Question Number 134670 by benjo_mathlover last updated on 06/Mar/21 $$\mid\:\mathrm{x}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:\mid\:=\:\sqrt{\mathrm{2}}\:\left(\mathrm{2x}^{\mathrm{2}} −\mathrm{1}\:\right) \\ $$$$\mathrm{find}\:\mathrm{solution} \\ $$ Answered by EDWIN88 last updated on 06/Mar/21 $$\left(\mathrm{1}\right)\:\mathrm{1}−\mathrm{x}^{\mathrm{2}} \:\geqslant\:\mathrm{0}\:\Rightarrow\:−\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{1}…
Question Number 69111 by Fawole last updated on 20/Sep/19 Commented by Rasheed.Sindhi last updated on 20/Sep/19 $$\left(\mathrm{2},\mathrm{11}\right),\left(\mathrm{11},\mathrm{2}\right),\left(\mathrm{5},\mathrm{10}\right)\:\&\:\left(\mathrm{10},\mathrm{5}\right). \\ $$ Commented by Fawole last updated on…
Question Number 69082 by Henri Boucatchou last updated on 19/Sep/19 $$\boldsymbol{{Solve}}\:\:\boldsymbol{{x}}^{\mathrm{2}} \:=\:\mathrm{16}^{\boldsymbol{{x}}} \\ $$ Commented by MJS last updated on 19/Sep/19 $${f}\left({x}\right)=\mathrm{16}^{{x}} −{x}^{\mathrm{2}} \\ $$$$…
Question Number 69073 by necxxx last updated on 19/Sep/19 $${A}\:{man}\:{wants}\:{to}\:{shear}\:\mathrm{17}\:{cars}\:{between} \\ $$$${his}\:\mathrm{3}\:{children}\:{in}\:{the}\:{ratio}\:\mathrm{1}:\mathrm{2},\:\mathrm{1}:\mathrm{3},\:\mathrm{1}:\mathrm{9} \\ $$$${respectively}.{How}\:{will}\:{he}\:{go}\:{about}\:{it}? \\ $$ Commented by necxxx last updated on 19/Sep/19 $${please}\:{help} \\…
Question Number 134553 by liberty last updated on 05/Mar/21 $$ \\ $$If three numbers are in Arithmetic progression prove that the square of middle number…
Question Number 3463 by prakash jain last updated on 13/Dec/15 $$\mathrm{A}\:\mathrm{car}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{and}\:\mathrm{uniformly} \\ $$$$\mathrm{accelerates}\:\mathrm{for}\:\mathrm{1}\:\mathrm{km},\:\mathrm{travels}\:\mathrm{with}\:\mathrm{uniform} \\ $$$$\mathrm{velocity}\:\mathrm{for}\:\mathrm{98}\:\mathrm{km}\:\mathrm{and}\:\mathrm{brakes}\:\mathrm{and}\:\mathrm{stop} \\ $$$$\mathrm{after}\:\mathrm{travelling}\:\mathrm{another}\:\mathrm{1}\:\mathrm{km}. \\ $$$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{above}\:\mathrm{experiment}\:\mathrm{being}\:\mathrm{done} \\ $$$$\mathrm{on}\:\mathrm{2}\:\mathrm{different}\:\mathrm{roads}\:\mathrm{1st}\:\mathrm{roads}\:\mathrm{has}\:\mathrm{higher} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{for}\:\mathrm{car}\:\mathrm{for}\:\mathrm{all}\:\mathrm{types} \\ $$$$\mathrm{than}\:\mathrm{2nd}\:\mathrm{road}.…
Can-someone-show-me-how-i-x-a-v-k-0-v-v-k-x-v-k-a-k-ii-Does-k-0-v-v-k-x-v-k-a-k-k-0-v-v-k-x-k-a-v-k-
Question Number 3411 by Filup last updated on 13/Dec/15 $$\mathrm{Can}\:\mathrm{someone}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}: \\ $$$$\left({i}\right)\:\:\:\:\left({x}+{a}\right)^{{v}} =\underset{{k}=\mathrm{0}} {\overset{{v}} {\sum}}\begin{pmatrix}{{v}}\\{{k}}\end{pmatrix}\:{x}^{{v}−{k}} {a}^{{k}} \\ $$$$\left({ii}\right)\:\:\mathrm{Does}: \\ $$$$\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{v}} {\sum}}\begin{pmatrix}{{v}}\\{{k}}\end{pmatrix}\:{x}^{{v}−{k}} {a}^{{k}} =\underset{{k}=\mathrm{0}} {\overset{{v}}…
Question Number 3385 by Filup last updated on 12/Dec/15 $$\mathrm{let}: \\ $$$$\:\:\:\:\:\:\:\:{S}=\underset{{i}={a}} {\overset{{n}} {\sum}}{x}_{{i}} \\ $$$$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\frac{{d}}{{dx}}\left(\underset{{i}={a}} {\overset{{n}} {\sum}}{x}_{{i}} \right)=\underset{{i}={a}} {\overset{{n}} {\sum}}\left(\frac{{d}}{{dx}}\left\{{x}_{{i}} \right\}\right) \\…
Question Number 68825 by peter frank last updated on 15/Sep/19 Answered by mind is power last updated on 16/Sep/19 $${dx}\left(\mathrm{1}+{e}^{\frac{{x}}{{y}}} \right)+{e}^{\frac{{x}}{{y}}} \left(\mathrm{1}−\frac{{x}}{{y}}\right){dy} \\ $$$${p}=\mathrm{1}+{e}^{\frac{{x}}{{y}}} \\…
Question Number 3275 by Filup last updated on 09/Dec/15 $$\mathrm{Prove}\:\mathrm{to}\:\mathrm{me}\:\mathrm{that}\:\mathrm{2}\:\mathrm{is}\:\mathrm{the}\:{only}\:\mathrm{even} \\ $$$$\mathrm{prime}\:\mathrm{number} \\ $$ Commented by Filup last updated on 09/Dec/15 $$\mathrm{For}\:\mathrm{prime}\:{P}\in\mathbb{P} \\ $$$$\mathrm{if}\:\:{P}=\frac{{x}}{{y}} \\…