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Author: Tinku Tara

Question-205681

Question Number 205681 by naka3546 last updated on 27/Mar/24 Answered by mr W last updated on 27/Mar/24 $${a}=\mathrm{1}\:{cm} \\ $$$${R}=\frac{\mathrm{1}}{\mathrm{3}}×\frac{\sqrt{\mathrm{3}}{a}}{\mathrm{2}}=\frac{\sqrt{\mathrm{3}}{a}}{\mathrm{6}} \\ $$$${r}=\frac{\sqrt{\mathrm{3}}{b}}{\mathrm{6}} \\ $$$$\frac{{b}}{{a}}=\frac{\frac{\sqrt{\mathrm{3}}{a}}{\mathrm{2}}−\mathrm{2}{R}}{\frac{\sqrt{\mathrm{3}}{a}}{\mathrm{2}}}=\frac{\mathrm{1}}{\mathrm{3}} \\…

Question-205660

Question Number 205660 by marie last updated on 26/Mar/24 Answered by Skabetix last updated on 26/Mar/24 $$\mathrm{E}{xercice}\:{n}°\mathrm{4} \\ $$$$\left.\mathrm{1}\right)\:{D}'{apres}\:{le}\:{theoreme}\:{de}\:{Pythagore}\:: \\ $$$${BC}^{\mathrm{2}} ={AC}^{\mathrm{2}} +{AB}^{\mathrm{2}} \\ $$$$\Leftrightarrow{BC}^{\mathrm{2}}…

Question-205631

Question Number 205631 by Lindemann last updated on 26/Mar/24 Answered by A5T last updated on 26/Mar/24 $${If}\:{angle}\:{between}\:{x}\:{and}\:{x}+\mathrm{17}\:{is}\:\mathrm{90}° \\ $$$$\left({x}+\mathrm{18}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} +\left({x}+\mathrm{17}\right)^{\mathrm{2}} \Rightarrow{x}=\mathrm{7} \\ $$$$\frac{\mathrm{7}×\mathrm{24}}{\mathrm{2}}={r}\left(\frac{\mathrm{7}+\mathrm{24}+\mathrm{25}}{\mathrm{2}}\right)\Rightarrow{r}=\mathrm{3} \\…

Question-205656

Question Number 205656 by SANOGO last updated on 26/Mar/24 Answered by TheHoneyCat last updated on 31/Mar/24 $$\left(\mathrm{2}\right)\Rightarrow\left(\mathrm{1}\right) \\ $$$$\mathrm{Soit}\:{c}\in\mathbb{R}^{\ast} \:\mathrm{tel}\:\mathrm{que}\:\forall{x}\in{X}\:\:\mid\mid{T}\left({x}\right)\mid\mid_{{Y}} \:\geqslant{c}\mid\mid{x}\mid\mid_{{X}} \\ $$$$\mathrm{Soit}\:\left({x},{x}'\right)\in{X}^{\mathrm{2}} \\ $$$$\mid\mid{T}\left({x}\right)−{T}\left({x}'\right)\mid\mid…

We-define-a-domino-as-being-and-ordered-pair-of-distinct-integers-A-suitable-sequence-of-dominos-is-a-list-of-distinct-dominoes-in-which-the-first-coordonate-of-each-pair-after-the-first-is-equal-to-

Question Number 205654 by Lindemann last updated on 26/Mar/24 $${We}\:{define}\:{a}\:{domino}\:{as}\:{being}\:{and}\:{ordered}\:{pair}\:{of}\:{distinct} \\ $$$${integers}.\:{A}\:{suitable}\:{sequence}\:{of}\:{dominos}\:{is}\:{a}\:{list}\:{of}\:{distinct} \\ $$$${dominoes}\:{in}\:{which}\:{the}\:{first}\:{coordonate}\:{of}\:{each}\:{pair}\:{after} \\ $$$${the}\:{first}\:{is}\:{equal}\:{to}\:{the}\:{second}\:{coordonate}\:{of}\:{the}\:{immediately} \\ $$$${preceding}\:{pair},\:{and}\:{in}\:{which}\:{the}\:{pairs}\:\left({i};{j}\right)\:{and}\:\left({j};{i}\right) \\ $$$${do}\:{not}\:{both}\:{appear}\:{for}\:{all}\:{i}\:{and}\:{j}.\:{Let}\:{D}_{\mathrm{40}} \:{the} \\ $$$${set}\:{of}\:{all}\:{dominoes}\:{whose}\:{coordonate}\:{are}\:{not}\:{greater} \\ $$$${than}\:\mathrm{40}.\:{Find}\:{the}\:{length}\:{of}\:{the}\:{longest}\:{suitable}\:{sequence}…