Question Number 456 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}:\:\:\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{6}=\mathrm{11} \\ $$$$ \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{6}=\mathrm{11} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{x}=\mathrm{11}−\mathrm{6}…
Question Number 131525 by mathlove last updated on 05/Feb/21 $$\:{if}\:\:\:\left({a}−{b}\right)\left({a}+{b}\right)=\mathrm{23} \\ $$$${then}\:\:{faind}\:\:\:{a}\centerdot{b}=? \\ $$ Answered by mr W last updated on 05/Feb/21 $${no}\:{unique}\:{solution}\:{for}\:{a},{b}\in{R}. \\ $$$${for}\:{a},{b}\in{Z}:…
Question Number 131527 by Sudip last updated on 05/Feb/21 Answered by Dwaipayan Shikari last updated on 05/Feb/21 $$\frac{\mathrm{2}}{\mathrm{7}}\int\frac{{t}}{{t}+\frac{\mathrm{22}}{\mathrm{7}}}{dt}+\frac{\mathrm{5}}{\mathrm{7}}\int\frac{\mathrm{1}}{{t}+\frac{\mathrm{22}}{\mathrm{7}}}{dt} \\ $$$$=\frac{\mathrm{2}}{\mathrm{7}}{t}−\frac{\mathrm{44}}{\mathrm{49}}{log}\left({t}+\frac{\mathrm{22}}{\mathrm{7}}\right)+\frac{\mathrm{5}}{\mathrm{7}}{log}\left({t}+\frac{\mathrm{22}}{\mathrm{7}}\right) \\ $$ Answered by mr…
Question Number 65988 by mmkkmm000m last updated on 07/Aug/19 $$\int{dx}/{x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on 07/Aug/19 $${let}\:{A}\:=\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:\Rightarrow{A}\:=\int\:\:\:\frac{{dx}}{\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:+\frac{\mathrm{3}}{\mathrm{4}}}…
Question Number 453 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}\:\:\:\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$$$\mathrm{42}{x}−\mathrm{45}=−\mathrm{72} \\ $$$$\mathrm{42}{x}=−\mathrm{72}+\mathrm{45}…
Question Number 451 by Karting7442 last updated on 25/Jan/15 $${solve}\:{the}\:{equation}\:{for}\:{x}\:\::\:\mathrm{5}−{x}=\:−\mathrm{3} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{5}−{x}=−\mathrm{3} \\ $$$${x}=\mathrm{5}+\mathrm{3}=\mathrm{8} \\ $$…
Question Number 131520 by EDWIN88 last updated on 05/Feb/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}+\mathrm{100}\right)^{\mathrm{3}} }\:\mathrm{dx}\:=? \\ $$ Commented by liberty last updated on 05/Feb/21…
Question Number 449 by 123456 last updated on 25/Jan/15 $$\mathrm{if}\:\mid{z}\mid=\mathrm{1},{z}\in\mathbb{C},{a}\in\mathbb{R} \\ $$$$\mathrm{find}\:\mathrm{max}\:\mathrm{value}\:\mathrm{of}\:\mid{z}^{\mathrm{2}} +{az}−\mathrm{1}\mid \\ $$ Answered by prakash jain last updated on 09/Jan/15 $${z}={i} \\…
Question Number 131517 by benjo_mathlover last updated on 05/Feb/21 $$\mathrm{Given}\:\int_{\mathrm{0}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\mathrm{2x}−\mathrm{1}\right)\mathrm{dx}+\int_{\mathrm{0}} ^{\mathrm{3}} \left(\int_{\mathrm{0}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)\mathrm{dx} \\ $$$$\mathrm{find}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:. \\ $$ Answered…
Question Number 65983 by Rio Michael last updated on 07/Aug/19 $$\:{Simplify}\: \\ $$$$\:\:\:\left(\mathrm{1}+\:\mathrm{2}{i}\sqrt{\mathrm{2}}\right)^{\mathrm{7}} \:−\:\left(\mathrm{1}\:+\mathrm{2}{i}\right)^{\mathrm{7}} \\ $$ Commented by Rio Michael last updated on 17/Aug/19 $${can}\:{i}\:{use}\:{de}\:{moivre}'{s}\:{theorem}?…