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Question Number 43682 Answers: 0 Comments: 1

Question Number 43679 Answers: 0 Comments: 1

Σ_(i=1) ^∞ (i^2 /(2^i ))=...

$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{i}^{\mathrm{2}} }{\mathrm{2}^{{i}} \:}=... \\ $$

Question Number 43676 Answers: 0 Comments: 2

1)calculate I = ∫_0 ^∞ (dx/(x^2 −i)) and J = ∫_0 ^∞ (dx/(x^2 +i)) 2) find the value of ∫_0 ^∞ (dx/(x^4 +1))

$$\left.\mathrm{1}\right){calculate}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:{and}\:\:{J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 43675 Answers: 0 Comments: 1

calculate ∫_1 ^2 (dx/(1+x^4 )) .

$${calculate}\:\:\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} }\:. \\ $$

Question Number 43665 Answers: 1 Comments: 1

1) if s_(n ) =α^n +β^n +λ^(n ) where α,β,λ are the root of ax^3 +bx^2 +cx+d=0 then show that s_(4 ) =((4abd+4b^2 c−2c)/a^3 )

$$\left.\mathrm{1}\right)\:{if}\:\:{s}_{{n}\:\:} \:=\alpha^{{n}} +\beta^{{n}} +\lambda^{{n}\:} \:{where}\:\alpha,\beta,\lambda \\ $$$${are}\:{the}\:{root}\:{of}\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\:{then}\:\:{show}\:{that}\:{s}_{\mathrm{4}\:} =\frac{\mathrm{4}{abd}+\mathrm{4}{b}^{\mathrm{2}} {c}−\mathrm{2}{c}}{{a}^{\mathrm{3}} } \\ $$

Question Number 43728 Answers: 1 Comments: 1

Question Number 43662 Answers: 0 Comments: 0

The number of ways in which 4 sides of a regular tetrahedron can be painted with different colours is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{4}\:\mathrm{sides} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\:\mathrm{tetrahedron}\:\mathrm{can}\:\mathrm{be}\:\mathrm{painted} \\ $$$$\mathrm{with}\:\mathrm{different}\:\mathrm{colours}\:\mathrm{is} \\ $$

Question Number 43659 Answers: 1 Comments: 2

An unfair coin with the probability of getting head in one toss = (1/5). If coin tosses n times, the probability of getting 2 heads is equal to the probability of getting 3 heads. Find n

$$\mathrm{An}\:\mathrm{unfair}\:\mathrm{coin}\:\mathrm{with}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{getting} \\ $$$$\mathrm{head}\:\mathrm{in}\:\mathrm{one}\:\mathrm{toss}\:=\:\frac{\mathrm{1}}{\mathrm{5}}. \\ $$$$\mathrm{If}\:\mathrm{coin}\:\mathrm{tosses}\:{n}\:\mathrm{times},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{getting}\:\mathrm{2}\:\mathrm{heads}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{getting}\:\mathrm{3}\:\mathrm{heads}.\:\mathrm{Find}\:{n} \\ $$

Question Number 43657 Answers: 3 Comments: 1

Question Number 43643 Answers: 3 Comments: 0

If sin^(−1) x+sin^(−1) (1−x) = cos^(−1) x, then x =

$$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}+\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} {x}, \\ $$$$\mathrm{then}\:\:{x}\:= \\ $$

Question Number 43642 Answers: 1 Comments: 0

The most general value of θ which satisfy both the equations cos θ= −(1/(√2)) and tan θ=1 is

$$\mathrm{The}\:\mathrm{most}\:\mathrm{general}\:\mathrm{value}\:\mathrm{of}\:\theta\:\mathrm{which} \\ $$$$\mathrm{satisfy}\:\mathrm{both}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{cos}\:\theta=\:−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}} \\ $$$$\mathrm{and}\:\:\mathrm{tan}\:\theta=\mathrm{1}\:\:\mathrm{is} \\ $$

Question Number 43641 Answers: 1 Comments: 0

In a triangle with one angle of 120°, the lengths of the sides form an AP. If the length of the greatest side is 7 cm., the area of the triangle is

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{one}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{120}°, \\ $$$$\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{form}\:\mathrm{an}\:\mathrm{AP}. \\ $$$$\mathrm{If}\:\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{side}\:\mathrm{is} \\ $$$$\mathrm{7}\:\mathrm{cm}.,\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$

Question Number 43638 Answers: 0 Comments: 0

Question Number 43630 Answers: 1 Comments: 0

If the roots of the equation x^3 −12x^2 +39x−28=0 are in AP, then their common difference will be

$$\mathrm{If}\:\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{3}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{39}{x}−\mathrm{28}=\mathrm{0}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{then} \\ $$$$\mathrm{their}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{will}\:\mathrm{be} \\ $$

Question Number 43629 Answers: 1 Comments: 0

If the sum of an infinite GP be 3 and the sum of the squares of its term is also 3, then its first term and common ratio are

$$\mathrm{If}\:\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{an}\:\mathrm{infinite}\:\mathrm{GP}\:\mathrm{be}\:\mathrm{3}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{squares}\:\mathrm{of}\:\mathrm{its}\:\mathrm{term}\:\mathrm{is}\:\mathrm{also}\:\mathrm{3}, \\ $$$$\mathrm{then}\:\mathrm{its}\:\mathrm{first}\:\mathrm{term}\:\mathrm{and}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{are} \\ $$

Question Number 43628 Answers: 1 Comments: 0

Three numbers form an increasing GP. If the middle number is doubled, then the new numbers are in AP. The common ratio of the GP is

$$\mathrm{Three}\:\mathrm{numbers}\:\mathrm{form}\:\mathrm{an}\:\mathrm{increasing}\:\mathrm{GP}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{number}\:\mathrm{is}\:\mathrm{doubled},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{new}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}.\:\mathrm{The}\:\mathrm{common}\:\mathrm{ratio} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{is} \\ $$

Question Number 43627 Answers: 0 Comments: 1

∫_( 0) ^(π^2 /4) ((sin (√x))/(√x)) dx =

$$\underset{\:\mathrm{0}} {\overset{\pi^{\mathrm{2}} /\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:\sqrt{{x}}}{\sqrt{{x}}}\:{dx}\:= \\ $$

Question Number 43626 Answers: 1 Comments: 0

∫ ((x cos x+1)/(√(2x^3 e^(sin x) +x^2 ))) dx =

$$\int\:\frac{{x}\:\mathrm{cos}\:{x}+\mathrm{1}}{\sqrt{\mathrm{2}{x}^{\mathrm{3}} {e}^{\mathrm{sin}\:{x}} +{x}^{\mathrm{2}} }}\:{dx}\:= \\ $$

Question Number 43625 Answers: 1 Comments: 0

∫_( 0) ^(π/4) ((√(tan x))/(sin x cos x)) dx = 2

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}\:{dx}\:=\:\mathrm{2} \\ $$

Question Number 43624 Answers: 1 Comments: 1

∫_( 0) ^1 ((tan^(−1) x)/(1+x^2 )) dx =

$$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{\mathrm{tan}^{−\mathrm{1}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:= \\ $$

Question Number 43623 Answers: 1 Comments: 3

let f(x)=∫_0 ^x (dt/(1+t^4 )) 1) find a explicit form of f(x) 2) calculate ∫_0 ^∞ (dt/(1+t^4 ))

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$

Question Number 43621 Answers: 1 Comments: 2

Question Number 43616 Answers: 1 Comments: 0

Solve: x^2 y′′ + xy′ − y = x , y_1 = x

$$\mathrm{Solve}:\:\:\:\mathrm{x}^{\mathrm{2}} \mathrm{y}''\:\:+\:\:\mathrm{xy}'\:\:−\:\mathrm{y}\:=\:\mathrm{x}\:,\:\:\:\:\:\:\:\:\mathrm{y}_{\mathrm{1}} \:=\:\mathrm{x} \\ $$

Question Number 43613 Answers: 0 Comments: 0

Be the vectors a^→ = (1, −1, 2), b^→ = (−5, k, k) and c^→ = (3, 1, 2) in the rectangular Cartesian coordinate system. For any vector r^→ , the equation r^→ ×a^→ + kb^→ = c^→ has a solution when k is equal to?

Question Number 43599 Answers: 0 Comments: 0

(dy/dx)(x^2 y^2 +xy)=1 Solve differential equation Thanks

$$\frac{{dy}}{{dx}}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} +{xy}\right)=\mathrm{1} \\ $$$$\mathrm{Solve}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{Thanks} \\ $$

Question Number 43608 Answers: 0 Comments: 3

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$$\mathrm{MJS}\:\left[\:\:\mathrm{12}/\mathrm{9}/\mathrm{18}\:\right]\:\mathrm{Code}\:−\:\mathrm{43569}\: \\ $$$$\mathrm{I}\:\mathrm{solved}\:\mathrm{one}\:\mathrm{of}\:\mathrm{these}\:,\:\mathrm{where}\:\mathrm{and}\:\mathrm{how}\:\mathrm{do} \\ $$$$\mathrm{i}\:\mathrm{get}\:\mathrm{the}\:\mathrm{prize}\:?\: \\ $$$$\mathrm{the}\:\mathrm{google}+\:\mathrm{page}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{really}\:\mathrm{tell}. \\ $$$$\mathrm{i}\:\mathrm{cannot}\:\mathrm{see}\:\mathrm{where}\:\mathrm{to}\:\mathrm{send}\:\mathrm{my}\:\mathrm{solution}\: \\ $$$$\mathrm{and}\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{see}\:\mathrm{any}\:\mathrm{guarantee}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{my} \\ $$$$\mathrm{copyright}\: \\ $$$$\mathrm{LYCON}\:\mathrm{TRIX}\:−\: \\ $$$$\mathrm{Gentlemen}\:,\:\mathrm{Download}\:\mathrm{Slack}\:\mathrm{app}\: \\ $$$$\mathrm{then}\:\mathrm{provide}\:\mathrm{your}\:\mathrm{email}\:,\:\mathrm{further}\:\mathrm{regime} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{operated}\:\mathrm{there}\: \\ $$$$\mathrm{we}\:\mathrm{won}'\mathrm{t}\:\mathrm{trouble}\:\mathrm{you}\:\mathrm{either}\:,\:\mathrm{we}\:\mathrm{care}\: \\ $$$$\mathrm{for}\:\mathrm{your}\:\mathrm{comfort}\:\mathrm{level}\: \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{the}\:\mathrm{general}\:\mathrm{manager}\:\mathrm{of}\:\mathrm{NS7UC}\: \\ $$$$\mathrm{initiave}\:,\:\mathrm{LYCON}\:\mathrm{TRIX} \\ $$

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