Question Number 21516 by Tinkutara last updated on 26/Sep/17 $$\mathrm{A}\:\mathrm{5}-\mathrm{kg}\:\mathrm{body}\:\mathrm{is}\:\mathrm{suspended}\:\mathrm{from}\:\mathrm{a}\:\mathrm{spring}- \\ $$$$\mathrm{balance},\:\mathrm{and}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{body}\:\mathrm{is} \\ $$$$\mathrm{balanced}\:\mathrm{on}\:\mathrm{a}\:\mathrm{pan}\:\mathrm{of}\:\mathrm{a}\:\mathrm{physical} \\ $$$$\mathrm{balance}.\:\mathrm{If}\:\mathrm{both}\:\mathrm{the}\:\mathrm{balances}\:\mathrm{are}\:\mathrm{kept} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{elevator},\:\mathrm{then}\:\mathrm{what}\:\mathrm{would}\:\mathrm{happen} \\ $$$$\mathrm{in}\:\mathrm{each}\:\mathrm{case}\:\mathrm{when}\:\mathrm{the}\:\mathrm{elevator}\:\mathrm{is}\:\mathrm{moving} \\ $$$$\mathrm{with}\:\mathrm{an}\:\mathrm{upward}\:\mathrm{acceleration}? \\ $$ Answered…
Question Number 87050 by jagoll last updated on 02/Apr/20 $$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}+\mathrm{1}}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{x}+\mathrm{y}\:+\:\mathrm{xy}\:=\:\mathrm{5}\:? \\ $$ Commented by john santu last updated on 02/Apr/20 $$\Rightarrow{x}+{y}+{xy}+\mathrm{1}\:=\:\mathrm{6}\:\Rightarrow{x}\left({y}+\mathrm{1}\right)=\mathrm{5}−{y}…
Question Number 87048 by Ar Brandon last updated on 02/Apr/20 $${Express}\:\:{into}\:\:{partial}\:\:{fractions} \\ $$$$\:\:\:\:\:\:\:\:\frac{{x}^{\mathrm{6}} }{{x}^{\mathrm{12}} +\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 87046 by Tajaddin last updated on 02/Apr/20 $$\int\frac{{dx}}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}} \\ $$ Answered by MJS last updated on 02/Apr/20 $$\int\frac{{dx}}{\mathrm{sin}^{\mathrm{3}} \:{x}\:+\mathrm{cos}^{\mathrm{3}} \:{x}}= \\…
Question Number 152580 by aupo14 last updated on 29/Aug/21 Answered by Lordose last updated on 29/Aug/21 $$\mathrm{I}\:=\:\int\mathrm{e}^{\mathrm{sec}^{\mathrm{2}} \left(\mathrm{x}\right)} \mathrm{tan}\left(\mathrm{x}\right)\mathrm{dx}\:\overset{\mathrm{u}=\mathrm{sec}\left(\mathrm{x}\right)} {=}\int\frac{\:\mathrm{e}^{\mathrm{u}^{\mathrm{2}} } }{\mathrm{u}}\mathrm{du}\:\overset{\mathrm{y}=\mathrm{u}^{\mathrm{2}} } {=}\:\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\:\mathrm{e}^{\mathrm{y}} }{\mathrm{y}}\mathrm{dy}…
Question Number 21510 by x² – y²@gmail.com last updated on 25/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21507 by Tinkutara last updated on 25/Sep/17 $$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ideal}\:\mathrm{spring}\:\mathrm{increases} \\ $$$$\mathrm{by}\:\mathrm{0}.\mathrm{1}\:\mathrm{cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{body}\:\mathrm{of}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{is} \\ $$$$\mathrm{suspended}\:\mathrm{from}\:\mathrm{it}.\:\mathrm{If}\:\mathrm{this}\:\mathrm{spring}\:\mathrm{is}\:\mathrm{laid} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{frictionless}\:\mathrm{horizontal}\:\mathrm{table}\:\mathrm{and} \\ $$$$\mathrm{bodies}\:\mathrm{of}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{each}\:\mathrm{are}\:\mathrm{suspended}\:\mathrm{from} \\ $$$$\mathrm{its}\:\mathrm{ends},\:\mathrm{then}\:\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{increase} \\ $$$$\mathrm{in}\:\mathrm{its}\:\mathrm{length}? \\ $$ Commented…
Question Number 152576 by Tawa11 last updated on 31/Aug/21 $$\int\:\frac{\mathrm{t}\:\:\:+\:\:\:\mathrm{13}}{\:\sqrt[{\mathrm{3}}]{\mathrm{t}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{5t}\:\:\:+\:\:\:\mathrm{6}}}\:\:\mathrm{dt} \\ $$ Commented by MATHkingElsenK last updated on 31/Aug/21 $${hello}\:\mathrm{5}{x}\:{no}\:\mathrm{5}{t} \\ $$ Terms of…
Question Number 21504 by mondodotto@gmail.com last updated on 25/Sep/17 Answered by $@ty@m last updated on 26/Sep/17 $${ATQ} \\ $$$$\boldsymbol{{S}}_{{n}} =\left(−\mathrm{1}\right)+\mathrm{1}+\mathrm{3}+\mathrm{5}+……+\left(\mathrm{2}{n}−\mathrm{3}\right) \\ $$$$\left({i}\right)\:\boldsymbol{{S}}_{\mathrm{50}} =\frac{\mathrm{50}}{\mathrm{2}}\left\{\left(−\mathrm{1}\right)+\left(\mathrm{2}×\mathrm{50}−\mathrm{3}\right)\right\} \\ $$$$=\mathrm{25}\left(−\mathrm{1}+\mathrm{97}\right)…
Question Number 21503 by mondodotto@gmail.com last updated on 25/Sep/17 Answered by $@ty@m last updated on 26/Sep/17 $${Let}\:\mathrm{4}{x}^{\mathrm{2}} ={t} \\ $$$$\Rightarrow\mathrm{8}{xdx}={dt} \\ $$$${Change}\:{of}\:{limits}: \\ $$$${As}\:{x}\rightarrow\mathrm{4},\:{t}\rightarrow\mathrm{64} \\…