Question Number 18440 by tawa tawa last updated on 21/Jul/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83966 by Rio Michael last updated on 08/Mar/20 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{complex}\:\mathrm{number}\:{z},\:\mathrm{if}\: \\ $$$$\:\mid{z}\mid\:<\:\mathrm{1},\:\mathrm{then}\:\mathrm{Re}\left({z}\:+\:\mathrm{1}\right)\:>\:\mathrm{0} \\ $$ Answered by mr W last updated on 08/Mar/20 $${let}\:{z}={a}+{bi} \\…
Question Number 18429 by tawa tawa last updated on 21/Jul/17 $$\mathrm{30cm}^{\mathrm{3}} \:\mathrm{of}\:\mathrm{hydrogen}\:\mathrm{at}\:\mathrm{s}.\mathrm{t}.\mathrm{p}\:\mathrm{combines}\:\mathrm{with}\:\mathrm{20cm}^{\mathrm{3}} \:\mathrm{of}\:\mathrm{oxygen}\:\mathrm{to}\:\mathrm{form}\:\mathrm{steam}\: \\ $$$$\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation},\:\:\mathrm{2H}_{\mathrm{2}} \:\left(\mathrm{g}\right)\:+\:\mathrm{O}_{\mathrm{2}} \:\left(\mathrm{g}\right)\:\rightarrow\:\mathrm{2H}_{\mathrm{2}} \mathrm{O}\:\left(\mathrm{g}\right). \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{total}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{gaseous}\:\mathrm{mixture}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{reaction}. \\ $$ Commented by tawa…
Question Number 83964 by Rio Michael last updated on 08/Mar/20 $$\mathrm{The}\:\mathrm{graph}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:=\:\frac{{a}\:+\:{bx}}{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)} \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{turning}\:\mathrm{point}\:\mathrm{at}\:{P}\left(\mathrm{2},−\mathrm{1}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{and}\:{b}\: \\ $$$$\mathrm{and}\:\mathrm{hence},\mathrm{sketch}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{showing}\:\mathrm{clearly}\:\mathrm{the} \\ $$$$\mathrm{turning}\:\mathrm{points},\:\mathrm{asympototes}\:\mathrm{and}\:\mathrm{intercept}\left(\mathrm{s}\right)\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{axes}. \\ $$ Answered by…
Question Number 18428 by tawa tawa last updated on 20/Jul/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83965 by Rio Michael last updated on 08/Mar/20 $$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove}\left(\mathrm{with}\:\mathrm{counter}−\mathrm{example}\right)\:\mathrm{that} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{For}\:\mathrm{all}\:\mathrm{two}\:\mathrm{dimensional}\:\mathrm{vectors}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}, \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{a}}.\boldsymbol{\mathrm{b}}\:=\:\boldsymbol{\mathrm{a}}.\:\boldsymbol{\mathrm{c}}\:\Rightarrow\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{c}}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{For}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}\:{a},{b}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{{a}\:+{b}}{\mathrm{2}}\:\geqslant\:\sqrt{{ab}}\: \\ $$ Commented by mr W…
Question Number 18415 by tawa tawa last updated on 20/Jul/17 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnetic}\:\mathrm{field}\:\mathrm{produced}\:\mathrm{at}\:\mathrm{ground}\:\mathrm{level}\:\mathrm{by}\:\mathrm{a}\:\mathrm{15A}\:\mathrm{current} \\ $$$$\mathrm{flowing}\:\mathrm{in}\:\mathrm{a}\:\mathrm{long}\:\mathrm{horizontal}\:\mathrm{wire}\:\mathrm{suspended}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of}\:\mathrm{7}.\mathrm{5m} \\ $$ Commented by tawa tawa last updated on 20/Jul/17 $$\mathrm{please}\:\mathrm{help}. \\…
Question Number 18411 by Tinkutara last updated on 20/Jul/17 $$\mathrm{A}\:\mathrm{glass}\:\mathrm{bulb}\:\mathrm{contains}\:\mathrm{2}.\mathrm{24}\:\mathrm{L}\:\mathrm{of}\:\mathrm{H}_{\mathrm{2}} \:\mathrm{and} \\ $$$$\mathrm{1}.\mathrm{12}\:\mathrm{L}\:\mathrm{of}\:\mathrm{D}_{\mathrm{2}} \:\mathrm{at}\:\mathrm{S}.\mathrm{T}.\mathrm{P}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{fully}\:\mathrm{evacuated}\:\mathrm{bulb}\:\mathrm{by}\:\mathrm{a}\:\mathrm{stopcock} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{small}\:\mathrm{opening}.\:\mathrm{The}\:\mathrm{stopcock}\:\mathrm{is} \\ $$$$\mathrm{opened}\:\mathrm{for}\:\mathrm{sometime}\:\mathrm{and}\:\mathrm{then}\:\mathrm{closed}. \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{bulb}\:\mathrm{now}\:\mathrm{contains}\:\mathrm{0}.\mathrm{1}\:\mathrm{g}\:\mathrm{of}\:\mathrm{D}_{\mathrm{2}} . \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{composition}…
Question Number 149467 by fotosy2k last updated on 05/Aug/21 Answered by mindispower last updated on 05/Aug/21 $${ln}\left({a}_{{n}} \right)={nln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$$${ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\Rightarrow\mathrm{0}\leqslant{ln}\left({a}_{{n}} \right)\leqslant{n}.\frac{\mathrm{1}}{{n}}\Rightarrow\mathrm{0}\leqslant{ln}\left({a}_{{n}} \right)\leqslant\mathrm{1} \\…
Question Number 18384 by Tinkutara last updated on 19/Jul/17 $$\mathrm{Let}\:{a},\:{b},\:{c}\:\in\:{R},\:{a}\:\neq\:\mathrm{0},\:\mathrm{such}\:\mathrm{that}\:{a}\:\mathrm{and} \\ $$$$\mathrm{4}{a}\:+\:\mathrm{3}{b}\:+\:\mathrm{2}{c}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{sign}.\:\mathrm{Show} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{can} \\ $$$$\mathrm{not}\:\mathrm{have}\:\mathrm{both}\:\mathrm{roots}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{1},\:\mathrm{2}\right). \\ $$ Answered by Tinkutara last…