Question Number 135795 by benjo_mathlover last updated on 16/Mar/21 $${What}\:{the}\:{value}\:{of}\:\left(\mathrm{1}−\mathrm{cot}\:\mathrm{23}°\right)\left(\mathrm{1}−\mathrm{cot}\:\mathrm{22}°\right). \\ $$ Answered by MJS_new last updated on 16/Mar/21 $$\left(\mathrm{1}−\mathrm{cot}\:\left(\frac{\mathrm{45}}{\mathrm{2}}−{x}\right)\right)\left(\mathrm{1}−\mathrm{cot}\:\left(\frac{\mathrm{45}}{\mathrm{2}}+{x}\right)\right)=\mathrm{2} \\ $$ Answered by liberty…
Question Number 70256 by behi83417@gmail.com last updated on 02/Oct/19 Commented by behi83417@gmail.com last updated on 02/Oct/19 $$\mathrm{ABCD},\mathrm{is}\:\mathrm{a}\:\mathrm{squre}. \\ $$$$\mathrm{F},\mathrm{is}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{AC}. \\ $$$$\mathrm{1}.\mathrm{if}:\:\:\:\boldsymbol{\mathrm{DF}}=\mathrm{4},\boldsymbol{\mathrm{EB}}=\mathrm{3},\mathrm{area}\:\mathrm{of}:\boldsymbol{\mathrm{ACE}}=? \\ $$$$\mathrm{2}.\mathrm{if}:\boldsymbol{\mathrm{AC}},\mathrm{be}\:\mathrm{diagonal},\mathrm{but}\:\mathrm{AF}\neq\mathrm{FC}\:\mathrm{and}: \\ $$$$\mathrm{DF}=\mathrm{4},\mathrm{FE}=\mathrm{2},\mathrm{EB}=\mathrm{3},\mathrm{now}\:\mathrm{find}\:\mathrm{area}\:\mathrm{of}:\mathrm{ACE}.…
Question Number 4720 by prakash jain last updated on 29/Feb/16 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{counterexample}\:\mathrm{that}\:\mathrm{if}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{number}\: \\ $$$$\mathrm{of}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series}\:\mathrm{are}\:\mathrm{given}\:\mathrm{then}\:\mathrm{a}\:\mathrm{infinite}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{formulas}\:\mathrm{for}\:{n}^{{th}} \:\mathrm{term}\:\mathrm{exists}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{finite}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}. \\ $$$$\mathrm{For}\:\mathrm{example} \\ $$$$\mathrm{33},\mathrm{9},\mathrm{33},\mathrm{44},? \\ $$$$\mathrm{4}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{given}\:\mathrm{if}\:{a}_{{n}} ={f}\left({n}\right)\:\mathrm{then}\:\mathrm{there}\:\mathrm{are}…
Question Number 4719 by prakash jain last updated on 29/Feb/16 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}} }{{n}}\leqslant\sqrt{\frac{{a}_{\mathrm{1}} ^{\mathrm{2}} +{a}_{\mathrm{2}} ^{\mathrm{2}} +…+{a}_{{n}} ^{\mathrm{2}} }{{n}}} \\ $$$$\mathrm{with}\:\mathrm{equality}\:\mathrm{holding}\:\mathrm{iff}\:{a}_{\mathrm{1}} ={a}_{\mathrm{2}}…
Question Number 135791 by benjo_mathlover last updated on 16/Mar/21 $${If}\:{x}^{\mathrm{2}} +\left(\mathrm{tan}\:\theta+\mathrm{cot}\:\theta\right){x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$${has}\:{two}\:{real}\:{solutions}\: \\ $$$$\left\{\:\mathrm{2}−\sqrt{\mathrm{3}}\:,\:\mathrm{2}+\sqrt{\mathrm{3}}\:\right\},\:{find}\:\begin{cases}{\mathrm{sin}\:\theta}\\{\mathrm{cos}\:\theta}\end{cases}\:. \\ $$ Answered by EDWIN88 last updated on 17/Mar/21 $$\mathrm{By}\:\mathrm{Vieta}'\mathrm{s}\:\Rightarrow\:\mathrm{x}_{\mathrm{1}}…
Question Number 70252 by Shamim last updated on 02/Oct/19 $$\mathrm{If},\:\mathrm{log}\:\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{6}\:\mathrm{and}\:\mathrm{log}\:\mathrm{14x}^{\mathrm{8y}} \:=\:\mathrm{3}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x},\:\mathrm{y}. \\ $$ Answered by MJS last updated on 02/Oct/19 $$\mathrm{log}\:{x}^{{y}} =\mathrm{6}\:\Rightarrow\:{y}\mathrm{log}\:{x}\:=\mathrm{6}…
Question Number 135790 by benjo_mathlover last updated on 16/Mar/21 $${Find}\:{the}\:{component}\:{form}\:{of} \\ $$$${the}\:{vector}\:{that}\:{reprecents}\:{the} \\ $$$${velocity}\:{of}\:{an}\:{airplane}\:{descending} \\ $$$${at}\:{speed}\:{of}\:\mathrm{150}\:{miles}\:{per}\:{hour} \\ $$$${at}\:{angle}\:\mathrm{20}°\:{below}\:{the}\:{horizontal} \\ $$ Terms of Service Privacy Policy…
Question Number 70253 by oyemi kemewari last updated on 02/Oct/19 Commented by mathmax by abdo last updated on 02/Oct/19 $${let}\:{I}\:=\int\:{u}^{\mathrm{2}} \sqrt{{u}^{\mathrm{2}} −\mathrm{2}}{du}\:{changement}\:{u}=\sqrt{\mathrm{2}}{ch}\left({x}\right)\:{give} \\ $$$${I}\:=\int\:\mathrm{2}{ch}^{\mathrm{2}} \left({x}\right)\sqrt{\mathrm{2}}{sh}\left({x}\right)\sqrt{\mathrm{2}}{sh}\left({x}\right){dx}…
Question Number 4716 by 123456 last updated on 28/Feb/16 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{T}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{does}? \\ $$$$\frac{\mathrm{1}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}{f}\left({t}\right){dt}\leqslant\sqrt{\frac{\mathrm{1}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}\left[{f}\left({t}\right)\right]^{\mathrm{2}} {dt}}\leqslant\frac{\mathrm{1}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}\mid{f}\left({t}\right)\mid{dt} \\ $$ Commented by…
Question Number 135785 by Chhing last updated on 16/Mar/21 $$ \\ $$$$\:\:\mathrm{Solve}\:\mathrm{differential}\:\mathrm{equations} \\ $$$$\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{y}'+\mathrm{6xy}=\mathrm{lnx} \\ $$$$\:\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$ Terms of Service Privacy…