Question Number 131517 by benjo_mathlover last updated on 05/Feb/21 $$\mathrm{Given}\:\int_{\mathrm{0}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\mathrm{2x}−\mathrm{1}\right)\mathrm{dx}+\int_{\mathrm{0}} ^{\mathrm{3}} \left(\int_{\mathrm{0}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)\mathrm{dx} \\ $$$$\mathrm{find}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:. \\ $$ Answered…
Question Number 65983 by Rio Michael last updated on 07/Aug/19 $$\:{Simplify}\: \\ $$$$\:\:\:\left(\mathrm{1}+\:\mathrm{2}{i}\sqrt{\mathrm{2}}\right)^{\mathrm{7}} \:−\:\left(\mathrm{1}\:+\mathrm{2}{i}\right)^{\mathrm{7}} \\ $$ Commented by Rio Michael last updated on 17/Aug/19 $${can}\:{i}\:{use}\:{de}\:{moivre}'{s}\:{theorem}?…
Question Number 65980 by Tony Lin last updated on 07/Aug/19 Commented by Tanmay chaudhury last updated on 07/Aug/19 Answered by Tanmay chaudhury last updated on…
Question Number 445 by 123456 last updated on 05/Jan/15 $$\mathrm{0}\leqslant\mid{f}\left({x}\right)\mid\leqslant\mid{g}\left({x}\right)\mid \\ $$$$\int{g}\left({x}\right)−{f}\left({x}\right)\:{dx}\leqslant\int{f}\left({x}\right)+{g}\left({x}\right)\:{dx}\:\:? \\ $$ Commented by prakash jain last updated on 05/Jan/15 $${f}\left({x}\right)=−\mathrm{1} \\ $$$${g}\left({x}\right)=\mathrm{1}…
Question Number 65981 by Tanmay chaudhury last updated on 07/Aug/19 Answered by jimful last updated on 07/Aug/19 $${let}\:{s}_{{n}} =\Sigma\mathrm{1}/{n}. \\ $$$$\Sigma\left({k}+\mathrm{1}\right)/{k}\:\bullet\Sigma{k}/\left({k}+\mathrm{1}\right) \\ $$$$=\left({n}+{s}_{{n}} \right)\left({n}−{s}_{{n}+\mathrm{1}} +\mathrm{1}\right)…
Question Number 443 by prakash jain last updated on 04/Jan/15 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of}\:{n}\:\mathrm{which}\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{10}^{{n}} \equiv\mathrm{1}\left(\mathrm{mod}\:\mathrm{7}^{{p}} \right)\:\mathrm{is}\:{n}=\mathrm{6}×\mathrm{7}^{{p}−\mathrm{1}} . \\ $$ Commented by 123456 last updated…
Question Number 440 by 123456 last updated on 25/Jan/15 $${a}\left({n}+\mathrm{1}\right)=\left[{a}\left({n}\right)+\mathrm{1}\right]\mathrm{cos}\left(\frac{\pi{n}}{\mathrm{2}}\right)+\left[{a}\left({n}−\mathrm{1}\right)+{n}\right]\mathrm{sin}\:\left(\frac{\pi{n}}{\mathrm{2}}\right) \\ $$$${a}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${a}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${a}\left(\mathrm{10}\right)=? \\ $$ Answered by prakash jain last updated on…
Question Number 131509 by snipers237 last updated on 05/Feb/21 $${Let}\:{a},{b},{c}\:\:{be}\:\:{no}\:{null}\:{integers}.\:{A}\:{ballot}\:{box}\:{contains}\:\:“{a}''\:{black}\:{bowls}\:{and}\:“{b}''{white}\:{bowls}. \\ $$$${After}\:{a}\:{print}\:{we}\:{put}\:{the}\:{bowl}\:{back}\:{in}\:{the}\:{ballot}\:{box}\:{with}\:“{c}''\:{another}\:{bowls}\:{of}\:{the}\:{same}\:{color}. \\ $$$${Prove}\:{that}\:{the}\:{probability}\:{to}\:{extract}\:{a}\:{green}\:{bowl}\:{at}\:{any}\:\:\:{print}\:{is}\:{always} \\ $$$${p}\:=\:\frac{{a}}{{a}+{b}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65972 by gunawan last updated on 07/Aug/19 $$\mathrm{If}\:\frac{\mathrm{log}_{\mathrm{2}} \:{a}}{\mathrm{log}_{\mathrm{3}} \:{b}}={m}\:\mathrm{and}\:\frac{\mathrm{log}_{\mathrm{3}} \:{a}}{\mathrm{log}_{\mathrm{2}} \:{b}}={n} \\ $$$${a}>\mathrm{1}\:\mathrm{and}\:{b}>\mathrm{1} \\ $$$$\mathrm{then}\:\frac{{m}}{{n}}=… \\ $$$${a}.\mathrm{log}_{\mathrm{2}} \:\mathrm{3} \\ $$$${b}.\:\mathrm{log}_{\mathrm{3}} \:\mathrm{2} \\…
Question Number 131505 by benjo_mathlover last updated on 05/Feb/21 $$\mathrm{If}\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{x}\right)\:?\: \\ $$$$\mathrm{true}\:\mathrm{or}\:\mathrm{false}? \\ $$ Commented by EDWIN88 last updated…