Question Number 4219 by Yozzii last updated on 02/Jan/16 Answered by prakash jain last updated on 02/Jan/16 $${f}\:'\left(\theta\right)=\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left(\theta+\delta\theta\right)−{f}\left(\theta\right)}{\delta\theta} \\ $$$$\mathrm{If}\:\mathrm{limit}\:\mathrm{exits} \\ $$$$\Rightarrow\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left(\theta+\delta\theta\right)={f}\left(\theta\right)+\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\:'\left(\theta\right)\delta\theta…
Question Number 4216 by Rasheed Soomro last updated on 02/Jan/16 $$\boldsymbol{\mathrm{D}}\mathrm{etermine}\:\mathrm{a}\:\mathrm{triplet}\:\left(\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\right)\:\mathrm{of}\:\mathrm{real}\:\mathrm{numbers}\: \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{relation}\:\boldsymbol{\mathrm{a}}^{−\mathrm{1}} +\boldsymbol{\mathrm{b}}^{−\mathrm{1}} =\boldsymbol{\mathrm{c}}^{−\mathrm{1}} \mathrm{and}\:\:\mathrm{satisfying}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{conditions} \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}>\boldsymbol{\mathrm{c}}\:\wedge\:\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}>\boldsymbol{\mathrm{a}}\:\wedge\:\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{a}}>\boldsymbol{\mathrm{b}}\:. \\ $$ Terms of Service…
Question Number 135285 by mnjuly1970 last updated on 11/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{pre}−{calculus} \\ $$$$\:\:{if}\:\:\:\:\:\:\:{log}_{\mathrm{48}} ^{\mathrm{72}} +{log}_{\mathrm{54}} ^{\mathrm{12}} \:={k}\: \\ $$$$\:\:\:\:\:\:{then}\:\:{log}_{\:\mathrm{12}} ^{\:\mathrm{27}} \:\:=??? \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 135284 by mey3nipaba last updated on 11/Mar/21 $$\mathrm{2}^{{x}} +\mathrm{4}^{{x}} =\mathrm{9}^{{x}} .\:{Solve}\:{for}\:{x} \\ $$ Commented by mey3nipaba last updated on 12/Mar/21 $${I}\:{need}\:{help}\:{immediately}\:{please} \\ $$…
Question Number 69746 by jagannath19 last updated on 27/Sep/19 Commented by jagannath19 last updated on 27/Sep/19 $${answer}\:{with}\:{explanation} \\ $$ Answered by mr W last updated…
Question Number 69741 by ajfour last updated on 27/Sep/19 Commented by mr W last updated on 27/Sep/19 Commented by mr W last updated on 27/Sep/19…
Question Number 69738 by Therealsincro last updated on 27/Sep/19 $${Sarah}\:{dances}\:{everyday}\:{of}\:{the}\:{week}, \\ $$$${including}\:{saturdays}\:{and}\:{sundays}. \\ $$$${In}\:{november}\:\mathrm{2018},\:{Sarah}\:{had}\:{to}\:{miss} \\ $$$${a}\:{few}\:{days}.\:{To}\:{control}\:{her}\:{absences} \\ $$$${she}\:{marks}\:{the}\:{day}\:{she}\:{missed}\:{class} \\ $$$${with}\:{a}\:\boldsymbol{{x}}\:{on}\:{the}\:{calendar}. \\ $$$${She}\:{marked}\:{the}\:\mathrm{5}{th},\:\mathrm{21}{st}\:{and}\:\mathrm{27}{th} \\ $$$${of}\:{november}. \\…
Question Number 4203 by Yozzii last updated on 01/Jan/16 $${I}\:{have}\:{no}\:{formal}\:{background}\:{in}\: \\ $$$${number}\:{theory},\:{but}\:{I}'{m}\:{curious} \\ $$$${of}\:{how}\:{to}\:{find}\:{positive}\:{integer}\:{solutions}\: \\ $$$$\left({x},{y},{z}\right)\:{to}\:{the}\:{equation}\:{x}^{{n}} +{y}^{{n}} ={z}^{{n}} \:{for}\: \\ $$$${n}\in\mathbb{Z}^{−} .\:{Fermat}'{s}\:{last}\:{theorem}\:{led} \\ $$$${me}\:{to}\:{this}.\:{Tell}\:{me}\:{about}\:{the}\:{cases} \\…
Question Number 4199 by Yozzii last updated on 01/Jan/16 $${Let}\:{p}\in\mathbb{P}\:{and}\:{m}\in\mathbb{Z}^{+} . \\ $$$${Find}\:\left({p},{m}\right)\:{such}\:{that}\:{p}^{{m}−\mathrm{1}} \left({p}−\mathrm{1}\right)=\mathrm{146410}. \\ $$ Answered by Rasheed Soomro last updated on 01/Jan/16 $${p}^{{m}−\mathrm{1}}…
Question Number 4196 by Rasheed Soomro last updated on 31/Dec/15 $$\:\:\mathrm{Q}#\mathrm{4140}\:\mathrm{is}\:\mathrm{again}\:\mathrm{asked}\:\mathrm{with}\:\mathrm{following}\:\mathrm{changes}: \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{b}}\right), \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{c}}\right), \\ $$$$\boldsymbol{\mathrm{c}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{d}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{d}}\right),\: \\ $$$$\boldsymbol{\mathrm{d}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{a}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{a}}\right), \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{a}}',\boldsymbol{\mathrm{b}}',\boldsymbol{\mathrm{c}}'\:\mathrm{and}\:\boldsymbol{\mathrm{d}}'\:\mathrm{are}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{line} \\ $$$$\mathrm{segments}\:\boldsymbol{\mathrm{ab}},\:\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cd}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{da}}\:\mathrm{respectively}. \\ $$…