Question Number 157562 by Ar Brandon last updated on 24/Oct/21 Answered by FongXD last updated on 24/Oct/21 $$\mathrm{Given}:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{3} \\ $$$$\mathrm{square}\:\mathrm{both}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\Leftrightarrow\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{2yz}+\mathrm{2xz}=\mathrm{9}…
Question Number 92013 by I want to learn more last updated on 04/May/20 $$\mathrm{Solve}: \\ $$$$\:\:\:\mathrm{2}^{\mathrm{x}} \:\:+\:\:\mathrm{3}^{\mathrm{y}} \:\:\:=\:\:\mathrm{72}\:\:\:\:\:…..\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\mathrm{2}^{\mathrm{y}} \:\:+\:\:\mathrm{3}^{\mathrm{x}} \:\:\:=\:\:\mathrm{108}\:\:\:\:\:…..\:\left(\mathrm{ii}\right) \\ $$ Commented…
Question Number 92008 by I want to learn more last updated on 04/May/20 $$\mathrm{Sum}\:\mathrm{of}\:\mathrm{infinite}\:\mathrm{series}:\:\:\mathrm{1}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{4}}\:\:+\:\:\frac{\mathrm{3}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}\:\:+\:\:\frac{\mathrm{3}.\mathrm{5}.\mathrm{7}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}\:\:+\:\:…\:\:\:\:\mathrm{is}\:? \\ $$ Commented by Prithwish Sen 1 last updated on 04/May/20…
Question Number 92000 by student work last updated on 04/May/20 $$\mathrm{proof}\:\mathrm{0}!!=\mathrm{1} \\ $$ Answered by $@ty@m123 last updated on 04/May/20 $${n}!={n}.\left({n}−\mathrm{1}\right)! \\ $$$$\Rightarrow\left({n}−\mathrm{1}\right)!=\frac{{n}!}{{n}} \\ $$$${Put}\:{n}=\mathrm{1}…
Question Number 26461 by ajfour last updated on 25/Dec/17 Commented by ajfour last updated on 25/Dec/17 $${A}\:{layer}\:{is}\:{cut}\:{from}\:{the}\:{back}\:{of}\: \\ $$$${upper}\:{large}\:{cuboid}\:\left({of}\:{front}\:\right. \\ $$$$\left.{surface}\:{area}\:\boldsymbol{{p}}\:{and}\:{volume}\:−\boldsymbol{{q}}\:\right). \\ $$$${This}\:{layer}\:{is}\:{of}\:{volume}\:\boldsymbol{{x}}^{\mathrm{3}} ,\:{where} \\…
Question Number 157494 by MathSh last updated on 23/Oct/21 Answered by MJS_new last updated on 24/Oct/21 $$\mathrm{let}\:{s}=\mathrm{sin}\:{x} \\ $$$$\sqrt{−\mathrm{9}{s}^{\mathrm{2}} +\mathrm{12}{s}+\mathrm{13}}=−\frac{\mathrm{4}{s}^{\mathrm{2}} −\mathrm{32}{s}−\mathrm{13}}{\mathrm{8}} \\ $$$${s}^{\mathrm{4}} −\mathrm{16}{s}^{\mathrm{3}} +\frac{\mathrm{187}}{\mathrm{2}}{s}^{\mathrm{2}}…
Question Number 157489 by MathSh last updated on 23/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{tan}\left(\mathrm{10x}\right)\:=\:\mathrm{tan}^{\mathrm{5}} \left(\mathrm{2x}\right) \\ $$$$ \\ $$ Answered by MJS_new last updated on 24/Oct/21 $$\mathrm{let}\:{t}=\mathrm{tan}\:\mathrm{2}{x}…
Question Number 26405 by math solver last updated on 25/Dec/17 Answered by prakash jain last updated on 25/Dec/17 $${r}^{\mathrm{2}} +\mathrm{1}=\left({r}+\mathrm{1}\right){r}−{r}+\mathrm{1} \\ $$$$\left({r}^{\mathrm{2}} +\mathrm{1}\right){r}!={r}\left({r}+\mathrm{1}\right)!−\left({r}−\mathrm{1}\right){r}! \\ $$$${sum}=\mathrm{1}\centerdot\mathrm{2}!−\mathrm{0}\centerdot\mathrm{1}!…
Question Number 91936 by MWSuSon last updated on 03/May/20 $${how}\:{to}\:{evaluate}\:{ln}\left({i}\right),\:{i}=\sqrt{−\mathrm{1}}. \\ $$ Commented by MWSuSon last updated on 03/May/20 thank you sir, but what if I'm looking for log(i) in base 2 or 10? Commented by mr W last…
Question Number 157457 by MathSh last updated on 23/Oct/21 $$\mathrm{xy}^{'} \:+\:\mathrm{y}\:=\:\mathrm{y}^{\mathrm{2}} \:\mathrm{ln}\:\mathrm{x} \\ $$$$ \\ $$ Answered by ajfour last updated on 23/Oct/21 $${xdy}+{ydx}={y}^{\mathrm{2}} \left(\mathrm{ln}\:{x}\right){dx}…