Question Number 44543 by ajfour last updated on 01/Oct/18 $${If}\:\:{y}\:={f}\left({x}\right)\:=\:{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:\:{at}\:{some}\:{x},\:{say}\:\:{x}=\:{p} \\ $$$$\int_{\mathrm{0}} ^{\:\:{p}} {ydx}\:=\:{y}\left({p}\right)=\:{y}\:'\left({p}\right)\:=\:{y}\:''\left({p}\right)=\:{p}\:, \\ $$$${then}\:{find}\:\boldsymbol{{p}}\:. \\ $$ Commented by MrW3 last…
Question Number 175593 by Shrinava last updated on 03/Sep/22 $$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{a}}&{\mathrm{log}\left(\mathrm{a}^{\boldsymbol{\mathrm{a}}} \right)}\\{\mathrm{1}}&{\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}}\:\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{8}}}\:\centerdot\:\mathrm{log}\left(\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}\right)}&{}\\{\mathrm{1}}&{\mathrm{b}}&{\mathrm{log}\left(\mathrm{b}^{\boldsymbol{\mathrm{b}}} \right)}\end{vmatrix}\geqslant\:\mathrm{0} \\ $$ Commented by Rasheed.Sindhi…
Question Number 44502 by Tip Top last updated on 30/Sep/18 $$\mathrm{If}\:\mathrm{a}>\mathrm{b},\mathrm{and}\:\mathrm{c}>\mathrm{d},\mathrm{prove}\:\mathrm{that}\:\mathrm{a}−\mathrm{c}\:\mathrm{may}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than}, \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{or}\:\mathrm{less}\:\mathrm{than}\:\mathrm{b}−\mathrm{d}. \\ $$$$ \\ $$ Answered by MrW3 last updated on 30/Sep/18 $${a}={b}+\delta,\:\delta>\mathrm{0}…
Question Number 175554 by Linton last updated on 02/Sep/22 $${x}^{\sqrt{{x}}} =\sqrt{{x}^{{x}} } \\ $$$${find}\:{x} \\ $$ Answered by mr W last updated on 02/Sep/22 $${x}=\mathrm{0}…
Question Number 175548 by Rasheed.Sindhi last updated on 02/Sep/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\begin{array}{|c|}{\overset{\underset{−} {\overline {\mid\bullet\mid}}} {\:\begin{array}{|c|}{\underset{} {\overset{} {\mathrm{2}+\mathrm{424}+\mathrm{44244}+\mathrm{4442444}+\centerdot\centerdot\centerdot{n}\:{terms}=?_{} ^{} }}}\\\hline\end{array}_{} ^{} }}\\\hline\end{array} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$…
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Question Number 44444 by peter frank last updated on 29/Sep/18 $${simplify}\:\:\:\:\sqrt{\left(\mathrm{4}{x}^{\mathrm{2}} {y}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\mathrm{8}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)^{\mathrm{4}} } \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18…
Question Number 175505 by EnterUsername last updated on 31/Aug/22 $${N}=\mathrm{64990691606209}\:\mathrm{is}\:\mathrm{a}\:\mathrm{semi}-\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{That}\:\mathrm{is},\:{N}={pq}\:\mathrm{where}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{prime}\:\mathrm{numbers}. \\ $$$$\mathrm{Find}\:{p}\:\mathrm{and}\:{q}: \\ $$ Commented by Ar Brandon last updated on 31/Aug/22 #include <stdio.h> int main(void) { long long i = 2, N = 64990691606209; for (; (N % i) != 0; i++); printf("p = %lld, q = %lld", i, N/i); return 0; }…
Question Number 109954 by Study last updated on 26/Aug/20 $$!\mathrm{3}=???? \\ $$ Answered by mathdave last updated on 26/Aug/20 $${solution} \\ $$$${recall}\:{that} \\ $$$$!{x}={x}!\underset{{n}=\mathrm{0}} {\overset{{x}}…
Question Number 175490 by Linton last updated on 31/Aug/22 $${solve} \\ $$$${f}\left({x}\right){f}\left({y}\right)=\:{f}\left({x}+{y}\right)+{xy} \\ $$$${f}:\mathbb{R}\Rightarrow\mathbb{R} \\ $$ Answered by ajfour last updated on 31/Aug/22 $${f}\left({x}\right){f}\left(\mathrm{0}\right)={f}\left({x}+\mathrm{0}\right)+\mathrm{0} \\…