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Category: Algebra

Question-193565

Question Number 193565 by Mingma last updated on 16/Jun/23 Answered by mr W last updated on 17/Jun/23 $${say}\:{at}\:{time}\:{x}\:{hours}\:{after}\:\mathrm{0}\:{o}'{clock}. \\ $$$${assume}\:{the}\:{hands}\:{move}\:{continuously}. \\ $$$${position}\:{of}\:{hour}\:{hand}:\:\mathrm{30}{x}\:° \\ $$$${position}\:{of}\:{minute}\:{hand}:\:\left({x}−\left[{x}\right]\right)×\mathrm{60}×\mathrm{6}\:° \\…

27t73-11-and-R-0-then-t-how-is-explontry-solution-

Question Number 193525 by mustafazaheen last updated on 16/Jun/23 $$\:\:\:\:\:\frac{\mathrm{27t73}}{\mathrm{11}} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{R}=\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{t}=? \\ $$$$\:\:\:\:\:\:\mathrm{how}\:\mathrm{is}\:\mathrm{explontry}\:\mathrm{solution} \\ $$ Answered by MM42 last updated on 16/Jun/23 $$\mathrm{3}−\mathrm{7}+{t}−\mathrm{7}+\mathrm{2}=\mathrm{11}{k}\Rightarrow−\mathrm{9}+{t}=\mathrm{11}{k}\Rightarrow{t}=\mathrm{9} \\…

Question-193492

Question Number 193492 by Socracious last updated on 15/Jun/23 Answered by a.lgnaoui last updated on 15/Jun/23 $$\mathrm{DE}\mid\mid\mathrm{BC}\:\: \\ $$$$\mathrm{tan}\:\mathrm{30}=\frac{\sqrt{\mathrm{3}}}{\mathrm{3}}=\frac{\boldsymbol{\mathrm{HB}}}{\boldsymbol{\mathrm{HA}}}=\frac{\boldsymbol{\mathrm{b}}}{\mathrm{2}\boldsymbol{\mathrm{x}}}\Rightarrow\:\:\boldsymbol{\mathrm{x}}=\frac{\boldsymbol{\mathrm{b}}\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{S}}=\boldsymbol{\mathrm{x}}.\frac{\boldsymbol{\mathrm{b}}}{\mathrm{2}}=\frac{\boldsymbol{\mathrm{b}}^{\mathrm{2}} }{\mathrm{4}}\sqrt{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Area}}=\frac{\mathrm{b}^{\mathrm{2}} \sqrt{\mathrm{3}}}{\mathrm{4}} \\ $$$$…

Proof-cot-1-1-sint-1-sint-1-sint-1-sint-t-2-

Question Number 193467 by aba last updated on 14/Jun/23 $$\mathrm{Proof}\:: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{1}+\mathrm{sint}}+\sqrt{\mathrm{1}−\mathrm{sint}}}{\:\sqrt{\mathrm{1}+\mathrm{sint}}−\sqrt{\mathrm{1}−\mathrm{sint}}}\right)=\frac{\mathrm{t}}{\mathrm{2}}\: \\ $$ Commented by MM42 last updated on 14/Jun/23 $${attention} \\ $$$${in}\:{all}\:\:{three}\:{arguments}\:\:{we}\:{used}\:{equalities}…

Nice-problem-Find-8-distinctive-numbers-N-0-such-that-these-are-simultaniously-true-1-a-b-c-d-e-f-g-h-2-a-2-b-2-c-2-d-2-e-2-f-2-g-2-h-2-3-a-3-b-3-c-3-d-3-

Question Number 193484 by Frix last updated on 15/Jun/23 $$\mathrm{Nice}\:\mathrm{problem}: \\ $$$$\mathrm{Find}\:\mathrm{8}\:\mathrm{distinctive}\:\mathrm{numbers}\:\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{these}\:\mathrm{are}\:\mathrm{simultaniously}\:\mathrm{true}: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:{a}+{b}+{c}+{d}\:=\:{e}+{f}+{g}+{h} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{e}^{\mathrm{2}} +{f}^{\mathrm{2}} +{g}^{\mathrm{2}} +{h}^{\mathrm{2}}…