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Category: Geometry

Is-the-following-proof-correct-i-0-1-i-2-i-1-2-4-8-16-32-Let-1-1-2-4-8-16-32-2-1-2-4-8-16-32-1-2-1-2-1-4-2-8-4-1-2-1-1-2-4-8-

Question Number 2138 by Filup last updated on 06/Nov/15 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{proof}\:\mathrm{correct}? \\ $$$$ \\ $$$$\Delta=\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{i}} \mathrm{2}^{{i}} =\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+… \\ $$$$ \\ $$$$\mathrm{Let}: \\ $$$$\Delta_{\mathrm{1}} =\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+……

Question-67615

Question Number 67615 by TawaTawa last updated on 29/Aug/19 Commented by TawaTawa last updated on 29/Aug/19 $$\mathrm{i}\:\mathrm{did}.\:\:\:\:\:\:\mathrm{A}\:\mathrm{of}\:\mathrm{Big}\:\mathrm{semi}\:\mathrm{circle}\:=\:\frac{\pi\mathrm{r}^{\mathrm{2}} }{\mathrm{2}}\:\:=\:\:\frac{\pi.\mathrm{2}^{\mathrm{2}} }{\mathrm{2}}\:\:=\:\:\mathrm{2}\pi \\ $$$$\mathrm{A}\:\mathrm{of}\:\mathrm{second}\:\mathrm{big}\:\mathrm{semicircle}\:\:=\:\:\frac{\pi\mathrm{r}^{\mathrm{2}} }{\mathrm{2}}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\pi \\ $$$$\mathrm{But}\:\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{what}\:\mathrm{to}\:\mathrm{do}\:\mathrm{again} \\…

Prove-that-1-15-lt-1-2-3-4-5-6-99-100-lt-1-10-

Question Number 2001 by Fitrah last updated on 29/Oct/15 $${Prove}\:{that}\:: \\ $$$$\frac{\mathrm{1}}{\mathrm{15}}\:<\:\frac{\mathrm{1}}{\mathrm{2}}\:\centerdot\:\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{5}}{\mathrm{6}}\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\frac{\mathrm{99}}{\mathrm{100}}\:<\:\frac{\mathrm{1}}{\mathrm{10}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

if-1-tan-1-1-tan-2-1-tan-3-1-tan-44-1-tan-45-50-7-1-3-50-7-1-3-x-7-find-x-

Question Number 1999 by Fitrah last updated on 29/Oct/15 $${if}\: \\ $$$$\left(\mathrm{1}\:+\:{tan}\:\mathrm{1}°\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{2}°\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{3}°\right)…… \\ $$$$\left…..\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{44}°\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{45}°\right)\overset{} {\:}=\:\:\left\{\:\:\:\sqrt[{\mathrm{3}}]{\left(\sqrt{\mathrm{50}}\:+\:\mathrm{7}\right)}\:−\:\sqrt[{\mathrm{3}}]{\left(\sqrt{\mathrm{50}}−\mathrm{7}\right)}\:\overset{\left({x}\:−\:\mathrm{7}\right)} {\right\}} \\ $$$$\: \\ $$$${find}\:{x}\:=\:…? \\ $$ Answered by Yozzi…

Prove-that-if-p-gt-q-gt-0-and-x-0-then-1-p-x-p-p-1-1-1-q-x-q-q-1-1-

Question Number 1928 by Yozzi last updated on 24/Oct/15 $${Prove}\:{that},\:{if}\:{p}>{q}>\mathrm{0}\:{and}\:{x}\geqslant\mathrm{0},\:{then} \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{{p}}\left(\frac{{x}^{{p}} }{{p}+\mathrm{1}}−\mathrm{1}\right)\geqslant\frac{\mathrm{1}}{{q}}\left(\frac{{x}^{{q}} }{{q}+\mathrm{1}}−\mathrm{1}\right).\: \\ $$ Commented by Rasheed Soomro last updated on 24/Oct/15 $${Prove}\:{that},\:{if}\:{p}>{q}>\mathrm{0}\:{and}\:{x}\geqslant\mathrm{0},\:{then}…