Question Number 63934 by gunawan last updated on 11/Jul/19 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\:{x}^{\mathrm{5}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{2}−{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{6}} \:\:\mathrm{is} \\ $$ Commented by Prithwish sen last updated on 14/Jul/19…
Question Number 63935 by gunawan last updated on 11/Jul/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{9}^{\mathrm{th}} \mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left[\mathrm{3}^{\mathrm{log}_{\mathrm{3}} \:\sqrt{\mathrm{25}^{{x}−\mathrm{1}} +\mathrm{7}}} +\:\mathrm{3}^{−\:\frac{\mathrm{1}}{\mathrm{8}}\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{5}^{{x}−\mathrm{1}} +\mathrm{1}\right)} \right]^{\mathrm{10}} \:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{180}\:\mathrm{and}\:\:{x}\:>\:\mathrm{1},\:\mathrm{then}\:{x}\:\mathrm{equals} \\ $$ Terms…
If-p-is-nearly-equal-to-q-and-n-gt-1-such-that-n-1-p-n-1-q-n-1-p-n-1-q-p-q-k-then-the-value-of-k-is-
Question Number 63915 by gunawan last updated on 11/Jul/19 $$\mathrm{If}\:{p}\:\mathrm{is}\:\mathrm{nearly}\:\mathrm{equal}\:\:\mathrm{to}\:{q}\:\:\mathrm{and}\:\:{n}\:>\:\mathrm{1},\:\mathrm{such} \\ $$$$\mathrm{that}\:\frac{\left({n}+\mathrm{1}\right){p}+\left({n}−\mathrm{1}\right){q}}{\left({n}−\mathrm{1}\right){p}+\left({n}+\mathrm{1}\right){q}}\:=\:\left(\frac{{p}}{{q}}\right)^{{k}} ,\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63909 by gunawan last updated on 11/Jul/19 $$\mathrm{The}\:\mathrm{integral}\:\mathrm{part}\:\mathrm{of}\:\left(\mathrm{8}\:+\:\mathrm{3}\sqrt{\mathrm{7}}\:\right)^{\mathrm{20}} \:\mathrm{is}\:\mathrm{even}. \\ $$ Commented by gunawan last updated on 11/Jul/19 $$\mathrm{true}\:\mathrm{or}\:\mathrm{false} \\ $$$$ \\ $$…
Question Number 63908 by gunawan last updated on 11/Jul/19 $$\mathrm{If}\:{R}=\left(\mathrm{5}\sqrt{\mathrm{5}}\:+\mathrm{11}\right)^{\mathrm{2}{n}+\mathrm{1}} =\:\left[{R}\right]+\:{F},\:\mathrm{where} \\ $$$$\left[{R}\right]\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{in}\:{R},\: \\ $$$$\mathrm{then}\:{RF}=\:\mathrm{2}^{\mathrm{2}{n}+\mathrm{1}} . \\ $$ Commented by gunawan last updated on 11/Jul/19…
Question Number 63907 by gunawan last updated on 11/Jul/19 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{5}} \:\mathrm{in}\:\left(\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +…\right)^{−\mathrm{3}/\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{21}. \\ $$ Commented by gunawan last updated on 11/Jul/19 $$\mathrm{true}\:\mathrm{or}\:\mathrm{false} \\…
Question Number 63865 by mmkkmm000m last updated on 10/Jul/19 $$\mathrm{If}\:\int\:\:\frac{\mathrm{4}\:{e}^{{x}} +\:\mathrm{6}\:{e}^{−{x}} }{\mathrm{9}\:{e}^{{x}} −\:\mathrm{4}\:{e}^{−{x}} }{dx}={Ax}+{B}\:\mathrm{log}\left(\mathrm{9}{e}^{\mathrm{2}{x}} −\mathrm{4}\right)+{C}, \\ $$$$\mathrm{then} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 63861 by gunawan last updated on 10/Jul/19 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{non}−\mathrm{zero}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{3}\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} +\left(\mathrm{1}−\mathrm{3}\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:\mathrm{is} \\ $$ Commented by kaivan.ahmadi last updated on 10/Jul/19 $${even}\:{powers}\:{of}\:{x}\left({odd}\:{terms}\right)\:{have}\:{nonzero}\:{coff} \\…
Question Number 63862 by gunawan last updated on 10/Jul/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{3rd}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left[{x}+{x}^{\mathrm{log}_{\mathrm{10}} {x}} \right]^{\mathrm{5}} \mathrm{is}\:\mathrm{10}^{\mathrm{6}} ,\:\mathrm{then}\:{x}\:\mathrm{may}\:\mathrm{be} \\ $$ Commented by kaivan.ahmadi last updated on 10/Jul/19…
Question Number 63860 by gunawan last updated on 10/Jul/19 $$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{even}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{condition}\:\mathrm{that}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{n}} \:\mathrm{may}\:\mathrm{have}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{also}\:\mathrm{is} \\ $$ Answered by mr W last updated…