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 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 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 18428 by tawa tawa last updated on 20/Jul/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18426 by Tinkutara last updated on 20/Jul/17 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{2}\:\mathrm{cot}\:\mathrm{2}{x}\:−\:\mathrm{3}\:\mathrm{cot}\:\mathrm{3}{x}\:=\:\mathrm{tan}\:\mathrm{2}{x} \\ $$$$\mathrm{has} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Two}\:\mathrm{solutions}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{One}\:\mathrm{solution}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{No}\:\mathrm{solution}\:\mathrm{in}\:\left(−\infty,\:\infty\right) \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Three}\:\mathrm{solution}\:\mathrm{in}\:\left(\mathrm{0},\:\pi\right) \\ $$ Terms of Service…
Question Number 83960 by john santu last updated on 08/Mar/20 $$\int\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$ Commented by mathmax by abdo last updated on 08/Mar/20 $${I}\:=\int\:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −{x}}}{dx}\:\Rightarrow\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{2}{x}−\mathrm{1}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 149498 by peter frank last updated on 05/Aug/21 $$ \\ $$$$\int\frac{{px}+{q}}{\:\sqrt{{x}^{\mathrm{2}} +{r}^{\mathrm{2}} }} \\ $$ Answered by MJS_new last updated on 05/Aug/21 $$\int\frac{{px}+{q}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 83961 by mathmax by abdo last updated on 08/Mar/20 $${find}\:{I}\:=\int\:{e}^{−{x}} \:{cos}^{\mathrm{4}} {xdx}\:\:{and}\:{J}\:=\int\:{e}^{−{x}} \:{sin}^{\mathrm{4}} \:{xdx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 83956 by jagoll last updated on 08/Mar/20 $$\mathrm{for}\:\mathrm{x}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{3x}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{2019}\right)\:.\: \\ $$ Commented by mr W last updated on 08/Mar/20 $$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{3x}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)\:\:\:…\left({i}\right)…
Question Number 18416 by Tinkutara last updated on 20/Jul/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{which}\:\mathrm{satisfies} \\ $$$$\frac{\left({x}\:−\:\mathrm{5}\right)^{\mathrm{10}} \left({x}\:−\:\mathrm{13}\right)^{\mathrm{20}} \left({x}\:−\:\mathrm{19}\right)^{\mathrm{13}} }{\left({x}\:−\:\mathrm{10}\right)^{\mathrm{18}} \left({x}\:−\:\mathrm{25}\right)^{\mathrm{19}} }\:\geqslant\:\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{2}\:\leqslant\:{x}\:\leqslant\:\mathrm{30}\:\mathrm{are} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{23} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{24}…