Question Number 78074 by Rio Michael last updated on 14/Jan/20 $${evaluate}\:\int_{\mathrm{1}} ^{\mathrm{4}} \mathrm{sinh}\:^{−\mathrm{1}} {x}\:{dx}\:\:{and}\:\underset{\mathrm{1}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}\mathrm{tanh}\:^{−\mathrm{1}} {x}\:{dx} \\ $$ Answered by mr W last updated…
Question Number 78075 by Rio Michael last updated on 14/Jan/20 $${expressing}\:\:{P}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} \:+\:{x}}{\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −\mathrm{2}\right)}\:{in}\:{partial}\:{fractions}\:{gives} \\ $$$${A}.\:\:\frac{{A}}{\left({x}−\mathrm{3}\right)}\:+\:\frac{{Bx}\:+\:{C}}{\left({x}^{\mathrm{2}} −\mathrm{2}\right)}\: \\ $$$${B}.\:\:\frac{{A}}{{x}−\mathrm{3}}\:+\:\frac{{B}}{{x}−\mathrm{2}}\:+\:\frac{{C}}{{x}+\mathrm{2}} \\ $$$${C}.\:\frac{{A}}{{x}−\mathrm{3}}\:+\:\frac{{B}}{{x}−\sqrt{\mathrm{2}}}\:+\:\frac{{C}}{{x}\:+\:\sqrt{\mathrm{2}}} \\ $$$${D}.\:\frac{{Ax}\:+\:{B}}{{x}−\mathrm{3}}\:+\:\frac{{C}}{{x}^{\mathrm{2}} −\mathrm{2}} \\ $$…
Question Number 12517 by tawa last updated on 24/Apr/17 $$\mathrm{A}\:\mathrm{spring}\:\mathrm{stretches}\:\mathrm{by}\:\mathrm{15cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{300g}\:\mathrm{hangs}\:\mathrm{down}\:\mathrm{from}\:\mathrm{it}. \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{spring}\:\mathrm{is}\:\mathrm{then}\:\mathrm{strethed}\:\mathrm{an}\:\mathrm{additional}\:\mathrm{10cm}\:\mathrm{and}\:\mathrm{realeased},\:\mathrm{calculate} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{spring}\:\mathrm{constant} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Angular}\:\mathrm{velocity} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{amplitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{oscillation} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{velocity} \\ $$$$\left(\mathrm{e}\right)\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mass} \\ $$$$\left(\mathrm{f}\right)\:\mathrm{The}\:\mathrm{period}\:\mathrm{T}\:\mathrm{and}\:\mathrm{frequency}\:\mathrm{f} \\…
Question Number 12419 by tawa last updated on 21/Apr/17 $$\mathrm{If}\:\mathrm{a}\:\mathrm{body}\:\mathrm{of}\:\mathrm{2kg}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{7200km}\:\mathrm{from}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{earth}\:.\:\mathrm{What}\:\mathrm{would}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{be}\:\mathrm{at}\:\mathrm{this}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{Earths}\:\mathrm{field}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{9}.\mathrm{6m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{b}\right)\:\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{c}\right)\:\mathrm{11}.\mathrm{3m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{d}\right)\:\mathrm{12}.\mathrm{7m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{e}\right)\:\mathrm{15}.\mathrm{6m}/\mathrm{s}^{\mathrm{2}} \\ $$ Answered by ajfour…
Question Number 12405 by Ms.Ramanujan last updated on 21/Apr/17 $${how}\:{to}\:{prove}\:{that}\:{there}\:{exist}\:{infinitely}\:{many}\:{rationals}\:{between}\:{any}\:{two}\:{irrationals}? \\ $$$$ \\ $$ Commented by FilupS last updated on 21/Apr/17 $${a}<{x}<{b} \\ $$$$\: \\…
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Question Number 77872 by berket last updated on 11/Jan/20 $${show}\:{that}\:{f}\left({x}\right)=\mathrm{2}{r}^{\mathrm{3}} +\mathrm{5}{x}−\mathrm{1}\:{has}\:{a}\:{zero}\:{in}\:{the}\:{interval}\:\left[\mathrm{0}.\mathrm{1}\right]. \\ $$ Commented by key of knowledge last updated on 11/Jan/20 $$\mathrm{r}^{\mathrm{3}} \:\mathrm{or}\:\mathrm{x}^{\mathrm{3}} \\…
Question Number 12331 by tawa last updated on 19/Apr/17 Answered by mrW1 last updated on 19/Apr/17 $${m}\frac{{v}^{\mathrm{2}} }{{r}}\leqslant\mu{mg} \\ $$$$\mu\geqslant\frac{{v}^{\mathrm{2}} }{{rg}}=\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{8}×\mathrm{9}.\mathrm{81}}=\mathrm{0}.\mathrm{32} \\ $$ Commented…
Question Number 12321 by tawa last updated on 19/Apr/17 $$\mathrm{When}\:\mathrm{a}\:\mathrm{known}\:\mathrm{standard}\:\mathrm{resistor}\:\mathrm{of}\:\mathrm{2}.\mathrm{0}\:\Omega\:\mathrm{is}\:\mathrm{connected}\:\mathrm{to}\:\mathrm{the}\:\mathrm{0}.\mathrm{0}\:\mathrm{cm}\:\mathrm{end}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{meter}\:\mathrm{bridge}.\:\mathrm{The}\:\mathrm{balance}\:\mathrm{point}\:\mathrm{is}\:\mathrm{found}\:\mathrm{to}\:\mathrm{be}\:\mathrm{at}\:\mathrm{55}.\mathrm{0cm}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{resistor}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12319 by tawa last updated on 19/Apr/17 Answered by chux last updated on 19/Apr/17 $$\frac{\mathrm{R}}{\mathrm{60}}=\frac{\mathrm{20}}{\mathrm{100}−\mathrm{60}} \\ $$$$\mathrm{R}=\frac{\mathrm{20}×\mathrm{60}}{\mathrm{40}}=\mathrm{30}\Omega \\ $$ Commented by tawa last…