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Author: Tinku Tara

Question-89033

Question Number 89033 by M±th+et£s last updated on 14/Apr/20 Answered by ajfour last updated on 15/Apr/20 $${let}\:{center}\:{of}\:{square}\:{be}\:{origin}. \\ $$$${eq}.\:{of}\:{left}\:{circle}: \\ $$$$\left({x}+\frac{{r}}{\mathrm{2}}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${let}\:{side}\:{of}\:{square}=\mathrm{2}{s}…

Question-89029

Question Number 89029 by Jidda28 last updated on 14/Apr/20 Commented by MJS last updated on 14/Apr/20 $${t}=\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}}\:\mathrm{or}\:{t}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}}}\:\mathrm{and}\:\mathrm{then}\:\mathrm{decompose} \\ $$$$\frac{{f}\left({t}\right)}{{t}^{\mathrm{8}} +\mathrm{1}}\:\mathrm{which}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{no}\:\mathrm{fun}\:\mathrm{dealing} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{factors} \\ $$ Terms…

Question-23492

Question Number 23492 by ajfour last updated on 31/Oct/17 Commented by ajfour last updated on 31/Oct/17 $$\:\:\:\:\:\:\:{Find}\:{the}\:{period}\:{of}\:{small}\: \\ $$$$\:\:\:\:\:{oscillations}\:{of}\:{the}\:{disc},\:{if} \\ $$$$\:\:\:\:\:\:{springs}\:{are}\:{attached}\:{at}\:{a}\: \\ $$$$\:\:\:\:\:\:\:\:{distance}\:{of}\:\boldsymbol{{a}}\:{from}\:{the} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{frictionless}\:{hinge}.…

A-rectangular-wire-frame-ABCD-is-in-vertical-plane-is-moving-with-a-constant-acceleration-a-into-the-plane-Direction-of-gravity-is-shown-in-figure-A-collar-can-move-on-wire-AC-of-length-l-Coefficie

Question Number 23489 by Tinkutara last updated on 31/Oct/17 $$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{wire}\:\mathrm{frame}\:{ABCD}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{vertical}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant} \\ $$$$\mathrm{acceleration}\:{a}\:\mathrm{into}\:\mathrm{the}\:\mathrm{plane}.\:\mathrm{Direction} \\ $$$$\mathrm{of}\:\mathrm{gravity}\:\mathrm{is}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{A}\:\mathrm{collar} \\ $$$$\mathrm{can}\:\mathrm{move}\:\mathrm{on}\:\mathrm{wire}\:{AC}\:\mathrm{of}\:\mathrm{length}\:{l}. \\ $$$$\mathrm{Coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{wire} \\ $$$$\mathrm{and}\:\mathrm{collar}\:\mathrm{is}\:\mu.\:\mathrm{Find} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{minimum}\:\mathrm{acceleration}\:{a}\:\mathrm{so}\:\mathrm{that} \\…

3-x-4-x-5-x-dx-

Question Number 89025 by M±th+et£s last updated on 14/Apr/20 $$\int\frac{\mathrm{3}^{{x}} +\mathrm{4}^{{x}} }{\mathrm{5}^{{x}} }{dx} \\ $$ Answered by $@ty@m123 last updated on 14/Apr/20 $$\int\left(\frac{\mathrm{3}}{\mathrm{5}}\right)^{{x}} {dx}+\int\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{x}} {dx}…