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Category: Geometry

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}…

Question-67430

Question Number 67430 by TawaTawa last updated on 27/Aug/19 Commented by MJS last updated on 27/Aug/19 $$\mathrm{coordinate}\:\mathrm{method} \\ $$$$\mathrm{turn}\:\mathrm{the}\:\mathrm{triangle}\:\rightarrow\:{CA}\:\mathrm{is}\:\mathrm{the}\:\mathrm{base} \\ $$$$\mathrm{side}\:\mathrm{length}\:={s} \\ $$$${s}=\mathrm{8}+{x}\:\Rightarrow\:{x}={s}−\mathrm{8} \\ $$$${C}=\begin{pmatrix}{−\frac{{s}}{\mathrm{2}}}\\{\mathrm{0}}\end{pmatrix}\:\:{A}=\begin{pmatrix}{\frac{{s}}{\mathrm{2}}}\\{\mathrm{0}}\end{pmatrix}\:\:{B}=\begin{pmatrix}{\mathrm{0}}\\{\frac{\sqrt{\mathrm{3}}{s}}{\mathrm{2}}}\end{pmatrix}…

Question-67422

Question Number 67422 by mr W last updated on 27/Aug/19 Commented by Prithwish sen last updated on 27/Aug/19 $$\bigtriangleup\mathrm{AMN}\:\mathrm{is}\:\mathrm{an}\:\mathrm{isoceles}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{AM}=\mathrm{AN} \\ $$$$\mathrm{AM}+\mathrm{BM}=\:\mathrm{AN}+\mathrm{D}^{'} \mathrm{N}=\mathrm{16} \\ $$$$\mathrm{Area}\:\mathrm{ABMND}^{'} =\:\mathrm{Area}\:\mathrm{of}\:\mathrm{ABCD}\:−\mathrm{Area}\:\mathrm{of}\:\bigtriangleup\mathrm{AMN}.…

Question-132869

Question Number 132869 by syamilkamil1 last updated on 17/Feb/21 Commented by syamilkamil1 last updated on 17/Feb/21 $${what}\:{is}\:{the}\:{radius}\:{of}\:{the}\:{circle}\:,\:{if}\:{length}\:{the}\:{square}\:\mathrm{2}\:{centimetres}? \\ $$ Commented by bramlexs22 last updated on…

how-0-1-

Question Number 1740 by tabrez8590@gmail last updated on 11/Sep/15 $${how}\:\:\mathrm{0}!=\mathrm{1} \\ $$ Commented by 123456 last updated on 11/Sep/15 $$\mathrm{1}!=\mathrm{1}\centerdot\mathrm{0}! \\ $$$$\mathrm{so}\:\mathrm{for}\:\mathrm{it}\:\mathrm{work}\:\mathrm{to}\:\mathrm{1}\:\mathrm{them}\:\mathrm{0}!=\mathrm{1} \\ $$ Answered…

Question-67254

Question Number 67254 by TawaTawa last updated on 24/Aug/19 Commented by Rasheed.Sindhi last updated on 24/Aug/19 $$\:\:\:\:\:{Analytical}\:{Method} \\ $$$${x}-{axis}:{Horizanal}\:{Chord} \\ $$$${y}-{axis}:{Vertical}\:{Chord} \\ $$$${Three}\:{points}\:{on}\:{the}\:{circle}: \\ $$$$\:{A}\left(\mathrm{6},\mathrm{0}\right),{B}\left(−\mathrm{2},\mathrm{0}\right)\:\&\:{C}\left(\mathrm{0},−\mathrm{3}\right)…