Question Number 89558 by peter frank last updated on 17/Apr/20 $${Show}\:{that}\:{difference} \\ $$$${of}\:{the}\:{focus}\:{distance} \\ $$$${of}\:{any}\:{point}\:{on}\:{hyperbola} \\ $$$${is}\:{equal}\:{to}\:{the}\:{length}\:{of} \\ $$$${the}\:{tranversed}\:{axis} \\ $$ Terms of Service Privacy…
Question Number 24023 by Tinkutara last updated on 11/Nov/17 $$\mathrm{Compounds}\:\mathrm{with}\:\mathrm{high}\:\mathrm{heat}\:\mathrm{of}\:\mathrm{formation} \\ $$$$\mathrm{are}\:\mathrm{less}\:\mathrm{stable}\:\mathrm{because} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{it}\:\mathrm{is}\:\mathrm{difficult}\:\mathrm{to}\:\mathrm{synthesize}\:\mathrm{them} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{energy}\:\mathrm{rich}\:\mathrm{state}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{instability} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{high}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to} \\ $$$$\mathrm{synthesize}\:\mathrm{them} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{molecules}\:\mathrm{of}\:\mathrm{such}\:\mathrm{compounds}\:\mathrm{are} \\ $$$$\mathrm{distorted} \\…
Question Number 24022 by Tinkutara last updated on 11/Nov/17 $$\mathrm{A}\:\mathrm{one}\:\mathrm{kg}\:\mathrm{ball}\:\mathrm{rolling}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth} \\ $$$$\mathrm{horizontal}\:\mathrm{surface}\:\mathrm{at}\:\mathrm{20}\:\mathrm{m}\:\mathrm{s}^{−\mathrm{1}} \:\mathrm{comes}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inclined}\:\mathrm{plane}\:\mathrm{making} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal}. \\ $$$$\mathrm{Calculate}\:\mathrm{K}.\mathrm{E}.\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{incline}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{up}\:\mathrm{the} \\ $$$$\mathrm{incline}\:\mathrm{will}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{roll}?\:\mathrm{Neglect} \\ $$$$\mathrm{friction}.…
Question Number 24010 by Tinkutara last updated on 11/Nov/17 $$\mathrm{Prove}\:\mathrm{that}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \centerdot\frac{{r}}{\:^{\mathrm{2}{n}} {C}_{{r}} }\:=\:\frac{{n}}{{n}\:+\:\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155083 by Tawa11 last updated on 25/Sep/21 Answered by physicstutes last updated on 25/Sep/21 $$\left(\mathrm{a}\right)\:{f}\left({x}\right)=\:\frac{\mathrm{2}}{{x}^{\mathrm{2}} }\:,\:{x}\:\neq\mathrm{0} \\ $$$${f}\left({x}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{differentiable}\:\mathrm{on}\:−\mathrm{1}<{x}<\mathrm{1} \\ $$$$\left(\mathrm{b}\right)\:{g}\left({x}\right)=\mid{x}\mid\:\mathrm{is}\:\mathrm{not}\:\mathrm{differentiable}\:\mathrm{on} \\ $$$$−\mathrm{1}<{x}<\mathrm{1} \\…
Question Number 155079 by mathdanisur last updated on 24/Sep/21 Commented by talminator2856791 last updated on 25/Sep/21 $$\:\mathrm{what}\:\mathrm{is}\:\mathrm{meant}\:\mathrm{by}\:\mathrm{k}\:=\:\mathrm{1},\mathrm{n}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 89540 by M±th+et£s last updated on 17/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{cos}\left({x}^{\mathrm{2}} \right)−\mathrm{1}+\frac{{x}^{\mathrm{4}} }{\mathrm{2}}}{{x}^{\mathrm{2}} \left({x}−{sin}\left({x}\right)\right)^{\mathrm{2}} } \\ $$ Commented by abdomathmax last updated on 17/Apr/20 $${let}\:{f}\left({x}\right)=\frac{{cos}\left({x}^{\mathrm{2}}…
Question Number 155075 by mr W last updated on 24/Sep/21 Commented by mr W last updated on 24/Sep/21 $${with}\:{exactly}\:{n}\:{turns}.\:\left(\mathrm{1}\leqslant{n}\leqslant\mathrm{15}\right) \\ $$$${the}\:{example}\:{above}\:{shows}\:{a}\:{route} \\ $$$${with}\:\mathrm{7}\:{turns}. \\ $$…
Question Number 155069 by mathdanisur last updated on 24/Sep/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{3} \\ $$$$\mathrm{and}\:\:\mathrm{0}\leqslant\boldsymbol{\lambda}\leqslant\mathrm{1}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}}{\mathrm{y}^{\mathrm{2}} +\lambda}\:+\:\frac{\mathrm{y}}{\mathrm{z}^{\mathrm{2}} +\lambda}\:+\:\frac{\mathrm{z}}{\mathrm{x}^{\mathrm{2}} +\lambda}\:\geqslant\:\frac{\mathrm{3}}{\lambda+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 89534 by mathocean1 last updated on 17/Apr/20 Commented by abdomathmax last updated on 17/Apr/20 $$\left.\mathrm{1}\right)\:{we}\:{have}\:{e}_{\mathrm{1}} \left(\mathrm{2},\mathrm{3}\right)\:\:{e}_{\mathrm{2}} \left(\mathrm{1},\mathrm{2}\right)\:{and}\:{e}_{\mathrm{3}} \left(\mathrm{4},\mathrm{5}\right) \\ $$$${let}\:{find}\:\:{x}\:{and}\:{y}\:/{e}_{\mathrm{3}} ={xe}_{\mathrm{1}} \:+{ye}_{\mathrm{2}} \:\Rightarrow…