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Category: Algebra

2-Z-1-a-1-b-Z-help-

Question Number 167722 by SAMIRA last updated on 23/Mar/22 $$\frac{\mathrm{2}}{\boldsymbol{\mathrm{Z}}}\:=\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}} \\ $$$$\boldsymbol{\mathrm{Z}}\:=\:???\:{help} \\ $$ Commented by MJS_new last updated on 23/Mar/22 $$\mathrm{law}\:\mathrm{of}\:\mathrm{adding}\:\mathrm{fractions} \\ $$$$\frac{{o}}{{p}}+\frac{{q}}{{r}}=\frac{{o}×{r}}{{p}×{r}}+\frac{{p}×{q}}{{p}×{r}}=\frac{{o}×{r}+{p}×{q}}{{p}×{r}} \\…

Question-102178

Question Number 102178 by dw last updated on 07/Jul/20 Answered by 1549442205 last updated on 07/Jul/20 $$\mathrm{Putting}\:\mathrm{x}=\mathrm{tan}\alpha,\mathrm{y}=\mathrm{tan}\beta\:\mathrm{we}\:\mathrm{have} \\ $$$$\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }=\sqrt{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \alpha}=\frac{\mathrm{1}}{\mathrm{cos}\alpha},\sqrt{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{cos}\beta} \\ $$$$\mathrm{x}\sqrt{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }+\mathrm{y}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…

Evalvate-the-following-integrals-1-x-3-6x-2-9x-dx-2-x-6-dx-x-4-24x-3-

Question Number 167700 by HongKing last updated on 23/Mar/22 $$\mathrm{Evalvate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integrals}: \\ $$$$\mathrm{1}.\:\int\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{6x}^{\mathrm{2}} \:+\:\mathrm{9x}\:\mathrm{dx}} \\ $$$$\mathrm{2}.\:\int\:\frac{\left(\mathrm{x}\:-\:\mathrm{6}\right)\:\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:-\:\mathrm{24x}\:+\:\mathrm{3}} \\ $$ Answered by MJS_new last updated on…

Question-167699

Question Number 167699 by HongKing last updated on 23/Mar/22 Answered by alephzero last updated on 23/Mar/22 $$\mathrm{1}.\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}}{{x}\:\mathrm{sin}\:{x}}\:\overset{\mathrm{use}\:\mathrm{L}'\mathrm{H}\hat {\mathrm{o}pital}'\mathrm{s}\:\mathrm{rule}} {=} \\ $$$$=\:\mathrm{lim}\:\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}+{x}\:\mathrm{cos}\:{x}}\:\overset{\mathrm{again}} {=} \\ $$$$=\:\mathrm{lim}\:\frac{\mathrm{cos}\:{x}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:=…

Question-167690

Question Number 167690 by peter frank last updated on 22/Mar/22 Answered by som(math1967) last updated on 23/Mar/22 $${by}\:{solving}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4}\:{and}\:\left({x}−\mathrm{2}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4} \\ $$$${x}=\mathrm{1}\:,{y}=\pm\sqrt{\mathrm{3}} \\…