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Question Number 43350 Answers: 1 Comments: 2

Question Number 43349 Answers: 2 Comments: 0

Question Number 43348 Answers: 1 Comments: 0

Question Number 43346 Answers: 1 Comments: 0

sin x−sin 5x=sin 3x find the angle that satisfied the equestion

$$\mathrm{sin}\:{x}−\mathrm{sin}\:\mathrm{5}{x}=\mathrm{sin}\:\mathrm{3}{x}\:{find}\:{the}\:{angle} \\ $$$${that}\:{satisfied}\:{the}\:{equestion} \\ $$$$ \\ $$

Question Number 43344 Answers: 0 Comments: 1

The number 1, 2, 3, ..., n are arranged in a random order. The probability that the digits 1, 2, 3, ..., k (k>n) appears as neighbours is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...,\:{n}\:\:\mathrm{are}\:\mathrm{arranged} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{random}\:\mathrm{order}.\:\mathrm{The}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...,\:{k}\:\left({k}>{n}\right)\:\mathrm{appears} \\ $$$$\mathrm{as}\:\mathrm{neighbours}\:\mathrm{is} \\ $$

Question Number 43343 Answers: 1 Comments: 0

how many odd numbers greater than 60000 can be made from the digits 5,6,7,8,9,0 if no number contains any digit more than once?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{odd}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{60000}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{0}\:\mathrm{if}\:\mathrm{no}\:\mathrm{number}\:\mathrm{contains} \\ $$$$\mathrm{any}\:\mathrm{digit}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}? \\ $$

Question Number 43342 Answers: 1 Comments: 0

using the substitution u=x+2, evaluate ∫_1 ^2 ((x−1)/((x+2)^4 ))

$$\mathrm{using}\:\mathrm{the}\:\mathrm{substitution}\:\mathrm{u}=\mathrm{x}+\mathrm{2},\:\mathrm{evaluate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$

Question Number 43341 Answers: 1 Comments: 0

write 2×7+3×8 4×9+5×10+6×11 using the sigma notation

$$\mathrm{write}\:\mathrm{2}×\mathrm{7}+\mathrm{3}×\mathrm{8}\:\mathrm{4}×\mathrm{9}+\mathrm{5}×\mathrm{10}+\mathrm{6}×\mathrm{11}\:\mathrm{using}\:\mathrm{the}\:\mathrm{sigma} \\ $$$$\mathrm{notation} \\ $$

Question Number 43338 Answers: 1 Comments: 1

Question Number 43337 Answers: 0 Comments: 3

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

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

Question Number 43324 Answers: 1 Comments: 0

Question Number 43323 Answers: 0 Comments: 0

Question Number 43322 Answers: 1 Comments: 1

Question Number 43331 Answers: 0 Comments: 5

Question Number 43319 Answers: 1 Comments: 0

Question Number 43288 Answers: 0 Comments: 2

Question Number 43268 Answers: 0 Comments: 5

probably, cos nx=2^(n−1) cos^n x−n2^(n−3) cos^(n−2) +(((n−3)n)/2)2^(n−5) cos^(n−4) x… wow

$$\mathrm{probably},\:\mathrm{cos}\:{nx}=\mathrm{2}^{{n}−\mathrm{1}} \mathrm{cos}^{{n}} \:{x}−{n}\mathrm{2}^{{n}−\mathrm{3}} \mathrm{cos}^{{n}−\mathrm{2}} \: \\ $$$$+\frac{\left({n}−\mathrm{3}\right){n}}{\mathrm{2}}\mathrm{2}^{{n}−\mathrm{5}} \mathrm{cos}^{{n}−\mathrm{4}} \:{x}\ldots \\ $$$$\mathrm{wow} \\ $$

Question Number 43265 Answers: 0 Comments: 3

Question Number 43264 Answers: 2 Comments: 1

Question Number 43263 Answers: 2 Comments: 0

Question Number 43260 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(4n^2 −1)) .

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} \:−\mathrm{1}}\:. \\ $$

Question Number 43259 Answers: 0 Comments: 1

calculate Σ_(n=2) ^∞ (((−1)^n )/(n^2 −1))

$${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 43252 Answers: 3 Comments: 2

Question Number 43226 Answers: 1 Comments: 0

If(x−(1/x)=7)thenthevalueofx^4 +(1/x^4 )is?

$$ \\ $$$${If}\left({x}−\frac{\mathrm{1}}{{x}}=\mathrm{7}\right){thenthevalueofx}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }{is}? \\ $$

Question Number 43224 Answers: 1 Comments: 0

how many square in a chess board.

$${how}\:{many}\:{square}\:{in}\:{a}\:{chess}\:{board}. \\ $$

Question Number 43267 Answers: 0 Comments: 2

cos 2x=2cos^2 −1 cos 3x=4cos^3 x−3cos x cos 4x=8cos^4 x−8cos^2 x+1 cos 5x=16cos^5 x−20cos^3 +5cos x cos 6x=32cos^6 x−48cos^4 x+18cos^2 x−1 cos 7x=64cos^7 x−112cos^5 x+56cos^3 x−4cos x cos 8x=128cos^8 x−256cos^6 x+160cos^4 x−32cos^2 x+1

$$\mathrm{cos}\:\mathrm{2}{x}=\mathrm{2cos}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{3}{x}=\mathrm{4cos}^{\mathrm{3}} \:{x}−\mathrm{3cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{4}{x}=\mathrm{8cos}^{\mathrm{4}} \:{x}−\mathrm{8cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{5}{x}=\mathrm{16cos}^{\mathrm{5}} \:{x}−\mathrm{20cos}^{\mathrm{3}} +\mathrm{5cos}\:{x}\: \\ $$$$\mathrm{cos}\:\mathrm{6}{x}=\mathrm{32cos}^{\mathrm{6}} \:{x}−\mathrm{48cos}^{\mathrm{4}} \:{x}+\mathrm{18cos}^{\mathrm{2}} \:{x}−\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{7}{x}=\mathrm{64cos}^{\mathrm{7}} \:{x}−\mathrm{112cos}^{\mathrm{5}} \:{x}+\mathrm{56cos}^{\mathrm{3}} \:{x}−\mathrm{4cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{8}{x}=\mathrm{128cos}^{\mathrm{8}} \:{x}−\mathrm{256cos}^{\mathrm{6}} \:{x}+\mathrm{160cos}^{\mathrm{4}} \:{x}−\mathrm{32cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$

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