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Question Number 28257 Answers: 0 Comments: 0

let give ( 2 3 −3) A = ( −1 0 1) ( −1 1 0 ) find a diagoal matrice D and a inversible matrice P wich verify A = P.D.P^(−1) and calculate A^n .

Question Number 28248 Answers: 1 Comments: 0

Question Number 28247 Answers: 0 Comments: 1

find the value of ∫_1 ^(+∞) ((lnx)/(1+x^2 ))dx .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{lnx}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 28242 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ e^(−x) lnxdx .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {lnxdx}\:\:. \\ $$

Question Number 28241 Answers: 1 Comments: 1

Question Number 28240 Answers: 1 Comments: 0

Question Number 28255 Answers: 0 Comments: 0

let give p=(_(1 −2) ^(1 −1) ) and D= (_(3 −6) ^(2 −2) ) calculate A= p.D.p^(−1) .

$${let}\:{give}\:{p}=\left(_{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:−\mathrm{2}} ^{\mathrm{1}\:\:\:\:\:\:\:\:\:\:−\mathrm{1}} \:\:\right)\:\:{and}\:\:{D}=\:\:\left(_{\mathrm{3}\:\:\:\:\:\:\:\:\:\:−\mathrm{6}} ^{\mathrm{2}\:\:\:\:\:\:\:\:−\mathrm{2}} \:\right)\:{calculate} \\ $$$${A}=\:{p}.{D}.{p}^{−\mathrm{1}} \:. \\ $$

Question Number 28256 Answers: 0 Comments: 0

let give A= _( () −1 1 1) ( 1 −1 1) find A^n for n integr. ( 1 1 −1)

$$\left.{let}\:{give}\:\:\:{A}=\:\:_{\:\:\:\:\left(\right.} \:−\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:−\mathrm{1}\:\:\:\:\mathrm{1}\right)\:\:\:\:\:\:\:{find}\:\:{A}^{{n}} \:\:{for}\:{n}\:{integr}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:−\mathrm{1}\right) \\ $$$$\:\:\:\: \\ $$

Question Number 28219 Answers: 0 Comments: 4

Question Number 28211 Answers: 0 Comments: 6

Question Number 28199 Answers: 1 Comments: 0

suppose one of the side of any box that can be carried onto an airplane must be less than 8m. Find the maximum value of such a box if the sum of the three sides can not exceed 46m.

$${suppose}\:{one}\:{of}\:{the}\:{side}\:{of}\:{any} \\ $$$${box}\:{that}\:{can}\:{be}\:{carried}\:{onto}\:{an} \\ $$$${airplane}\:{must}\:{be}\:{less}\:{than}\:\mathrm{8}{m}. \\ $$$${Find}\:{the}\:{maximum}\:{value}\:{of}\:{such} \\ $$$${a}\:{box}\:{if}\:{the}\:{sum}\:{of}\:{the}\:{three}\:{sides} \\ $$$${can}\:{not}\:{exceed}\:\mathrm{46}{m}. \\ $$

Question Number 28198 Answers: 1 Comments: 0

Find the shortest distance from the origin to the curve xy=3

$${Find}\:{the}\:{shortest}\:{distance}\:{from} \\ $$$${the}\:{origin}\:{to}\:{the}\:{curve}\:{xy}=\mathrm{3} \\ $$

Question Number 28190 Answers: 1 Comments: 2

Question Number 28189 Answers: 0 Comments: 2

Question Number 28188 Answers: 0 Comments: 0

Question Number 28186 Answers: 0 Comments: 1

Find the number of positive integers x such that [(x/(m−1))]=[(x/(m+1))], for a particular integer m≥2. [ ] means G.I.F.

$${Find}\:{the}\:{number}\:{of}\:{positive}\:{integers} \\ $$$${x}\:{such}\:{that}\:\left[\frac{{x}}{{m}−\mathrm{1}}\right]=\left[\frac{{x}}{{m}+\mathrm{1}}\right],\:{for}\:{a} \\ $$$${particular}\:{integer}\:{m}\geqslant\mathrm{2}. \\ $$$$\left[\:\right]\:{means}\:{G}.{I}.{F}. \\ $$

Question Number 28179 Answers: 0 Comments: 1

Question Number 28177 Answers: 0 Comments: 1

Question Number 28174 Answers: 0 Comments: 2

if the sum of root 7x+px−q=0 is 7 then p= ??

$$\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{root}\:\mathrm{7x}+\mathrm{px}−\mathrm{q}=\mathrm{0}\:\mathrm{is}\:\mathrm{7}\:\mathrm{then}\:\mathrm{p}= \\ $$$$?? \\ $$

Question Number 28171 Answers: 1 Comments: 1

Question Number 28170 Answers: 0 Comments: 0

find ∫_0 ^1 ((1 −e^(−x) − e^(−(1/x)) )/x)dx .

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{1}\:−{e}^{−{x}} −\:{e}^{−\frac{\mathrm{1}}{{x}}} }{{x}}{dx}\:\:. \\ $$

Question Number 28169 Answers: 0 Comments: 1

prove that ∫_0 ^1 (((lnx)^k )/(1−x))dx=(−1)^k (k!)ξ(k+1) .

$${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{\left({lnx}\right)^{{k}} }{\mathrm{1}−{x}}{dx}=\left(−\mathrm{1}\right)^{{k}} \:\left({k}!\right)\xi\left({k}+\mathrm{1}\right)\:\:. \\ $$

Question Number 28168 Answers: 0 Comments: 0

find the nature of Σ_(n=1) ^∞ arcos(1−(1/n^a ))z^n with a>1.

$${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} {arcos}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{{a}} }\right){z}^{{n}} \:\:{with}\:{a}>\mathrm{1}. \\ $$

Question Number 28166 Answers: 0 Comments: 0

let give w= e^(i((2π)/n)) and Z= Σ_(k=0) ^(n−1) w^k^2 find ∣Z∣^2 in form of double sum.

$${let}\:{give}\:{w}=\:{e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:\:{and}\:\:{Z}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{w}^{{k}^{\mathrm{2}} } \:\:\:{find}\:\mid{Z}\mid^{\mathrm{2}} \:{in} \\ $$$${form}\:{of}\:{double}\:{sum}. \\ $$

Question Number 28165 Answers: 0 Comments: 0

let give w= e^(i((2π)/n)) calculate Σ_(k=0) ^(n−1) (1+w^k )^n .

$${let}\:{give}\:{w}=\:{e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:{calculate}\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(\mathrm{1}+{w}^{{k}} \right)^{{n}} \:. \\ $$

Question Number 28164 Answers: 1 Comments: 0

simplify A=cos^4 θ +cos^4 (θ+(π/4)) +cos^4 (θ +((2π)/4)) +cos^4 (θ +((3π)/4)).

$${simplify}\: \\ $$$${A}={cos}^{\mathrm{4}} \theta\:+{cos}^{\mathrm{4}} \left(\theta+\frac{\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{2}\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{3}\pi}{\mathrm{4}}\right). \\ $$

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