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Category: Geometry

Question-11221

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}} \\…

Three-interior-angles-of-a-polygon-are-160-each-If-the-other-interior-angles-are-120-each-find-the-number-of-sides-of-the-polygon-

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-11183

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}}…

x-dx-x-1-1-3-

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…

Straight-line-lx-my-1-is-tangent-to-the-curve-ax-n-by-n-1-Prove-that-l-a-n-n-1-m-b-n-n-1-1-

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…

lim-x-1-1-x-e-t-2-dt-x-2-1-a-1-b-0-c-e-2-d-e-

Question Number 10829 by Saham last updated on 26/Feb/17 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\int_{\:\mathrm{1}} ^{\:\mathrm{x}} \:\:\:\frac{\mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \:\left(\mathrm{dt}\right)}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{1}\:\left(\mathrm{b}\right)\:\mathrm{0}\:\left(\mathrm{c}\right)\:\mathrm{e}/\mathrm{2}\:\left(\mathrm{d}\right)\:\mathrm{e} \\ $$ Answered by bahmanfeshki last updated…