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Question Number 222622 Answers: 0 Comments: 0

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Σ_(n = 1) ^∞ (1/(cosh^4 [n ln((√2) + 1)]))

$$\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{cosh}^{\mathrm{4}} \left[\mathrm{n}\:\mathrm{ln}\left(\sqrt{\mathrm{2}}\:\:+\:\:\mathrm{1}\right)\right]} \\ $$

Question Number 222373 Answers: 2 Comments: 0

An 80 kg man floats with 4% of his volume above the surface in fresh water.what is his volume? what volume would be above the surface in Sea water?How great is the upthrust on him in air due to the air he displaces? density of sea water =1030kgm^-3, density of fresh water=1000kgm^-3?

Question Number 222276 Answers: 0 Comments: 0

Prove; Σ_(k = 1) ^∞ (k/(sinh(πk))) = ((Γ((1/4))^4 − 8π^2 )/(32π^3 ))

$$ \\ $$$$\:\mathrm{Prove};\:\underset{{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}}{\mathrm{sinh}\left(\pi{k}\right)}\:=\:\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} −\:\mathrm{8}\pi^{\mathrm{2}} }{\mathrm{32}\pi^{\mathrm{3}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 222195 Answers: 1 Comments: 0

f(x)=x^3 +(√x)+sin x f=?

$${f}\left({x}\right)={x}^{\mathrm{3}} +\sqrt{{x}}+\mathrm{sin}\:{x} \\ $$$${f}=? \\ $$

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A man standing 10m away from a plane mirror moves towards the mirror with a speed of 2m/s. Calculate (a) The speed with which his image in the mirrow approaches him (b) How far is the man from his image after 3 seconds.

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Ip = ((p1q0)/(p0q0))×100

$$\boldsymbol{{Ip}}\:=\:\frac{\mathrm{p1q0}}{\mathrm{p0q0}}×\mathrm{100} \\ $$

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Question Number 221228 Answers: 1 Comments: 0

Σ_(n = 1) ^∞ Σ_(m = 1) ^∞ (1/((m^2 + n^2 )^2 ))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{{m}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({m}^{\mathrm{2}} \:+\:{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 221060 Answers: 1 Comments: 0

Please what’s TSA of a frustrum of a cone? Any easy method?

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An object is thrown vertically upward from the top of a building 20m high. If the object passes the point it was thrown 4 seconds on it way down, find the. (a) Velocity at which the object was thrown. (b) time taken when the object is 10m above the level it was thrown. (c) time taken when the object is 10m below the level it was thrown. (d) Velocity with which the object hit the ground. [Take g = 10m/s²]

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please help me .The photos I upload becomes blurred HELP please

$${please}\:{help}\:{me}\:.{The}\:{photos}\:{I}\:{upload} \\ $$$${becomes}\:{blurred} \\ $$$${HELP}\:{please} \\ $$

Question Number 220007 Answers: 2 Comments: 1

Question Number 219988 Answers: 1 Comments: 1

let s>1 be a real number. for all continues function f:[0,1]→R such that ∫_( 0) ^( 1) f(x)=0, determind of the exist a positive constant K(s) statisfying: (∫_0 ^( 1) f(x)∙Li_s (x)dx)^2 ≥K(s)∫_( 0) ^( 1) (f(x))^2 ∙Li_(2s−1 ) where Li_s (x)=Σ_(k=1) ^∞ (x^k /k^s ) is the polylogarithm function. if such a constants exists, find the optimal value of K(s).

$$ \\ $$$$\:\:\:\:\mathrm{let}\:{s}>\mathrm{1}\:\mathrm{be}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}.\:\mathrm{for}\:\mathrm{all}\:\mathrm{continues}\:\mathrm{function}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\:\:\:\mathrm{such}\:\mathrm{that}\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)=\mathrm{0},\:\mathrm{determind}\:\mathrm{of}\:\mathrm{the}\:\mathrm{exist}\:\mathrm{a} \\ $$$$\:\:\:\:\:\mathrm{positive}\:\mathrm{constant}\:{K}\left({s}\right)\:\mathrm{statisfying}: \\ $$$$\:\:\:\left(\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)\centerdot\mathrm{Li}_{{s}} \left({x}\right){dx}\right)^{\mathrm{2}} \geqslant{K}\left({s}\right)\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \left({f}\left({x}\right)\right)^{\mathrm{2}} \centerdot\mathrm{Li}_{\mathrm{2}{s}−\mathrm{1}\:} \\ $$$$\:\:\:\mathrm{where}\:\mathrm{Li}_{{s}} \left({x}\right)=\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{k}} }{{k}^{{s}} }\:\mathrm{is}\:\mathrm{the}\:\mathrm{polylogarithm}\:\mathrm{function}.\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\mathrm{if}\:\mathrm{such}\:\mathrm{a}\:\mathrm{constants}\:\mathrm{exists},\:\mathrm{find}\:\mathrm{the}\:\mathrm{optimal}\:\mathrm{value}\:\mathrm{of}\:{K}\left({s}\right).\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

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