Question Number 120855 by mnjuly1970 last updated on 03/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:{elementary}\:\:{calculus}… \\ $$$$\:\:::\:\alpha,\beta\:{are}\:{roots}\:{of}\:\:{equation} \\ $$$$\:\:\:\:\:{of}\::\:{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:{define}\:::\:{t}_{{n}} =\alpha^{{n}} −\beta^{{n}} \:\left({n}\geqslant\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:{then}\:\:{evaluate}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{A}=\frac{{t}_{\mathrm{10}} −\mathrm{2}{t}_{\mathrm{8}}…
Question Number 55312 by Joel578 last updated on 21/Feb/19 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{system} \\ $$$$\begin{cases}{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:{z}}\\{\mathrm{2}{x}\:+\:\mathrm{2}{y}\:+\:{z}\:=\:{k}}\end{cases} \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{xy}\:+\:{zk}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{system} \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{unique}\:\mathrm{solution}\:\mathrm{is}\:… \\ $$ Answered by mr W last…
Question Number 120839 by bramlexs22 last updated on 03/Nov/20 Answered by mindispower last updated on 03/Nov/20 $${x}\in\mathbb{Z}−\left\{\mathrm{1}\right\} \\ $$$$\Rightarrow\underset{{k}=\mathrm{2}} {\overset{{x}−\mathrm{1}} {\sum}}\frac{{x}−{k}}{{x}−\mathrm{1}}=\mathrm{5} \\ $$$$\Rightarrow\left(\frac{{x}−\mathrm{2}+\mathrm{1}}{{x}−\mathrm{1}}\right)\left(\frac{{x}−\mathrm{2}}{\mathrm{2}}\right)=\mathrm{5} \\ $$$$\Rightarrow\mathrm{10}\left({x}−\mathrm{1}\right)=\left({x}−\mathrm{2}\right)\left({x}−\mathrm{1}\right)=\mathrm{0}…
Question Number 55300 by Tawa1 last updated on 20/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 21/Feb/19 $${p}=\mathrm{2}\left(\mathrm{2}{x}+{x}\right) \\ $$$$\frac{{dp}}{{dt}}=\mathrm{6}\frac{{dx}}{{dt}} \\ $$$${A}=\mathrm{2}{x}×{x}=\mathrm{2}{x}^{\mathrm{2}} \\ $$$$\frac{{dA}}{{dt}}=\mathrm{4}{x}×\frac{{dx}}{{dt}} \\ $$$$\mathrm{18}=\mathrm{4}×\mathrm{1}×\frac{{dx}}{{dt}}\:\left[\mathrm{2}{x}=\mathrm{2}\:{length}\:{given}\right]…
Question Number 55284 by Mikael_Marshall last updated on 20/Feb/19 $$\mathrm{5}^{{x}−\mathrm{2}} −\mathrm{5}^{{x}} +\mathrm{5}^{{x}+\mathrm{1}} =\mathrm{505} \\ $$ Commented by Kunal12588 last updated on 20/Feb/19 $$\left(\mathrm{5}^{{x}} ×\mathrm{5}^{−\mathrm{2}} \right)−\mathrm{5}^{{x}}…
Question Number 120809 by liberty last updated on 02/Nov/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{found}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way} \\ $$$$\mathrm{that}\:\mathrm{any}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:{a}\:\mathrm{and}\:{b}\:\left(\:{a}\neq{b}\right)\: \\ $$$$\mathrm{satisfy}\:\mathrm{the}\:\mathrm{next}\:\mathrm{inequality}\:\mid{a}−{b}\mid\geqslant\frac{{ab}}{\mathrm{100}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 186329 by ajfour last updated on 03/Feb/23 Answered by ajfour last updated on 03/Feb/23 $${Cubic}\:{curve}:\:{y}={x}^{\mathrm{3}} −{x} \\ $$$${Parabola}:\:\:{x}={h}+\left({y}−{k}\right)^{\mathrm{2}} \\ $$$${x}={h}+\left({p}−{k}\right)^{\mathrm{2}} \\ $$$${p}^{\mathrm{3}} −{p}={c}…
Question Number 55258 by 7008984239 last updated on 20/Feb/19 $$\mathrm{3}{x}+\mathrm{5}{y}=?_{} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 186330 by Rupesh123 last updated on 03/Feb/23 Commented by MJS_new last updated on 03/Feb/23 $$\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 120780 by mathace last updated on 02/Nov/20 $${solve}\:{x}^{\mathrm{2}^{{x}} } =−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by Anuragkar last updated on 02/Nov/20 $${Use}\:\:{Lambert}\:{W}\:{function}\:{to}\:{work}\:{it}\:{out}…… \\ $$ Commented…