Question Number 209521 by mokys last updated on 12/Jul/24 $${find}\:{the}\:{integral}\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} +{a}^{\mathrm{4}} }\:{by}\:{complex}\:{number}\:?\: \\ $$ Answered by mathmax last updated on 14/Jul/24 $${I}=\int\:\frac{{dx}}{{x}^{\mathrm{4}} −{i}^{\mathrm{2}} {a}^{\mathrm{4}} }=\int\frac{{dx}}{\left({x}^{\mathrm{2}}…
Question Number 209520 by Ismoiljon_008 last updated on 12/Jul/24 $$ \\ $$$$\:\:\:{At}\:{what}\:{value}\:{of}\:\:{a}\:{does}\:{the}\:{system} \\ $$$$\:\:\:{of}\:{equations}\:{have}\:\mathrm{4}\:{solutions}\:? \\ $$$$\:\:\:\left\{\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{0}\right. \\ $$$$\:\:\:\left\{\left({x}−{a}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right. \\ $$$$ \\…
Question Number 209506 by Ismoiljon_008 last updated on 11/Jul/24 Commented by Ismoiljon_008 last updated on 11/Jul/24 $${Help}\:{please} \\ $$ Commented by mr W last updated…
Question Number 209465 by RoseAli last updated on 10/Jul/24 Answered by mr W last updated on 10/Jul/24 $${x}−\mathrm{2}=\mathrm{0}\:\Rightarrow{x}=\mathrm{2} \\ $$$${x}−\mathrm{2}=\pm\mathrm{1}\:\Rightarrow{x}=\mathrm{1}\:{or}\:\mathrm{3} \\ $$$$\mathrm{10}{x}^{\mathrm{2}} −\mathrm{1}=\mathrm{3}{x}\:\Rightarrow\left(\mathrm{2}{x}−\mathrm{1}\right)\left(\mathrm{5}{x}+\mathrm{1}\right)=\mathrm{0}\:\Rightarrow{x}=−\frac{\mathrm{1}}{\mathrm{5}}\:{or}\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{5}\:{solutions}…
Question Number 209433 by essaad last updated on 10/Jul/24 Answered by A5T last updated on 10/Jul/24 $${S}_{{p}} =\frac{\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}×…×\left(\mathrm{2}{p}\right)}{\mathrm{2}×\mathrm{4}×\mathrm{6}×…×\mathrm{2}{p}}=\frac{\left(\mathrm{2}{p}\right)!}{\mathrm{2}^{{p}} \left(\mathrm{1}×\mathrm{2}×…×{p}\right)} \\ $$$$=\frac{\left(\mathrm{2}{p}\right)!}{\mathrm{2}^{{p}} {p}!}\Rightarrow{C} \\ $$ Terms…
Question Number 209450 by RoseAli last updated on 10/Jul/24 Answered by Spillover last updated on 10/Jul/24 $${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} \\ $$$${g}\left({x}\right)=\sqrt{{x}−\mathrm{2}} \\ $$$$\left({fog}\right)\left({x}\right)=? \\ $$$$\left({gof}\right)\left({x}\right)=? \\ $$$${fog}\left({x}\right)={f}\left[{g}\left({x}\right)\right]…
Question Number 209474 by Ismoiljon_008 last updated on 10/Jul/24 Commented by Ismoiljon_008 last updated on 10/Jul/24 $${help}\:{me}\:{please} \\ $$ Answered by Frix last updated on…
Question Number 209341 by Tawa11 last updated on 07/Jul/24 $$\mathrm{solve}\:\:\:\:\mathrm{x}^{\mathrm{log}\:\mathrm{27}} \:\:+\:\:\mathrm{9}^{\mathrm{log}\:\mathrm{x}} \:\:=\:\:\:\mathrm{36} \\ $$ Answered by Frix last updated on 07/Jul/24 $${x}^{\mathrm{log}_{{b}} \:\mathrm{27}} ={x}^{\frac{\mathrm{3ln}\:\mathrm{3}}{\mathrm{ln}\:{b}}} \\…
Question Number 209347 by RoseAli last updated on 07/Jul/24 Answered by Berbere last updated on 07/Jul/24 $$\int_{−\mathrm{4}} ^{\mathrm{4}} {f}\left({x}\right){dx}=\mathrm{2}\underset{\mathrm{0}} {\int}^{\mathrm{4}} {f}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{4}}…
Question Number 209304 by RoseAli last updated on 06/Jul/24 Answered by A5T last updated on 06/Jul/24 $${a}^{{x}} +{b}^{{x}} =\mathrm{62} \\ $$$${a}+{b}=\mathrm{8};{ab}=\mathrm{1} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\left({a}+{b}\right)^{\mathrm{2}}…