Question Number 194563 by pete last updated on 10/Jul/23 $$\mathrm{A}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{12kg}\:\mathrm{rests}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{inclined} \\ $$$$\mathrm{plane}\:\mathrm{which}\:\mathrm{is}\:\mathrm{6m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{1m}\:\mathrm{high}. \\ $$$$\mathrm{The}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{light}\:\mathrm{inextensible} \\ $$$$\mathrm{string}\:\mathrm{which}\:\mathrm{passes}\:\mathrm{over}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{pulley} \\ $$$$\mathrm{fixed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{to}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of} \\ $$$$\mathrm{4kg}\:\mathrm{which}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{freely}.\:\mathrm{With}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{taut},\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{rest}. \\ $$$$\mathrm{Using}\:\mathrm{Polya}\:\mathrm{problem}\:\mathrm{solving}\:\mathrm{approach} \\…
Question Number 194559 by MM42 last updated on 09/Jul/23 $${repeat}\:{question} \\ $$$${Shiw}\:{that}\:: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{2}{i}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{i}}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}+{i}}\:\:? \\ $$ Answered by witcher3 last updated…
Question Number 194526 by mathlove last updated on 09/Jul/23 $$\frac{{f}\left({x}+\mathrm{1}\right)}{{f}\left({x}\right)}={x}^{\mathrm{2}\:\:\:\:\:\:\:\:} \:\:\:\:{f}\left({x}\right)=? \\ $$$$\frac{{f}\left(\mathrm{6}\right)}{{f}\left(\mathrm{3}\right)}=? \\ $$ Answered by JDamian last updated on 09/Jul/23 $$\frac{{f}\left(\mathrm{6}\right)}{{f}\left(\mathrm{3}\right)}=\frac{{f}\left(\mathrm{6}\right)}{{f}\left(\mathrm{3}\right)}×\frac{{f}\left(\mathrm{5}\right)}{{f}\left(\mathrm{5}\right)}×\frac{{f}\left(\mathrm{4}\right)}{{f}\left(\mathrm{4}\right)}= \\ $$$$=\frac{{f}\left(\mathrm{6}\right)}{{f}\left(\mathrm{5}\right)}×\frac{{f}\left(\mathrm{5}\right)}{{f}\left(\mathrm{4}\right)}×\frac{{f}\left(\mathrm{4}\right)}{{f}\left(\mathrm{3}\right)}=\mathrm{5}^{\mathrm{2}}…
Question Number 194552 by BaliramKumar last updated on 09/Jul/23 $$\mathrm{If}\:{a},\:{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\&\:\mathrm{4cos}^{\mathrm{2}} \theta\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} +\mathrm{5}}{{a}+\mathrm{3}{b}},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left({a}+{b}\right)\:\mathrm{will}\:\mathrm{be}: \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{7}}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{5}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{11}}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{17}}{\mathrm{12}} \\ $$ Commented by Frix last updated on…
Question Number 194522 by cortano12 last updated on 09/Jul/23 Answered by witcher3 last updated on 09/Jul/23 $$\mathrm{u}=\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{5}} \\ $$$$\mathrm{v}=\sqrt[{\mathrm{3}}]{\mathrm{7}−\mathrm{x}} \\ $$$$\mathrm{u}^{\mathrm{3}} +\mathrm{v}^{\mathrm{3}} =\mathrm{2p} \\ $$$$\frac{\mathrm{v}−\mathrm{u}}{\mathrm{u}+\mathrm{v}}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{v}^{\mathrm{3}}…
Question Number 194548 by horsebrand11 last updated on 09/Jul/23 Commented by horsebrand11 last updated on 09/Jul/23 $$\:\underline{\gtrdot^{} } \\ $$ Answered by AST last updated…
Question Number 194518 by otchereabdullai@gmail.com last updated on 09/Jul/23 Commented by otchereabdullai@gmail.com last updated on 09/Jul/23 $${please}\:{help}\:{me}\:{with}\:{the}\:{b}\:{part} \\ $$ Answered by mr W last updated…
Question Number 194536 by Kiyanoush last updated on 09/Jul/23 $$\overset{\underline{ }} {\:} \\ $$ Commented by MM42 last updated on 09/Jul/23 $$\: \\ $$ Commented…
Question Number 194560 by Denis last updated on 09/Jul/23 Answered by MM42 last updated on 10/Jul/23 $$\Delta{XAB}\:\:{is}\:\:{equilatral}\:{triangle} \\ $$$$\angle\:{XAD}=\angle{XBC}=\mathrm{30}^{\mathrm{0}} \: \\ $$$${S}_{\mathrm{1}} ={S}_{\mathrm{2}} \Rightarrow{S}_{\mathrm{1}} +{S}_{\mathrm{2}}…
Question Number 194528 by BaliramKumar last updated on 09/Jul/23 $$\bigstar\:\mathrm{Let}\:\mathrm{N}\:\mathrm{be}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{where}\:\mathrm{N}\leq\mathrm{100}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{If}\:\mathrm{HCF}\left(\mathrm{N},\:\mathrm{100}\right)\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{N}\:? \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{400}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{1000}\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2000}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{4000} \\ $$ Answered by mahdipoor last updated on 09/Jul/23…