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x^2 +x=y^4 +y^3 +y^2 +y x^4 +(x+1)^4 =y^2 +(y+1)^2 find x and y of is…

$${x}^{\mathrm{2}} +{x}={y}^{\mathrm{4}} +{y}^{\mathrm{3}} +{y}^{\mathrm{2}} +{y} \\ $$$${x}^{\mathrm{4}} +\left({x}+\mathrm{1}\right)^{\mathrm{4}} ={y}^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}\:{x}\:\mathrm{and}\:{y}\:\:\mathrm{of}\:\mathrm{is}\ldots \\ $$$$ \\ $$

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A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match?

$$\mathrm{A}\:\mathrm{drawer}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{brown}\:\mathrm{socks}\:\mathrm{and}\:\mathrm{4} \\ $$$$\mathrm{blue}\:\mathrm{socks}\:\mathrm{well}\:\mathrm{mixed}.\:\mathrm{A}\:\mathrm{man}\:\mathrm{reaches} \\ $$$$\mathrm{the}\:\mathrm{drawer}\:\mathrm{and}\:\mathrm{pulls}\:\mathrm{out}\:\mathrm{2}\:\mathrm{socks}\:\mathrm{at} \\ $$$$\mathrm{random}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{they}\:\mathrm{match}? \\ $$

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If z= cos θ + isin θ , 0<θ<(π/6) , then prove that argument of 1−z^4 = 2θ − (π/2) .

$$\mathrm{If}\:\mathrm{z}=\:\mathrm{cos}\:\theta\:+\:\mathrm{isin}\:\theta\:,\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{6}}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{argument}\:\mathrm{of}\:\:\mathrm{1}−\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{2}\theta\:−\:\frac{\pi}{\mathrm{2}}\:. \\ $$

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A particle starts from rest with acceleration(30+6t) ms^(−2) at time t. Where will the particle come to rest again?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{with}\:\mathrm{acceleration}\left(\mathrm{30}+\mathrm{6t}\right) \\ $$$$\mathrm{ms}^{−\mathrm{2}} \:\mathrm{at}\:\mathrm{time}\:\mathrm{t}.\:\mathrm{Where}\:\mathrm{will}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{come}\:\mathrm{to}\:\mathrm{rest} \\ $$$$\mathrm{again}? \\ $$

Question Number 43353 Answers: 2 Comments: 1

Given the functions f(x)=2x−1 and f•g(x)=x^2 −x+2, find g(x)

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{functions}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}\:\mathrm{and}\:\mathrm{f}\bullet\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{2}, \\ $$$$\mathrm{find}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$

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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

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

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

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

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