Question Number 194599 by pete last updated on 10/Jul/23 $$\mathrm{A}\:\mathrm{tank}\:\mathrm{contains}\:\mathrm{300}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{fluid}\:\mathrm{in}\: \\ $$$$\mathrm{which}\:\mathrm{20}\:\mathrm{grams}\:\mathrm{of}\:\mathrm{salt}\:\mathrm{is}\:\mathrm{dissolved}.\: \\ $$$$\mathrm{Brine}\:\mathrm{containing}\:\:\mathrm{1}\:\mathrm{gm}\:\mathrm{of}\:\mathrm{salt}\:\mathrm{per}\:\mathrm{litre} \\ $$$$\:\mathrm{is}\:\mathrm{then}\:\mathrm{pumped}\:\mathrm{into}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{a}\:\mathrm{rate} \\ $$$$\:\mathrm{of}\:\mathrm{4L}/\mathrm{min};\:\mathrm{the}\:\mathrm{well}\:\mathrm{mixed}\:\mathrm{solution}\: \\ $$$$\mathrm{is}\:\mathrm{pumped}\:\mathrm{out}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{rate}. \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{N}\left(\mathrm{t}\right)\:\mathrm{of}\:\mathrm{grams}\:\mathrm{of} \\ $$$$\:\mathrm{salt}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}.\: \\…
Question Number 194598 by malwan last updated on 10/Jul/23 $${please} \\ $$$${what}\:{is}\:{the}\:{best}\:{android} \\ $$$${apps}\:{to}\:{drow}\:{complex}\: \\ $$$${functions}\:{and}\:{fractals}\:? \\ $$ Commented by TheHoneyCat last updated on 14/Jul/23…
Question Number 194593 by pascal889 last updated on 10/Jul/23 Answered by MM42 last updated on 10/Jul/23 $${u}_{{n}} ={u}_{{n}−\mathrm{1}} +{n}+\mathrm{1}\:\:\:;{n}\geqslant\mathrm{2}\:\:,\:\:\:{u}_{\mathrm{1}} =\mathrm{4} \\ $$$${u}_{{n}} ={u}_{{n}−\mathrm{1}} +\left({n}+\mathrm{1}\right) \\…
Question Number 194563 by pete last updated on 10/Jul/23 $$\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…