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certificate-x-2n-1-Can-always-be-x-1-be-divisible-

Question Number 212513 by MrGaster last updated on 16/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}{n}} −\mathrm{1} \\ $$$$\mathrm{Can}\:\mathrm{always}\:\mathrm{be}\:{x}+\mathrm{1}\:\mathrm{be}\:\mathrm{divisible}\:\:\:\:\:\:\:\:\: \\ $$ Answered by A5T last updated on 16/Oct/24 $${x}\equiv−\mathrm{1}\left({mod}\:{x}+\mathrm{1}\right)\Rightarrow{x}^{\mathrm{2}{n}}…

Given-that-x-R-the-set-of-real-numbers-d-an-n-N-the-set-of-positive-naturalu-nmbers-prove-that-cos-x-cos-2x-cos-3x-cos-n-1-x-n-2-

Question Number 212492 by MrGaster last updated on 15/Oct/24 $$\mathrm{Given}\:\mathrm{that}\:{x}\:\in\:\mathbb{R}\left(\right. \\ $$$$\:\left(\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{real}\:\mathrm{numbers}\right)\mathrm{d} \\ $$$$\mathrm{an}\:{n}\:\in\:\mathbb{N}^{\ast} \\ $$$$\left(\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{naturalu}\right. \\ $$$$\left.\mathrm{nmbers}\right)\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\mid\mathrm{cos}\:{x}\mid+\mid\mathrm{cos}\:\mathrm{2}{x}\mid+\mid\mathrm{cos}\:\mathrm{3}{x}\mid+\ldots+\mid\mathrm{cos}\left({n}+\mathrm{1}\right){x}\mid\geq\frac{{n}}{\mathrm{2}} \\ $$ Terms of Service…

1-In-a-plane-there-are-nt-poins-arranged-such-that-nostraight-line-passesg-throuh-more-than-3-points-h-Wat-is-the-maximume-numbr-of-straight-lines-thatcan-pass-throughy-exactl-3-points2-If-thee-nu

Question Number 212462 by MrGaster last updated on 14/Oct/24 $$\mathrm{1}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{there}\:\mathrm{are}\:\mathrm{nt} \\ $$$$\mathrm{poins}\:\mathrm{arranged}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{nostraight}\:\mathrm{line}\:\mathrm{passesg} \\ $$$$\mathrm{throuh}\:\mathrm{more}\:\mathrm{than}\:\mathrm{3}\:\mathrm{points}.\mathrm{h} \\ $$$$\mathrm{Wat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximume} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\: \\ $$$$\mathrm{thatcan}\:\mathrm{pass}\:\mathrm{throughy} \\ $$$$\mathrm{exactl}\:\mathrm{3}\:\mathrm{points2}.\:\mathrm{If}\:\mathrm{thee} \\…

9x-2-49-x-3-dx-

Question Number 212456 by Hanuda354 last updated on 14/Oct/24 $$\int\:\:\frac{\sqrt{\mathrm{9}{x}^{\mathrm{2}} −\mathrm{49}}}{{x}^{\mathrm{3}} }\:\:{dx}\:=\:? \\ $$ Answered by Sutrisno last updated on 14/Oct/24 $$\int\frac{\sqrt{\left(\mathrm{3}{x}\right)^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }}{{x}^{\mathrm{3}} }{dx}…

0-e-s-s-5-ds-2-e-t-2-2-dt-0-sint-2-dt-n-0-1-n-2n-1-0-sin-x-x-dx-n-1-arctan-2-n-2-lim-t-0-2020-

Question Number 212416 by MrGaster last updated on 13/Oct/24 $$\frac{\frac{\int_{\mathrm{0}} ^{+\infty} {e}^{−{s}} {s}^{\mathrm{5}} {ds}}{\mathrm{2}}+\frac{\int_{−\infty} ^{+\infty} {e}^{−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}} {dt}}{\int_{\mathrm{0}} ^{+\infty} \mathrm{sin}{t}^{\mathrm{2}} {dt}}\left(\frac{\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}+\mathrm{1}}}{\int_{\mathrm{0}} ^{+\infty}…