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Author: Tinku Tara

dx-sec-x-csc-x-

Question Number 82185 by jagoll last updated on 19/Feb/20 $$\int\:\frac{{dx}}{\mathrm{sec}\:{x}\:+\:{csc}\:{x}}\:=\:?\: \\ $$ Commented by john santu last updated on 19/Feb/20 $$\mathrm{sec}\:{x}+\:{csc}\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}} \\ $$$$\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}\:. \\ $$$$\int\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}\:{dx}\:=\:…

A-ball-is-dropped-vertically-from-a-height-d-above-the-ground-It-hits-the-ground-and-bounces-up-vertically-to-a-height-d-2-Neglecting-subsequent-motion-and-air-resistance-its-velocity-V-varies-wit

Question Number 16647 by Tinkutara last updated on 24/Jun/17 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{dropped}\:\mathrm{vertically}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{height}\:{d}\:\mathrm{above}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{It}\:\mathrm{hits}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{and}\:\mathrm{bounces}\:\mathrm{up}\:\mathrm{vertically}\:\mathrm{to}\:\mathrm{a} \\ $$$$\mathrm{height}\:\frac{{d}}{\mathrm{2}}.\:\mathrm{Neglecting}\:\mathrm{subsequent} \\ $$$$\mathrm{motion}\:\mathrm{and}\:\mathrm{air}\:\mathrm{resistance}\:\mathrm{its}\:\mathrm{velocity} \\ $$$${V}\:\mathrm{varies}\:\mathrm{with}\:\mathrm{height}\:{h}\:\mathrm{above}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{is} \\ $$ Commented…

A-body-is-at-rest-at-x-0-At-t-0-it-starts-moving-in-the-positive-x-direction-with-a-constant-acceleration-At-the-same-instant-another-body-passes-through-x-0-moving-in-the-positive-x-directio

Question Number 16645 by Tinkutara last updated on 24/Jun/17 $$\mathrm{A}\:\mathrm{body}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{at}\:{x}\:=\:\mathrm{0}.\:\mathrm{At}\:{t}\:=\:\mathrm{0},\:\mathrm{it} \\ $$$$\mathrm{starts}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{the}\:\mathrm{positive}\:{x}-\mathrm{direction} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{acceleration}.\:\mathrm{At}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{instant}\:\mathrm{another}\:\mathrm{body}\:\mathrm{passes} \\ $$$$\mathrm{through}\:{x}\:=\:\mathrm{0}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{the}\:\mathrm{positive} \\ $$$${x}-\mathrm{direction}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{speed}.\:\mathrm{The} \\ $$$$\mathrm{position}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{body}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${x}_{\mathrm{1}} \left({t}\right)\:\mathrm{after}\:\mathrm{time}\:'{t}'\:\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}…

Find-a-point-on-the-curve-y-x-where-the-tangent-makes-an-angle-45-with-the-positive-x-axis-

Question Number 147713 by Odhiambojr last updated on 22/Jul/21 $${Find}\:{a}\:{point}\:{on}\:{the}\:{curve}\:{y}=\sqrt{{x}} \\ $$$${where}\:{the}\:{tangent}\:{makes}\:{an}\:{angle}\: \\ $$$$\mathrm{45}°\:{with}\:{the}\:{positive}\:{x}-{axis} \\ $$ Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\frac{{dy}}{{dx}}\:=\:\mathrm{tan}\left(\theta\left({x}\right)\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}} \\…

Question-82176

Question Number 82176 by oyemi kemewari last updated on 19/Feb/20 Commented by jagoll last updated on 19/Feb/20 $$\left(\mathrm{1}{b}\right)\:\sqrt{\mathrm{32}−\mathrm{2}\sqrt{\mathrm{135}}}\:=\:\sqrt{\mathrm{27}+\mathrm{5}−\mathrm{2}\sqrt{\mathrm{27}×\mathrm{5}}} \\ $$$$=\:\sqrt{\mathrm{27}}−\sqrt{\mathrm{5}}\:=\:\mathrm{3}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}} \\ $$ Commented by jagoll…

Prove-that-p-is-a-prime-number-if-and-only-if-every-equiangular-polygon-with-p-sides-of-rational-lengths-is-regular-

Question Number 16641 by Tinkutara last updated on 24/Jun/17 $$\mathrm{Prove}\:\mathrm{that}\:{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{if}\:\mathrm{and} \\ $$$$\mathrm{only}\:\mathrm{if}\:\mathrm{every}\:\mathrm{equiangular}\:\mathrm{polygon}\:\mathrm{with} \\ $$$${p}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{lengths}\:\mathrm{is}\:\mathrm{regular}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Resoudre-log-a-x-2-gt-log-a-2-3x-2-avec-a-R-1-NB-a-et-a-2-sont-les-bases-des-logarithmes-des-nombres-de-l-ine-galite-les-resultats-se-donnerons-soua-forme-d-ine-galite-selon-les-

Question Number 147714 by puissant last updated on 22/Jul/21 $$\mathrm{Resoudre} \\ $$$$\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} \right)\:>\:\mathrm{log}_{\mathrm{a}^{\mathrm{2}} } \left(\mathrm{3x}−\mathrm{2}\right) \\ $$$$\mathrm{avec}\:\:\mathrm{a}\in\mathbb{R}_{+} \backslash\left\{\mathrm{1}\right\} \\ $$$$\mathrm{NB}:\:\mathrm{a}\:\mathrm{et}\:\mathrm{a}^{\mathrm{2}} \:\mathrm{sont}\:\mathrm{les}\:\mathrm{bases}\:\mathrm{des}\:\mathrm{logarithmes} \\ $$$$\mathrm{des}\:\mathrm{nombres}\:\mathrm{de}\:\mathrm{l}'\mathrm{in}\acute {\mathrm{e}galite}..…