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Question Number 54955 Answers: 1 Comments: 0

Let vector set {u_1 , u_2 , u_3 , u_4 } in C^n free linear. So that {u_1 +αu_2 , u_2 +αu_3 , u_3 +αu_4 , u_4 +αu_1 } too free linear , scalar α have to...

$$\mathrm{Let}\:\mathrm{vector}\:\mathrm{set}\:\left\{{u}_{\mathrm{1}} ,\:{u}_{\mathrm{2}} ,\:{u}_{\mathrm{3}} ,\:{u}_{\mathrm{4}} \right\}\:\mathrm{in}\:\mathbb{C}^{{n}} \\ $$$$\mathrm{free}\:\mathrm{linear}.\:\mathrm{So}\:\mathrm{that}\: \\ $$$$\left\{{u}_{\mathrm{1}} +\alpha{u}_{\mathrm{2}} ,\:{u}_{\mathrm{2}} +\alpha{u}_{\mathrm{3}} ,\:{u}_{\mathrm{3}} +\alpha{u}_{\mathrm{4}} ,\:{u}_{\mathrm{4}} +\alpha{u}_{\mathrm{1}} \right\} \\ $$$$\mathrm{too}\:\mathrm{free}\:\mathrm{linear}\:,\:\mathrm{scalar}\:\alpha\:\mathrm{have}\:\mathrm{to}... \\ $$

Question Number 54953 Answers: 1 Comments: 1

The characteristic polynomial matrices [(1,(−2),3),(4,5,(−6)),((−7),8,9) ]is...

$$\mathrm{The}\:\mathrm{characteristic}\:\mathrm{polynomial} \\ $$$$\mathrm{matrices}\:\begin{bmatrix}{\mathrm{1}}&{−\mathrm{2}}&{\mathrm{3}}\\{\mathrm{4}}&{\mathrm{5}}&{−\mathrm{6}}\\{−\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}\end{bmatrix}\mathrm{is}... \\ $$

Question Number 54952 Answers: 0 Comments: 1

If T : C→C is linear transformation and x ∈ C, then T(x)=...

$$\mathrm{If}\:\:{T}\::\:\mathbb{C}\rightarrow\mathbb{C}\:\:\mathrm{is}\:\mathrm{linear}\:\mathrm{transformation} \\ $$$$\mathrm{and}\:{x}\:\in\:\mathbb{C},\:\mathrm{then}\:{T}\left({x}\right)=... \\ $$

Question Number 54948 Answers: 0 Comments: 1

α,β are the roots and prove that α^n +β^n =2[cos nΠ/2]

$$\alpha,\beta\:{are}\:{the}\:{roots}\:{and}\:{prove}\:{that}\:\alpha^{{n}} +\beta^{{n}} =\mathrm{2}\left[\mathrm{cos}\:{n}\Pi/\mathrm{2}\right] \\ $$

Question Number 54944 Answers: 2 Comments: 1

lim_(x→0) (x/(3^x − 1))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{{x}}{\mathrm{3}^{{x}} \:−\:\mathrm{1}} \\ $$

Question Number 54939 Answers: 0 Comments: 3

coordinate x^2 to basis {x^2 +x, x+1, x^2 +1} at P_2 is...

$$\mathrm{coordinate}\:{x}^{\mathrm{2}} \:\mathrm{to}\:\mathrm{basis}\:\left\{{x}^{\mathrm{2}} +{x},\:{x}+\mathrm{1},\:{x}^{\mathrm{2}} +\mathrm{1}\right\} \\ $$$$\mathrm{at}\:\mathrm{P}_{\mathrm{2}} \:\mathrm{is}... \\ $$

Question Number 54938 Answers: 0 Comments: 1

If A= [(2,1),(1,2) ],then A^(2006) =...

$$\mathrm{If}\:{A}=\begin{bmatrix}{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{2}}\end{bmatrix},\mathrm{then}\:{A}^{\mathrm{2006}} =... \\ $$

Question Number 54937 Answers: 1 Comments: 0

If A matrices order 1999×2006, then minimal value of rank(A)+null(A)

$$\mathrm{If}\:{A}\:\mathrm{matrices}\:\mathrm{order}\:\mathrm{1999}×\mathrm{2006}, \\ $$$$\mathrm{then}\:\mathrm{minimal}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{rank}\left({A}\right)+{null}\left({A}\right) \\ $$$$ \\ $$

Question Number 54936 Answers: 1 Comments: 1

let f(θ) = ∫_0 ^1 (√(x^2 +2(cosθ)x +1))dx with θ ∈ R . 1) calculate f(θ) 2) find the value of g(θ)=∫_0 ^1 ((xsinθ)/(√(x^2 +2cosθ x +1)))dx

$${let}\:{f}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}}{dx}\:\:\:{with}\:\theta\:\in\:{R}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{g}\left(\theta\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xsin}\theta}{\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{cos}\theta\:{x}\:+\mathrm{1}}}{dx} \\ $$

Question Number 54923 Answers: 0 Comments: 9

Is tan 1° rational or irrational? Give your proof.

$${Is}\:\mathrm{tan}\:\mathrm{1}°\:{rational}\:{or}\:{irrational}? \\ $$$${Give}\:{your}\:{proof}. \\ $$

Question Number 54919 Answers: 1 Comments: 1

calculate ∫_1 ^(√2) (x^3 +1)(√(x^2 −1))dx

$${calculate}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{2}}} \left({x}^{\mathrm{3}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$

Question Number 54909 Answers: 0 Comments: 5

Do you know a geometrical proof of the irrationality of number (√2) ?

$${Do}\:{you}\:{know}\:{a}\:{geometrical}\:{proof} \\ $$$${of}\:{the}\:{irrationality}\:{of}\:{number}\:\sqrt{\mathrm{2}}\:? \\ $$

Question Number 54903 Answers: 1 Comments: 0

Question Number 54901 Answers: 1 Comments: 1

Question Number 54897 Answers: 2 Comments: 1

Find value of n so 120 ∣ 5n(n^2 −1)

$$\mathrm{Find}\:\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{so}\:\mathrm{120}\:\mid\:\mathrm{5}{n}\left({n}^{\mathrm{2}} −\mathrm{1}\right) \\ $$

Question Number 54896 Answers: 1 Comments: 1

∫(√)(x2+2x+2)

$$\int\sqrt{}\left({x}\mathrm{2}+\mathrm{2}{x}+\mathrm{2}\right) \\ $$

Question Number 54880 Answers: 2 Comments: 0

If x^2 −y^2 =a^2 find (d^2 y/dx^2 ) if a is constant.

$${If}\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} ={a}^{\mathrm{2}} \:\:{find}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:{if}\:{a}\:{is} \\ $$$${constant}. \\ $$

Question Number 54876 Answers: 1 Comments: 1

find the coefficientof x^2 in the binomial expansion of (x^2 +(2/x))^4

$$\mathrm{find}\:\mathrm{the}\:\mathrm{coefficientof}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{binomial} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{x}}\right)^{\mathrm{4}} \\ $$

Question Number 54875 Answers: 2 Comments: 0

Given that((log(3x+1)^(2x−1) )/(log(3x+1)))=5,find the value of x.

$$\mathrm{Given}\:\mathrm{that}\frac{\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{2x}−\mathrm{1}} }{\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)}=\mathrm{5},\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 54869 Answers: 1 Comments: 0

Question Number 54868 Answers: 0 Comments: 1

Question Number 54860 Answers: 1 Comments: 1

Question Number 54858 Answers: 2 Comments: 0

(Q1) The expansion (x−(1/(3x)))^(12) (i) find the term independent of x (ii) find the term x^4 (Q2) There are some nut in a bag. when 2 ounces of peanut are added to the mixture, the percentage of peanut becomes 20% . Richard added 2 ounces of cashew to the mixture and the percentage of cashew nut was 33.33% . find the percentage of cashew nut that were there initially. please sir help

$$\left({Q}\mathrm{1}\right)\:{The}\:{expansion}\:\left({x}−\frac{\mathrm{1}}{\mathrm{3}{x}}\right)^{\mathrm{12}} \\ $$$$\left({i}\right)\:{find}\:{the}\:{term}\:{independent}\:{of}\:{x} \\ $$$$\left({ii}\right)\:{find}\:{the}\:{term}\:{x}^{\mathrm{4}} \\ $$$$\left({Q}\mathrm{2}\right)\:{There}\:{are}\:{some}\:{nut}\:{in}\:{a}\:{bag}.\:{when} \\ $$$$\:\mathrm{2}\:{ounces}\:{of}\:{peanut}\:{are}\:{added}\:{to}\:{the} \\ $$$${mixture},\:{the}\:{percentage}\:{of}\:{peanut}\: \\ $$$${becomes}\:\mathrm{20\%}\:.\:{Richard}\:\:{added}\:\:\mathrm{2}\: \\ $$$${ounces}\:{of}\:{cashew}\:{to}\:{the}\:{mixture}\:{and} \\ $$$${the}\:{percentage}\:{of}\:{cashew}\:{nut}\:{was}\: \\ $$$$\mathrm{33}.\mathrm{33\%}\:.\:{find}\:{the}\:{percentage}\:{of}\: \\ $$$${cashew}\:{nut}\:{that}\:{were}\:{there}\:{initially}. \\ $$$${please}\:{sir}\:{help} \\ $$

Question Number 54857 Answers: 1 Comments: 0

Question Number 54856 Answers: 1 Comments: 2

Question Number 54841 Answers: 1 Comments: 0

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