Question Number 66108 by Rio Michael last updated on 09/Aug/19 $${Given}\:{that}\:{the}\:{binomial}\:{expansion}\:{of}\:\frac{\mathrm{2}\:+\:{kx}}{\left(\mathrm{2}−\mathrm{5}{x}\right)^{\mathrm{2}\:} }\:,\:\mid{x}\mid\:<\:\frac{\mathrm{2}}{\mathrm{5}\:}\:,{in}\:{ascending} \\ $$$${powers}\:{of}\:{x}\:{is}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{7}}{\mathrm{4}}{x}\:+\:{Ax}^{\mathrm{2}} \:+\:…,\:{find}\:{the}\:{values}\:{of}\:{A}\:{and}\:{k} \\ $$ Commented by mr W last updated on 09/Aug/19…
Question Number 66109 by Rio Michael last updated on 09/Aug/19 Commented by Rio Michael last updated on 09/Aug/19 $${The}\:{diagram}\:{above}\:{shows}\:{a}\:{uniform}\:{semi}−{circular}\:{lamina}\:{of}\:{radius}\:\mathrm{2}{a} \\ $$$$,{center}\:{O}.\:{The}\:{distance}\:{of}\:{the}\:{centre}\:{of}\:{mass}\:{form}\:{P},\:{vertically}\:{above}\:{O}\:{is} \\ $$$$ \\ $$$${A}\:\:\frac{\mathrm{6}{a}\pi−\mathrm{8}{a}}{\mathrm{3}\pi}…
Question Number 572 by kth last updated on 29/Jan/15 $${xy}=\mathrm{6}\left({x}+{y}\right) \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{325} \\ $$$${x}=? \\ $$$${y}=? \\ $$$$ \\ $$ Answered by prakash…
Question Number 131641 by liberty last updated on 07/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{if}\::\:\mathrm{2f}\left(\mathrm{x}\right)−\mathrm{x}\:\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}}\right)=\mathrm{3} \\ $$$$\mathrm{when}\:\mathrm{x}\neq\:\mathrm{2}\:?\: \\ $$ Answered by EDWIN88 last updated on 07/Feb/21 $$\left(\mathrm{1}\right)\:\mathrm{2f}\left(\mathrm{x}\right)−\mathrm{x}\:\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}}\right)=\:\mathrm{3} \\ $$$$\:\mathrm{replacing}\:\mathrm{x}\:\mathrm{by}\:\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}} \\…
Question Number 66106 by Umar last updated on 09/Aug/19 $$\mathrm{In}\:\mathrm{an}\:\mathrm{electrolysis}\:\mathrm{experiment},\:\mathrm{the}\:\mathrm{ammeter} \\ $$$$\mathrm{records}\:\mathrm{a}\:\mathrm{steady}\:\mathrm{current}\:\mathrm{of}\:\mathrm{1A}.\:\mathrm{The}\:\mathrm{mass} \\ $$$$\mathrm{of}\:\mathrm{copper}\:\mathrm{deposited}\:\mathrm{in}\:\mathrm{30minutes}\:\mathrm{is}\:\mathrm{0}.\mathrm{66g}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{error}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ammeter}\:\mathrm{reading}. \\ $$$$\:\:\:\mathrm{the}\:\mathrm{electrical}\:\mathrm{equivalent}\:\mathrm{of}\:\mathrm{cu}\:\mathrm{is}\:\mathrm{3}.\mathrm{3}×\mathrm{10}^{−\mathrm{4}} \mathrm{g}/\mathrm{C}. \\ $$ Terms of Service Privacy…
Question Number 571 by 123456 last updated on 30/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$$\:{if}\:{f},{g}\:{are}\:{continuos}\:{into}\:\left[{a},{b}\right]\:{and} \\ $$$${g}\:{never}\:{change}\:{sign}\:{into}\:\left[{a},{b}\right]\:{then} \\ $$$$\exists{c}\in\left[{a},{b}\right]\:{such}\:{that} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}{f}\left({x}\right){g}\left({x}\right){dx}={f}\left({c}\right)\underset{{a}} {\overset{{b}} {\int}}{g}\left({x}\right){dx} \\ $$ Answered…
Question Number 131640 by Salman_Abir last updated on 07/Feb/21 Answered by EDWIN88 last updated on 07/Feb/21 $$ \\ $$$$\mathrm{Du}\:\mathrm{bist}\:\mathrm{wundersch}\ddot {\mathrm{o}n} \\ $$ Commented by EDWIN88…
Question Number 66107 by Rio Michael last updated on 09/Aug/19 $${Given}\:{that}\:{S}_{{n}} \:=\:\frac{{a}\left(\mathrm{1}\:−{r}^{{n}} \right)}{\mathrm{1}−{r}}\:,\:{r}\:\neq\:\mathrm{1},\:{show}\:{that}\:\frac{{S}_{\mathrm{3}{n}} \:−{S}_{\mathrm{2}{n}} }{{S}_{{n}} \:}\:=\:{r}^{\mathrm{2}{n}} \\ $$$${hence}\:{given}\:{that}\:{r}\:=\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{{S}_{\mathrm{3}{n}} \:−{S}_{\mathrm{2}{n}} }{{S}_{{n}} }\right) \\ $$…
Question Number 570 by defgd last updated on 28/Jan/15 $$\int\:\frac{\mathrm{1}+{x}}{\left(\mathrm{2}+{x}\right)^{\mathrm{2}} }\:{e}^{{x}} \:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66104 by Rio Michael last updated on 09/Aug/19 $${f}\left({x}\right)=\:\mathrm{2}{x}^{\mathrm{3}} −{x}−\mathrm{4} \\ $$$${show}\:{that}\:{the}\:{equation}\:{f}\left({x}\right)\:=\mathrm{0}\:{has}\:{root}\:{between}\:\mathrm{1}\:{and}\:\mathrm{2} \\ $$$${show}\:{that}\:{the}\:{equation}\:{f}\left({x}\right)\:=\mathrm{0}\:{can}\:{be}\:{written}\:{as}\: \\ $$$$\:\:{x}\:=\:\sqrt{\left(\frac{\mathrm{2}}{{x}}\:+\frac{\mathrm{1}}{\mathrm{2}}\right)} \\ $$$${use}\:{the}\:{iteration} \\ $$$$\:{x}_{{n}+\mathrm{1}\:} \:=\:\sqrt{\left(\frac{\mathrm{2}}{{x}_{{n}} }\:+\frac{\mathrm{1}}{\mathrm{2}}\right)\:,} \\…