Question Number 140548 by liberty last updated on 09/May/21 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{vmatrix}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\:\:\mathrm{csc}^{\mathrm{2}} \mathrm{x}}\\{\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\:\:\mathrm{tan}\:\:^{\mathrm{2}} \mathrm{x}}\end{vmatrix} \\ $$$$\mathrm{evaluate}\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}. \\ $$ Answered by EDWIN88…
Question Number 9478 by tawakalitu last updated on 10/Dec/16 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140550 by liberty last updated on 09/May/21 Commented by mr W last updated on 09/May/21 $${what}\:{do}\:{you}\:{get}\:{with}\:{this}\:{example}: \\ $$$${x}=−\mathrm{135} \\ $$$${y}=\mathrm{100} \\ $$$${which}\:{fulfills}\:\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{5},\:{but} \\…
Question Number 75013 by necxxx last updated on 05/Dec/19 $${The}\:{largest}\:{interval}\:{for}\:{which} \\ $$$${x}^{\mathrm{12}} −{x}^{\mathrm{9}} +{x}^{\mathrm{4}} −{x}+\mathrm{1}>\mathrm{0}\:{is} \\ $$$$\left({a}\right)−\mathrm{4}<{x}\leqslant\mathrm{0} \\ $$$$\left({b}\right)\mathrm{0}<{x}<\mathrm{1} \\ $$$$\left({c}\right)−\mathrm{100}<{x}<\mathrm{100} \\ $$$$\left({d}\right)−\infty<{x}<\infty \\ $$…
Question Number 140545 by I want to learn more last updated on 09/May/21 Commented by mr W last updated on 09/May/21 $${AL}={AE}=\mathrm{3} \\ $$ Answered…
Question Number 9474 by tawakalitu last updated on 10/Dec/16 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9471 by tawakalitu last updated on 09/Dec/16 $$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\mathrm{a}\:+\:\left(\mathrm{a}\:+\:\mathrm{d}\right)\:+\:\left(\mathrm{a}\:+\:\mathrm{2d}\right)\:+\:…\:+\:\left[\mathrm{a}\:+\:\left(\mathrm{n}\:−\:\mathrm{1}\right)\mathrm{d}\right]\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{n}\left[\mathrm{2a}\:+\:\left(\mathrm{n}\:−\:\mathrm{1}\right)\mathrm{d}\right]\: \\ $$ Answered by mrW last updated on 10/Dec/16 $$\mathrm{for}\:\mathrm{n}=\mathrm{1}: \\ $$$$\mathrm{a}\overset{!} {=}\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{1}×\left[\mathrm{2a}+\left(\mathrm{1}−\mathrm{1}\right)\mathrm{d}\right]=\mathrm{a}…
Question Number 9470 by tawakalitu last updated on 09/Dec/16 $$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}. \\ $$$$\frac{\mathrm{1}}{\mathrm{1}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{2}.\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{3}.\mathrm{7}}\:+\:…\:+\:\frac{\mathrm{1}}{\left(\mathrm{2n}\:−\:\mathrm{1}\right)\left(\mathrm{2n}\:+\:\mathrm{1}\right)}\:=\:\frac{\mathrm{n}}{\mathrm{2n}\:+\:\mathrm{1}} \\ $$ Commented by mrW last updated on 10/Dec/16 $$\mathrm{please}\:\mathrm{check}\:\mathrm{the}\:\mathrm{question}! \\ $$$$\mathrm{should}\:\mathrm{it}\:\mathrm{be}\:\mathrm{following}? \\…
Question Number 9467 by tawakalitu last updated on 09/Dec/16 $$\int\mathrm{x}^{\mathrm{2}} \left(\sqrt{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\right)\:\mathrm{dx} \\ $$ Answered by mrW last updated on 09/Dec/16 $$\mathrm{x}=\mathrm{sin}\:\mathrm{t} \\ $$$$\mathrm{dx}=\mathrm{cos}\:\mathrm{t}\:\mathrm{dt} \\…
Question Number 75001 by necxxx last updated on 05/Dec/19 $${A}\:{block}\:{of}\:{mass}\:\mathrm{0}.\mathrm{2}{kg}\:{rests}\:{on}\:{an}\:{incline} \\ $$$${plane}\:{of}\:\mathrm{30}°\:{to}\:{the}\:{horizontal}\:{with}\:{a} \\ $$$${velocity}\:{of}\:\mathrm{12}{m}/{s}.{If}\:{the}\:{coefficient}\:{of} \\ $$$${sliding}\:{friction}\:{is}\:\mathrm{0}.\mathrm{16}, \\ $$$$\left({i}\right){determine}\:{how}\:{far}\:{up}\:{the}\:{plane}\:{the} \\ $$$${mass}\:{travels}\:{before}\:{stoping}. \\ $$$$\left({ii}\right){if}\:{the}\:{block}\:{returns},{what}\:{is}\:{the} \\ $$$${velocity}\:{of}\:{the}\:{block}\:{at}\:{the}\:{bottom}\:{of}\:{the} \\…