Question Number 143200 by Guddone last updated on 11/Jun/21 Answered by Dwaipayan Shikari last updated on 11/Jun/21 $$\mathrm{2}{x}+\mathrm{3}{y}=\begin{bmatrix}{\mathrm{2}\:\:\mathrm{3}}\\{\mathrm{4}\:\:\mathrm{0}}\end{bmatrix}\Rightarrow\mathrm{6}{x}+\mathrm{9}{y}=\begin{bmatrix}{\:\mathrm{6}\:\:\:\:\mathrm{9}}\\{\:\mathrm{12}\:\:\mathrm{0}}\end{bmatrix}\rightarrow\left({a}\right) \\ $$$$\mathrm{3}{x}+\mathrm{2}{y}=\begin{bmatrix}{\mathrm{2}\:\:−\mathrm{2}}\\{−\mathrm{1}\:\:\mathrm{5}}\end{bmatrix}\Rightarrow\mathrm{6}{x}+\mathrm{4}{y}=\begin{bmatrix}{\:\mathrm{4}\:\:−\mathrm{4}}\\{\:−\mathrm{2}\:\:\mathrm{10}}\end{bmatrix}\rightarrow\left({b}\right) \\ $$$${a}−{b}\:\Rightarrow\mathrm{5}{y}=\begin{bmatrix}{\mathrm{2}\:\:\:\:\:\:\mathrm{13}\:\:}\\{\mathrm{14}\:−\mathrm{10}}\end{bmatrix}\Rightarrow{y}=\begin{bmatrix}{\frac{\mathrm{2}}{\mathrm{5}}\:\:\frac{\mathrm{13}}{\mathrm{5}}}\\{\frac{\mathrm{14}}{\mathrm{5}}\:−\mathrm{2}}\end{bmatrix} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\begin{bmatrix}{\mathrm{2}\:\mathrm{3}}\\{\mathrm{4}\:\mathrm{0}}\end{bmatrix}−\begin{bmatrix}{\frac{\mathrm{6}}{\mathrm{5}}\:\frac{\mathrm{39}}{\mathrm{5}}}\\{\:\frac{\mathrm{42}}{\mathrm{5}}\:\:−\mathrm{6}}\end{bmatrix}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\begin{bmatrix}{\frac{\mathrm{4}}{\mathrm{5}}\:\frac{−\mathrm{24}}{\mathrm{5}}}\\{\frac{−\mathrm{22}}{\mathrm{5}}\:\:\mathrm{6}}\end{bmatrix}\right)=\begin{bmatrix}{\frac{\mathrm{2}}{\mathrm{5}}\:−\frac{\mathrm{12}}{\mathrm{5}}}\\{−\frac{\mathrm{11}}{\mathrm{5}}\:\:\:\mathrm{3}}\end{bmatrix} \\…
Question Number 12130 by sujith last updated on 14/Apr/17 $$\int\sqrt{{a}+{x}/{a}−{x}\:} \\ $$$$−\sqrt{{a}−{x}/{a}+{x}} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17 $$\frac{{a}+{x}}{{a}−{x}}={t}^{\mathrm{2}} \Rightarrow\frac{{a}+{x}−{a}+{x}}{{a}+{x}+{a}−{x}}=\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{2}} +\mathrm{1}}\Rightarrow{x}={a}\frac{{t}^{\mathrm{2}}…
Question Number 12127 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/Apr/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17 $${in}\:{triangle}:{ABC}\:{we}\:{have}: \\ $$$${AB}={m},{AC}={n},{AD}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}, \\ $$$${BD}\bot{DC},\measuredangle{BDA}=\measuredangle{ADC}. \\ $$$${find}:{BD}\:{and}\:{DC}\:{in}\:{term}\:{of}:\:{m},{n}. \\ $$…
Question Number 12126 by tawa last updated on 13/Apr/17 Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}{ab}+\mathrm{2}{ac}+\mathrm{2}{bc}=\mathrm{0} \\ $$$$\Rightarrow{ab}+{bc}+{ca}=−\mathrm{21} \\ $$$${A}=\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right) \\…
Question Number 143193 by mohammad17 last updated on 11/Jun/21 $${prove}\:{that}\:{the}\:{function}\:{f}\left({x}\right)={x}^{\mathrm{2}} \:\:,{x}\varepsilon\left[\mathrm{1},\mathrm{4}\right] \\ $$$${is}\:{Riemannian}\:{integral}\:? \\ $$ Answered by mathmax by abdo last updated on 11/Jun/21 $$\int_{\mathrm{1}}…
Question Number 143192 by BHOOPENDRA last updated on 11/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143194 by ZiYangLee last updated on 11/Jun/21 $$\mathrm{Suppose}\:{z}^{\mathrm{50}} +{z}^{\mathrm{25}} +{m}=\mathrm{0},\:\mathrm{where}\:{z}=\frac{\mathrm{1}+{i}}{\:\sqrt{\mathrm{2}}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{m}. \\ $$ Answered by Olaf_Thorendsen last updated on 11/Jun/21 $${z}\:=\:\frac{\mathrm{1}+{i}}{\:\sqrt{\mathrm{2}}}\:=\:{e}^{{i}\frac{\pi}{\mathrm{4}}} \\…
Question Number 77655 by TawaTawa last updated on 08/Jan/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\:\:\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{25}} \:+\:\mathrm{x}^{\mathrm{49}} \:+\:\mathrm{x}^{\mathrm{81}} \:\:\mathrm{is}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\:\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{1} \\ $$ Commented by jagoll last updated on 08/Jan/20…
Question Number 143191 by mohammad17 last updated on 11/Jun/21 Answered by mathmax by abdo last updated on 11/Jun/21 $$\int_{\mathrm{0}} ^{\mathrm{3}} \:\int_{\sqrt{\frac{\mathrm{x}}{\mathrm{3}}}} ^{\mathrm{1}} \:\left(\mathrm{y}^{\mathrm{3}} \:+\mathrm{1}\right)^{\mathrm{3}} \mathrm{dydx}\:=\int_{\mathrm{0}}…
Question Number 143190 by Ar Brandon last updated on 11/Jun/21 $$\int_{\mathbb{R}} \frac{\mathrm{e}^{\mathrm{its}} }{\mathrm{s}+\mathrm{3}}\mathrm{ds} \\ $$ Commented by mohammad17 last updated on 11/Jun/21 $${w}=\frac{\mathrm{1}}{{s}+\mathrm{3}}\Rightarrow{s}=\frac{\mathrm{1}}{{w}}−\mathrm{3}\Rightarrow{ds}=−\frac{\mathrm{1}}{{w}^{\mathrm{2}} }{dw} \\…