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AllQuestion and Answers: Page 1514

Question Number 48735 Answers: 1 Comments: 0

The roots of the equation 2^(x+2) ∙ 3^((3x)/(x−1)) = 9 are given by

$$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{2}^{{x}+\mathrm{2}} \centerdot\:\mathrm{3}^{\frac{\mathrm{3}{x}}{{x}−\mathrm{1}}} =\:\mathrm{9}\:\mathrm{are}\:\mathrm{given}\:\mathrm{by} \\ $$

Question Number 48729 Answers: 1 Comments: 0

Question Number 48725 Answers: 1 Comments: 3

∫ ∫ (√(x^2 + y^2 )) dx dy, (√(3y)) ≤ x ≤ (√(4 − y^2 )) , 0 ≤ y ≤ 2

$$\int\:\int\:\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\:\:\:\mathrm{dx}\:\mathrm{dy},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{3y}}\:\:\:\leqslant\:\:\mathrm{x}\:\:\leqslant\:\:\sqrt{\mathrm{4}\:−\:\mathrm{y}^{\mathrm{2}} }\:\:,\:\:\:\:\:\:\:\:\:\mathrm{0}\:\leqslant\:\mathrm{y}\:\leqslant\:\mathrm{2} \\ $$

Question Number 48724 Answers: 1 Comments: 1

Hey, everyone! Could someone help in this question below? The vectors (1, 2, 5), (3, 2, 1) and (9, 2, −11) in R^3 generate the vector subspace to wich belongs the vector? a) (−20, −8, 12) b) (2, 10, 33) c) (9, 10, 18) d) (5, 2, −2) e) (31, 18, 0) Why are my posts never resolved?

$${Hey},\:{everyone}! \\ $$$${Could}\:\:{someone}\:{help}\:{in}\:{this}\:{question}\:{below}? \\ $$$${The}\:{vectors}\:\left(\mathrm{1},\:\mathrm{2},\:\mathrm{5}\right),\:\left(\mathrm{3},\:\mathrm{2},\:\mathrm{1}\right)\:{and}\:\left(\mathrm{9},\:\mathrm{2},\:−\mathrm{11}\right)\:{in}\:\mathbb{R}^{\mathrm{3}} \:{generate}\:{the}\:{vector}\:{subspace}\:{to}\:{wich}\:{belongs}\:{the}\:{vector}? \\ $$$$\left.{a}\right)\:\left(−\mathrm{20},\:−\mathrm{8},\:\mathrm{12}\right) \\ $$$$\left.{b}\right)\:\left(\mathrm{2},\:\mathrm{10},\:\mathrm{33}\right) \\ $$$$\left.{c}\right)\:\left(\mathrm{9},\:\mathrm{10},\:\mathrm{18}\right) \\ $$$$\left.{d}\right)\:\left(\mathrm{5},\:\mathrm{2},\:−\mathrm{2}\right) \\ $$$$\left.{e}\right)\:\left(\mathrm{31},\:\mathrm{18},\:\mathrm{0}\right) \\ $$$${Why}\:{are}\:{my}\:{posts}\:{never}\:{resolved}? \\ $$$$ \\ $$$$ \\ $$

Question Number 48720 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((x^2 −2cosx+1)/(x^4 +x^2 +1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{\mathrm{2}} \:−\mathrm{2}{cosx}+\mathrm{1}}{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 48719 Answers: 1 Comments: 1

find ∫ ((x−2)/(√(x^2 +4x−3)))dx

$${find}\:\:\int\:\:\:\:\frac{{x}−\mathrm{2}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{3}}}{dx} \\ $$

Question Number 48718 Answers: 1 Comments: 2

let I_n =∫_0 ^1 (1−t^2 )^n dt 1) calculate I_n by recurrence 2)find the value of Σ_(k=0) ^n (((−1)^k )/(2k+1))C_n ^k

$${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{{n}} {dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} \:{by}\:{recurrence} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{2}{k}+\mathrm{1}}{C}_{{n}} ^{{k}} \\ $$

Question Number 48717 Answers: 0 Comments: 1

let f(x)=∫_0 ^(π/4) ln(1+xtant)dt 1) find f(x) at a simple form 2)calculate ∫_0 ^(π/4) ln(1+2tan(t))dt

$${let}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{xtant}\right){dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right)\:{at}\:{a}\:{simple}\:{form} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+\mathrm{2}{tan}\left({t}\right)\right){dt} \\ $$

Question Number 48715 Answers: 0 Comments: 4

1) find f(λ) =∫_0 ^1 (dx/(2+e^(−λx) )) with λ>0 2)calculate ∫_0 ^1 (x/((2+e^(−λx) )^2 ))dx 3) find the value of ∫_0 ^1 (dx/(2 +e^(−x(√3)) ))dx and ∫_0 ^1 (x/((2+e^(−x(√3)) )^2 ))dx

$$\left.\mathrm{1}\right)\:{find}\:\:{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{\mathrm{2}+{e}^{−\lambda{x}} }\:\:{with}\:\lambda>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{x}}{\left(\mathrm{2}+{e}^{−\lambda{x}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\mathrm{2}\:+{e}^{−{x}\sqrt{\mathrm{3}}} }{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}}{\left(\mathrm{2}+{e}^{−{x}\sqrt{\mathrm{3}}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 48711 Answers: 1 Comments: 1

Question Number 48703 Answers: 1 Comments: 0

Question Number 48687 Answers: 0 Comments: 0

f(x)=sin (x) f(x)+f′((1/x))=(1/2)(√2) find x?

$${f}\left({x}\right)=\mathrm{sin}\:\left({x}\right) \\ $$$${f}\left({x}\right)+{f}'\left(\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{2}} \\ $$$$\mathrm{find}\:{x}? \\ $$

Question Number 48705 Answers: 3 Comments: 2

Q.1→ Coefficient of a^8 b^4 c^9 d^9 in expansion of (abc+abd+acd+bcd)^(10) =? Q.2→ Coefficient of (1/x) in expansion of (1+x)^n (1+(1/x))^n =? Q.3→ If x^m occurs in expansion of (x+(1/x^2 ))^(2n) , then its coefficient=?

$${Q}.\mathrm{1}\rightarrow \\ $$$${Coefficient}\:{of}\:{a}^{\mathrm{8}} {b}^{\mathrm{4}} {c}^{\mathrm{9}} {d}^{\mathrm{9}} \:{in}\:{expansion} \\ $$$${of}\:\left({abc}+{abd}+{acd}+{bcd}\right)^{\mathrm{10}} \:=? \\ $$$$ \\ $$$${Q}.\mathrm{2}\rightarrow \\ $$$${Coefficient}\:{of}\:\frac{\mathrm{1}}{{x}}\:{in}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{n}} =? \\ $$$$ \\ $$$${Q}.\mathrm{3}\rightarrow \\ $$$${If}\:{x}^{{m}} \:{occurs}\:{in}\:{expansion}\:{of}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}{n}} ,\:{then}\:{its}\:{coefficient}=? \\ $$

Question Number 48678 Answers: 0 Comments: 0

Question Number 48677 Answers: 1 Comments: 0

Question Number 48676 Answers: 1 Comments: 0

Question Number 48675 Answers: 2 Comments: 0

Find remainder when 27^(40) is divided by 12 ?

$${Find}\:{remainder}\:{when}\:\mathrm{27}^{\mathrm{40}} \:{is}\:{divided} \\ $$$${by}\:\mathrm{12}\:? \\ $$

Question Number 48668 Answers: 1 Comments: 3

let f(x)=(e^(−2x) /(x+1)) 1) calculate f^((n)) (x) and f^((n)) (0) . 2) develop f at integr serie .

$${let}\:{f}\left({x}\right)=\frac{{e}^{−\mathrm{2}{x}} }{{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right)\:. \\ $$$$\left.\mathrm{2}\right)\:{develop}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 48667 Answers: 1 Comments: 1

find ∫_0 ^1 ((arctan(x))/(√(1+x^2 ))) dx .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left({x}\right)}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx}\:. \\ $$

Question Number 48664 Answers: 0 Comments: 3

A travels in a desert, reaches an oasis and rests. Then B comes in, followed by C. After a while they discuss, what to lunch on; B opens a lunch box with 5 chapatis, C had got 3 chapatis. A had got nothing. They lunched together sharing equally. Then A says he got to move on, and gave B 8 bucks, asking him to share it with C, and he leaves. B kept 5 bucks and gave C 3 bucks. C did not agree and was asking to share it equally. B denied. They reach a village where they put forth their issue where the judicial head gives a judgement quite surprising to both B and C. What should that be?

$${A}\:{travels}\:{in}\:{a}\:{desert},\:{reaches}\:{an} \\ $$$${oasis}\:{and}\:{rests}.\:{Then}\:{B}\:{comes}\:{in}, \\ $$$${followed}\:{by}\:{C}.\:{After}\:{a}\:{while}\:{they} \\ $$$${discuss},\:{what}\:{to}\:{lunch}\:{on};\: \\ $$$${B}\:{opens}\:{a}\:{lunch}\:{box}\:{with}\:\mathrm{5}\:{chapatis}, \\ $$$${C}\:{had}\:{got}\:\mathrm{3}\:{chapatis}.\:{A}\:{had}\:{got} \\ $$$${nothing}.\:{They}\:{lunched}\:{together} \\ $$$${sharing}\:{equally}.\:{Then}\:{A}\:{says}\:{he} \\ $$$${got}\:{to}\:{move}\:{on},\:{and}\:{gave}\:{B}\: \\ $$$$\mathrm{8}\:{bucks},\:{asking}\:{him}\:{to}\:{share}\:{it} \\ $$$${with}\:{C},\:{and}\:{he}\:{leaves}. \\ $$$${B}\:{kept}\:\mathrm{5}\:{bucks}\:{and}\:{gave}\:{C}\:\:\mathrm{3}\:{bucks}. \\ $$$${C}\:{did}\:{not}\:{agree}\:{and}\:{was}\:{asking} \\ $$$${to}\:{share}\:{it}\:{equally}.\:{B}\:{denied}.\:{They} \\ $$$${reach}\:{a}\:{village}\:{where}\:{they}\:{put}\:{forth} \\ $$$${their}\:{issue}\:{where}\:{the}\:{judicial}\:{head} \\ $$$${gives}\:{a}\:{judgement}\:{quite}\:{surprising} \\ $$$${to}\:{both}\:{B}\:{and}\:{C}. \\ $$$${What}\:{should}\:{that}\:{be}? \\ $$

Question Number 48659 Answers: 1 Comments: 0

Find x 3sec[2(x+(π/6))]= 4

$$\mathrm{Find}\:\mathrm{x} \\ $$$$\mathrm{3sec}\left[\mathrm{2}\left(\mathrm{x}+\frac{\pi}{\mathrm{6}}\right)\right]=\:\mathrm{4} \\ $$

Question Number 48656 Answers: 0 Comments: 3

Question Number 48653 Answers: 1 Comments: 1

Question Number 48643 Answers: 1 Comments: 2

Question Number 48638 Answers: 1 Comments: 4

Question Number 48616 Answers: 0 Comments: 1

find four numbers such that the sum of every two and the sum of all four should be perfect squaresk

$${find}\:{four}\:{numbers}\:{such}\:{that}\:{the}\:{sum}\:{of}\:{every}\:{two}\:{and}\:{the}\:{sum}\:{of}\:{all}\:{four}\:{should}\:{be}\:{perfect}\:{squaresk}\: \\ $$

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