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Question Number 114554 Answers: 1 Comments: 0

Given a matrix A = (((a b)),((c d)) ) satisfies the equation A^2 +λA+7I = 0 where I= (((1 0)),((0 1)) ) . Find the value of trace of A

$${Given}\:{a}\:{matrix}\:{A}\:=\:\begin{pmatrix}{{a}\:\:\:{b}}\\{{c}\:\:\:{d}}\end{pmatrix}\:{satisfies} \\ $$$${the}\:{equation}\:{A}^{\mathrm{2}} +\lambda{A}+\mathrm{7}{I}\:=\:\mathrm{0} \\ $$$${where}\:{I}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}\:.\:{Find}\:{the}\:{value}\:{of}\: \\ $$$${trace}\:{of}\:{A}\: \\ $$

Question Number 114551 Answers: 1 Comments: 3

The value of x in the given equation 4^x −3^(x−(1/2)) = 3^(x+(1/2)) −2^(2x−1) , is _,

$${The}\:{value}\:{of}\:{x}\:{in}\:{the}\:{given}\:{equation} \\ $$$$\mathrm{4}^{{x}} −\mathrm{3}^{{x}−\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\mathrm{3}^{{x}+\frac{\mathrm{1}}{\mathrm{2}}} \:−\mathrm{2}^{\mathrm{2}{x}−\mathrm{1}} \:,\:{is}\:\_, \\ $$

Question Number 114543 Answers: 2 Comments: 0

lim_(x→0) ((x^2 arctan (2x))/(x cos x+tan x)) ?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} \:\mathrm{arctan}\:\left(\mathrm{2}{x}\right)}{{x}\:\mathrm{cos}\:{x}+\mathrm{tan}\:{x}}\:? \\ $$

Question Number 114541 Answers: 1 Comments: 0

Question Number 114539 Answers: 2 Comments: 1

lim_(x→0) [ ((sinh x − sin x)/x^3 ) ] = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\left[\:\frac{\mathrm{sinh}\:{x}\:−\:\mathrm{sin}\:{x}}{{x}^{\mathrm{3}} }\:\right]\:\:=\:\:? \\ $$

Question Number 114538 Answers: 1 Comments: 4

how many trees can be planted in one square meter area if the distance between each tow trees is 3cm?

$${how}\:{many}\:{trees}\:{can}\:{be}\:{planted}\:{in}\:{one} \\ $$$${square}\:{meter}\:{area}\:{if}\:{the}\:{distance}\: \\ $$$${between}\:{each}\:{tow}\:{trees}\:{is}\:\mathrm{3}{cm}? \\ $$

Question Number 114536 Answers: 0 Comments: 2

Question Number 114533 Answers: 1 Comments: 0

Question Number 114526 Answers: 1 Comments: 2

(1/π)∫_0 ^π e^(2cos θ) dθ ?

$$\frac{\mathrm{1}}{\pi}\underset{\mathrm{0}} {\overset{\pi} {\int}}\:{e}^{\mathrm{2cos}\:\theta} \:{d}\theta\:? \\ $$

Question Number 114514 Answers: 1 Comments: 2

Question Number 114512 Answers: 1 Comments: 4

Question Number 114511 Answers: 2 Comments: 3

Find numbers which are common terms of the two following arithmetic progression: 3,7,11,...,407 and 2,9,16,...,709

$$\mathrm{Find}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{are}\:\mathrm{common} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{following}\:\mathrm{arithmetic} \\ $$$$\mathrm{progression}: \\ $$$$\mathrm{3},\mathrm{7},\mathrm{11},...,\mathrm{407}\:\mathrm{and}\:\mathrm{2},\mathrm{9},\mathrm{16},...,\mathrm{709} \\ $$

Question Number 114485 Answers: 3 Comments: 0

Question Number 114482 Answers: 1 Comments: 0

Question Number 114480 Answers: 3 Comments: 1

Question Number 114475 Answers: 0 Comments: 5

Question Number 114472 Answers: 0 Comments: 2

... calculus... evaluate :: I=∫_0 ^( (π/2)) ((tan(2x))/( (√(sin^4 (x)+4cos^2 (x)))−(√(cos^4 (x)+4sin^2 (x) )))) dx= ??? ...m.n.july.1970....

$$\:\:\:\:\:\:\:\:\:...\:\:{calculus}... \\ $$$${evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}\left(\mathrm{2}{x}\right)}{\:\sqrt{{sin}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{cos}^{\mathrm{2}} \left({x}\right)}−\sqrt{{cos}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{sin}^{\mathrm{2}} \left({x}\right)\:}}\:{dx}=\:??? \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:...{m}.{n}.{july}.\mathrm{1970}.... \\ $$$$ \\ $$

Question Number 114467 Answers: 1 Comments: 0

∫x sin^n (x) dx

$$\int{x}\:{sin}^{{n}} \left({x}\right)\:{dx} \\ $$

Question Number 114461 Answers: 1 Comments: 1

Question Number 114447 Answers: 4 Comments: 1

Question Number 114433 Answers: 1 Comments: 0

find sum of the series 1^2 −3^2 +5^2 −7^2 +9^2 −11^2 +...+(4n−3)^2 −(4n−1)^2

$${find}\:{sum}\:{of}\:{the}\:{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} +...+\left(\mathrm{4}{n}−\mathrm{3}\right)^{\mathrm{2}} −\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 114422 Answers: 3 Comments: 3

The solution set of ∣((x+1)/x)∣+∣x+1∣=(((x+1)^2 )/(∣x∣)) is

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\: \\ $$$$\:\mid\frac{{x}+\mathrm{1}}{{x}}\mid+\mid{x}+\mathrm{1}\mid=\frac{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{\mid{x}\mid}\:\:\mathrm{is} \\ $$

Question Number 114420 Answers: 2 Comments: 4

Solution of ∣ x−1 ∣≥∣ x−3 ∣ is

$$\mathrm{Solution}\:\mathrm{of}\:\:\mid\:{x}−\mathrm{1}\:\mid\geqslant\mid\:{x}−\mathrm{3}\:\mid\:\mathrm{is} \\ $$

Question Number 114411 Answers: 2 Comments: 0

lim_(x→0) (((1+x)^(−(3/4)) −(1+x)^(−(1/4)) )/(2x)) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{\mathrm{2}{x}}\:=? \\ $$

Question Number 114409 Answers: 1 Comments: 0

find solution set of equation sin x = 2 , x ∈ C .

$${find}\:{solution}\:{set}\:{of}\:{equation} \\ $$$$\:\mathrm{sin}\:{x}\:=\:\mathrm{2}\:,\:{x}\:\in\:\mathbb{C}\:. \\ $$

Question Number 114405 Answers: 2 Comments: 0

lim_(x→0) ((x tan x)/( (√3) cos x−sin^2 x−(√3))) ?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{tan}\:{x}}{\:\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{sin}\:^{\mathrm{2}} {x}−\sqrt{\mathrm{3}}}\:? \\ $$

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