},\mathrm{z}\:=\:? \\ $$ Answered by A5T last updated on 14/Oct/24 $$\mathrm{3}\left({ii}\right)+\left({i}\right)\Rightarrow\mathrm{14}{x}+\mathrm{5}{z}=\mathrm{10}…\left({iv}\right) \\ $$$$\mathrm{5}\left({ii}\right)+\left({iii}\right)\Rightarrow\mathrm{19}{x}+\mathrm{13}{z}=\mathrm{19}…\left({v}\right) \\ $$$$\mathrm{13}\left({iv}\right)−\mathrm{5}\left({v}\right)\Rightarrow\mathrm{87}{x}=\mathrm{35}\Rightarrow{x}=\frac{\mathrm{35}}{\mathrm{87}}\Rightarrow{z}=\frac{\mathrm{76}}{\mathrm{87}}\Rightarrow{y}=\frac{\mathrm{205}}{\mathrm{87}} \\…

Question-212470

Question Number 212470 by Spillover last updated on 14/Oct/24 Answered by Ar Brandon last updated on 14/Oct/24 $$\Omega=\int_{\mathrm{0}} ^{\infty} \frac{\left(\mathrm{1}−{x}\right)\mathrm{ln}{x}}{\mathrm{1}−{x}^{\mathrm{6}} }{dx} \\ $$$$\:\:\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{\mathrm{1}−{x}^{\mathrm{6}}…

prove-0-dx-x-4-25x-2-160-0-dx-x-4-95x-2-2560-

Question Number 212461 by MrGaster last updated on 14/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{25}{x}^{\mathrm{2}} +\mathrm{160}}}=\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{95}{x}^{\mathrm{2}} +\mathrm{2560}}} \\ $$ Commented by Ghisom…

1-In-a-plane-there-are-nt-poins-arranged-such-that-nostraight-line-passesg-throuh-more-than-3-points-h-Wat-is-the-maximume-numbr-of-straight-lines-thatcan-pass-throughy-exactl-3-points2-If-thee-nu

Question Number 212462 by MrGaster last updated on 14/Oct/24 $$\mathrm{1}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{there}\:\mathrm{are}\:\mathrm{nt} \\ $$$$\mathrm{poins}\:\mathrm{arranged}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{nostraight}\:\mathrm{line}\:\mathrm{passesg} \\ $$$$\mathrm{throuh}\:\mathrm{more}\:\mathrm{than}\:\mathrm{3}\:\mathrm{points}.\mathrm{h} \\ $$$$\mathrm{Wat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximume} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\: \\ $$$$\mathrm{thatcan}\:\mathrm{pass}\:\mathrm{throughy} \\ $$$$\mathrm{exactl}\:\mathrm{3}\:\mathrm{points2}.\:\mathrm{If}\:\mathrm{thee} \\…

9x-2-49-x-3-dx-

Question Number 212456 by Hanuda354 last updated on 14/Oct/24 $$\int\:\:\frac{\sqrt{\mathrm{9}{x}^{\mathrm{2}} −\mathrm{49}}}{{x}^{\mathrm{3}} }\:\:{dx}\:=\:? \\ $$ Answered by Sutrisno last updated on 14/Oct/24 $$\int\frac{\sqrt{\left(\mathrm{3}{x}\right)^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }}{{x}^{\mathrm{3}} }{dx}…

Question-212457

Question Number 212457 by 281981 last updated on 14/Oct/24 Answered by som(math1967) last updated on 14/Oct/24 $$\:\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{b}}&{{c}}&{{a}}\\{{c}}&{{a}}&{{b}}\end{vmatrix}=\mathrm{0} \\ $$$$\Rightarrow{a}\left({bc}−{a}^{\mathrm{2}} \right)−{b}\left({b}^{\mathrm{2}} −{ca}\right)+{c}\left({ab}−{c}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$$\Rightarrow{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…