Question Number 76948 by Master last updated on 01/Jan/20 Answered by mr W last updated on 02/Jan/20 $${let}\:\alpha=\angle{A} \\ $$$$\angle{B}=\frac{\pi}{\mathrm{2}}−\frac{\alpha}{\mathrm{2}} \\ $$$${AB}={AC}=\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{sin}\:\frac{\alpha}{\mathrm{2}}} \\ $$$$\left(\sqrt{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{2}}…
Question Number 11403 by JAZAR last updated on 24/Mar/17 $${how}\:{can}\:{demonstred}\:{that}\: \\ $$$${cos}\left(\mathrm{2}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{1}=−{cos}^{\mathrm{2}} {x} \\ $$ Commented by sm3l2996 last updated on 24/Mar/17 $$\mathrm{I}\:\mathrm{think}\:\mathrm{that}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{not}\:\mathrm{correct} \\ $$$$\mathrm{because}\:\mathrm{cos}\left(\mathrm{2}\pi\right)−\mathrm{sin}\left(\mathrm{2}\pi\right)−\mathrm{1}=\mathrm{0}\neq−\mathrm{cos}^{\mathrm{2}}…
Question Number 11343 by jaskaurrangerleader@gmail.com last updated on 21/Mar/17 $${n}_{\boldsymbol{\mathrm{c}}_{\boldsymbol{\mathrm{n}}} } =\frac{{n}\mathrm{1}}{\left({n}−{n}\right)} \\ $$ Commented by FilupS last updated on 21/Mar/17 $$\frac{{n}}{{n}−{n}}=\mathrm{undefined} \\ $$ Terms…
Question Number 11344 by jaskaurrangerleader@gmail.com last updated on 21/Mar/17 $${n}_{{c}_{{n}} } =\frac{{n}!}{\left({n}−{n}\right)!{n}!} \\ $$ Commented by FilupS last updated on 21/Mar/17 $$\frac{{n}!}{\left({n}−{n}\right)!\centerdot{n}!}=\frac{\mathrm{1}}{\mathrm{0}!} \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}}=\mathrm{1} \\…
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Question Number 11221 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 17/Mar/17 Commented by mrW1 last updated on 18/Mar/17 $${center}\:{point}\:{of}\:{the}\:{circle}\:{M}\left({a},{a}\right) \\ $$$${radius}\:{of}\:{the}\:{circle}\:{R}=\left({a}−\mathrm{1}\right)\sqrt{\mathrm{2}} \\ $$$$\mathrm{sin}\:\frac{\theta}{\mathrm{2}}=\frac{{R}}{{a}\sqrt{\mathrm{2}}}=\mid\frac{{a}−\mathrm{1}}{{a}}\mid\leqslant\mathrm{1} \\ $$$$\theta=\mathrm{2sin}^{−\mathrm{1}} \left(\mid\frac{{a}−\mathrm{1}}{{a}}\mid\right),\:\mid{a}\mid\geqslant\frac{\mathrm{1}}{\mathrm{2}} \\…
Question Number 142282 by pete last updated on 29/May/21 $$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{polygon}\:\mathrm{are}\:\mathrm{160}° \\ $$$$\mathrm{each}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{other}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{are}\:\mathrm{120}°\:\mathrm{each}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}. \\ $$ Answered by som(math1967) last updated on 29/May/21 $$\boldsymbol{{let}}\:\boldsymbol{{no}}\:\boldsymbol{{of}}\:\boldsymbol{{sides}}=\boldsymbol{{n}} \\…
Question Number 11183 by Nayon last updated on 15/Mar/17 Answered by mrW1 last updated on 16/Mar/17 $${let}\:{x}=\frac{{AD}}{{AB}} \\ $$$$\Rightarrow{DE}={x}×{BC} \\ $$$${a}={ABC}=\frac{\mathrm{1}}{\mathrm{2}}×{BC}×{h} \\ $$$${ADC}=\frac{\mathrm{1}}{\mathrm{2}}×{DE}×{h}=\frac{\mathrm{1}}{\mathrm{2}}×{x}×{BC}×{h}={xa} \\ $$$${ADE}=\frac{\mathrm{1}}{\mathrm{2}}×{DE}×{x}×{h}=\frac{\mathrm{1}}{\mathrm{2}}×{x}×{BC}×{x}×{h}={x}^{\mathrm{2}}…
Question Number 11148 by suci last updated on 14/Mar/17 $$\int\frac{{x}\:{dx}}{\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}=….??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:\frac{\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{5}/\mathrm{3}} }{\mathrm{5}}\:−\frac{\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{2}/\mathrm{3}} }{\mathrm{2}}\:+{C}\: \\ $$ Commented…
Question Number 142218 by Dwaipayan Shikari last updated on 27/May/21 $${Straight}\:{line}\:{lx}+{my}=\mathrm{1}\:\:{is}\:{tangent}\:{to}\:{the}\:{curve}\:\left({ax}\right)^{{n}} +\left({by}\right)^{{n}} =\mathrm{1} \\ $$$${Prove}\:{that}\:\left(\frac{{l}}{{a}}\right)^{\frac{{n}}{{n}−\mathrm{1}}} +\left(\frac{{m}}{{b}}\right)^{\frac{{n}}{{n}−\mathrm{1}}} =\mathrm{1} \\ $$ Answered by som(math1967) last updated on…