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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)).

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

Question Number 28163 Answers: 0 Comments: 0

let give z= e^(i((2π)/(5 ))) and a= z +z^4 , b= z^2 +z^3 find a equation wich have a and for rootsthen find the values of cos(((2π)/(5)))), sin(((2π)/5)),cos(((4π)/5)) ,sin(((4π)/5)) ,cos((π/5)).

$${let}\:{give}\:{z}=\:{e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{5}\:}} \:\:\:\:{and}\:\:{a}=\:{z}\:+{z}^{\mathrm{4}} \:\:\:\:,\:\:\:{b}=\:{z}^{\mathrm{2}} +{z}^{\mathrm{3}} \\ $$$${find}\:{a}\:{equation}\:{wich}\:{have}\:{a}\:{and}\:{for}\:{rootsthen}\:{find} \\ $$$${the}\:{values}\:{of}\:{cos}\left(\frac{\mathrm{2}\pi}{\left.\mathrm{5}\right)}\right),\:{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right),{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{cos}\left(\frac{\pi}{\mathrm{5}}\right). \\ $$

Question Number 28162 Answers: 0 Comments: 1

find ∫_(1/2) ^2 (1+(1/x^2 ))arctanxdx.

$${find}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanxdx}. \\ $$

Question Number 28161 Answers: 0 Comments: 0

find the value of ∫∫_W ln(1+x+y)dxdy with W={(x,y)∈R^2 / x+y≤1 and x≥0 and y≥0}.

$${find}\:{the}\:{value}\:{of}\:\int\int_{{W}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy}\:{with} \\ $$$${W}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}+{y}\leqslant\mathrm{1}\:{and}\:{x}\geqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\}. \\ $$

Question Number 28160 Answers: 0 Comments: 2

find ∫∫_D (√(xy)) dxdy with D={(x,y)∈R^ /(x^2 +y^2 )^2 ≤xy}

$${find}\:\int\int_{{D}} \:\:\sqrt{{xy}}\:{dxdy}\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{} \:/\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} \leqslant{xy}\right\} \\ $$

Question Number 28159 Answers: 0 Comments: 1

let give D=[0,(π/2)]×[0,(1/2)] find the value of ∫∫_D ((dxdy)/(ycosx +1)) .

$${let}\:{give}\:{D}=\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right]×\left[\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\int\int_{{D}} \:\:\:\frac{{dxdy}}{{ycosx}\:+\mathrm{1}}\:\:. \\ $$

Question Number 28158 Answers: 1 Comments: 0

calculate ∫∫_(x^2 +y^2 ≤1) ((dxdy)/(3+x^2 +y^2 )) .

$${calculate}\:\int\int_{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\mathrm{3}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:. \\ $$

Question Number 28185 Answers: 1 Comments: 0

M, N are endpoints of a diameter 4x−y=15 of circle x^2 +y^2 −6x+6y−16=0 ; and are also on the tangents at the end points of the major axis of an ellipse respectively, such that MN is also tangent to the same ellipse at point P. If the major axis of the ellipse is along y=x, find eccentricity, length of latus rectum, centre and equation of derectrices.

$${M},\:{N}\:{are}\:{endpoints}\:{of}\:{a}\:{diameter} \\ $$$$\:\mathrm{4}{x}−{y}=\mathrm{15}\:\:{of}\:{circle} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}{y}−\mathrm{16}=\mathrm{0}\:;\:{and}\:{are} \\ $$$${also}\:{on}\:{the}\:{tangents}\:{at}\:{the}\:{end} \\ $$$${points}\:{of}\:{the}\:{major}\:{axis}\:{of}\:{an} \\ $$$${ellipse}\:{respectively},\:{such}\:{that} \\ $$$${MN}\:{is}\:{also}\:{tangent}\:{to}\:{the}\:{same} \\ $$$${ellipse}\:{at}\:{point}\:{P}. \\ $$$${If}\:{the}\:{major}\:{axis}\:{of}\:{the}\:{ellipse} \\ $$$${is}\:{along}\:{y}={x},\:{find} \\ $$$$\:\:\:{eccentricity},\:{length}\:{of}\:{latus} \\ $$$${rectum},\:{centre}\:{and}\:{equation}\:{of} \\ $$$${derectrices}. \\ $$

Question Number 28151 Answers: 0 Comments: 4

lim_(x→1) ((1/(log_e x)) − (x/(x − 1)))

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\left(\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{e}} \mathrm{x}}\:−\:\frac{\mathrm{x}}{\mathrm{x}\:−\:\mathrm{1}}\right) \\ $$

Question Number 28139 Answers: 1 Comments: 0

Question Number 28138 Answers: 0 Comments: 1

studie and?give the graph for the function f(x)= e^x −x^e .

$${studie}\:{and}?{give}\:{the}\:{graph}\:{for}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:{e}^{{x}} \:\:−{x}^{{e}} \:\:\:\:\:. \\ $$

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