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Question-69616

Question Number 69616 by azizullah last updated on 25/Sep/19 Commented by Prithwish sen last updated on 25/Sep/19 $$\mathrm{After}\:\mathrm{10}\:\mathrm{years}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{will}\:\mathrm{be}\:\mathrm{40}+\mathrm{20}=\mathrm{60}\:\mathrm{years} \\ $$$$\mathrm{After}\:\mathrm{10}\:\mathrm{years} \\ $$$$\:\:\:\mathrm{shabena}\:\mathrm{will}\:\mathrm{be}\:=\:\frac{\mathrm{1}}{\mathrm{3}}×\mathrm{60}\:=\:\mathrm{20}\:\mathrm{years} \\ $$$$\mathrm{maria}\:\mathrm{will}\:\mathrm{be}\:=\frac{\mathrm{2}}{\mathrm{3}}\:×\mathrm{60}\:=\:\mathrm{40}\:\mathrm{years} \\…

Prove-that-inside-a-square-a-semi-circle-which-touches-all-the-four-sides-of-the-square-is-possible-with-ruler-and-compass-

Question Number 4080 by Rasheed Soomro last updated on 27/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{square},\:\mathrm{a}\:\mathrm{semi}-\mathrm{circle}, \\ $$$$\mathrm{which}\:\mathrm{touches}\:\mathrm{all}\:\mathrm{the}\:\mathrm{four}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{square},\:\mathrm{is}\:\mathrm{possible}\:\mathrm{with}\:\boldsymbol{\mathrm{ruler}}\:\mathrm{and}\:\boldsymbol{\mathrm{compass}}. \\ $$ Commented by Rasheed Soomro last updated on 29/Dec/15…

For-two-co-planer-circles-to-be-tangent-necessary-and-sufficient-condition-is-I-think-the-distance-between-the-centers-of-circles-must-be-equal-to-r-1-r-2-or-r-1-r-2-where-r

Question Number 4077 by Rasheed Soomro last updated on 28/Dec/15 $$\mathrm{For}\:\mathrm{two}\:\boldsymbol{\mathrm{co}}-\boldsymbol{\mathrm{planer}}\:\mathrm{circles}\:\mathrm{to}\:\mathrm{be}\:\mathrm{tangent} \\ $$$$\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient}\:\mathrm{condition}\:\mathrm{is}, \\ $$$$\mathrm{I}\:\mathrm{think} \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{centers}\:\mathrm{of}\: \\ $$$$\:\:\:\:\mathrm{circles}\:\:\mathrm{must}\:\mathrm{be}\:\mathrm{equal}\:\mathrm{to}\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} +\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:\mathrm{or}\:\mid\boldsymbol{\mathrm{r}}_{\mathrm{1}} −\boldsymbol{\mathrm{r}}_{\mathrm{2}} \mid\:, \\ $$$$\:\:\:\:\:\mathrm{where}\:\:\boldsymbol{\mathrm{r}}_{\mathrm{1}}…

Question-4075

Question Number 4075 by Yozzii last updated on 27/Dec/15 Answered by prakash jain last updated on 28/Dec/15 $$\:^{\mathrm{2}{r}} {C}_{{r}} =\frac{\mathrm{2}{r}!}{{r}!{r}!} \\ $$$$\mathrm{2}^{{r}} \centerdot{r}!=\mathrm{2}\centerdot\mathrm{4}\centerdot\mathrm{6}\centerdot…\centerdot\mathrm{2}{r} \\ $$$$\mathrm{2}{r}!=\mathrm{1}\centerdot\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{4}\centerdot…\centerdot\left(\mathrm{2}{r}−\mathrm{1}\right)\centerdot\mathrm{2}{r}…

Question-69608

Question Number 69608 by TawaTawa last updated on 25/Sep/19 Commented by Prithwish sen last updated on 27/Sep/19 $$\left.\boldsymbol{\mathrm{a}}\right)\:\mid\boldsymbol{\mathrm{AB}}\mid=\mathrm{2}\sqrt{\mathrm{2}}=\:\mathrm{2}.\mathrm{8m} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{perimeter}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{ALB}}\:=\frac{\mathrm{2}×\pi×\mathrm{2}×\mathrm{270}}{\mathrm{360}}\mathrm{m}=\:\mathrm{9}.\mathrm{4m} \\ $$ Commented by TawaTawa…