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AllQuestion and Answers: Page 1322

Question Number 81005 Answers: 1 Comments: 0

Question Number 81003 Answers: 0 Comments: 4

(E): sin2x=cosx+sinx−(1/2) 1. show that (E) is equivalent to (E′): 2cos^2 X−(√2)cosX−(1/2)=0 with X=x−(π/4).

$$\left(\mathrm{E}\right):\:\mathrm{sin2}{x}={cosx}+{sinx}−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{1}.\:{show}\:{that}\:\left(\mathrm{E}\right)\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\: \\ $$$$\left(\mathrm{E}'\right):\:\mathrm{2cos}^{\mathrm{2}} \mathrm{X}−\sqrt{\mathrm{2}}\mathrm{cosX}−\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$$$\mathrm{with}\:\mathrm{X}={x}−\frac{\pi}{\mathrm{4}}. \\ $$

Question Number 80998 Answers: 1 Comments: 1

Question Number 80997 Answers: 0 Comments: 4

give a rational fraction example : cancelling in -1 and 2 having as a set defnition R

$${give}\:{a}\:{rational}\:{fraction}\:{example}\:: \\ $$$${cancelling}\:{in}\:-\mathrm{1}\:{and}\:\mathrm{2}\:{having}\:{as}\:{a}\:{set}\:{defnition}\:\mathbb{R} \\ $$

Question Number 80994 Answers: 0 Comments: 1

donnre un exenple de fraction rationnelle: 1)s′annulant en -1 et 2 ayant pour ensemble definition R

$$\mathrm{donnre}\:\mathrm{un}\:\mathrm{exenple}\:\mathrm{de}\:\mathrm{fraction}\:\mathrm{rationnelle}: \\ $$$$\left.\mathrm{1}\right)\mathrm{s}'\mathrm{annulant}\:\mathrm{en}\:-\mathrm{1}\:\mathrm{et}\:\mathrm{2}\:\mathrm{ayant}\:\mathrm{pour}\:\mathrm{ensemble}\:\mathrm{definition}\:\mathbb{R} \\ $$

Question Number 80983 Answers: 0 Comments: 8

if lim_(x→0) ((ae^x −bsin x+ce^(−x) )/(xsin x)) = 2 what is a+b+c ?

$${if}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{ae}^{{x}} −{b}\mathrm{sin}\:{x}+{ce}^{−{x}} }{{x}\mathrm{sin}\:{x}}\:=\:\mathrm{2} \\ $$$${what}\:{is}\:{a}+{b}+{c}\:? \\ $$

Question Number 80982 Answers: 0 Comments: 3

Question Number 80977 Answers: 1 Comments: 6

Question Number 80974 Answers: 0 Comments: 2

Show that gcd (a , a + x) ∣ x hence show that any two consecutive integers are coprime

$$\:\mathrm{Show}\:\mathrm{that}\:\mathrm{gcd}\:\left({a}\:,\:{a}\:+\:{x}\right)\:\mid\:{x} \\ $$$${hence}\:{show}\:{that}\:{any}\:{two}\:{consecutive} \\ $$$${integers}\:{are}\:{coprime} \\ $$

Question Number 80973 Answers: 0 Comments: 0

Given that f(x) = { ((2x−7, 0 < x < 6)),((2^x , 7 < x < 8)) :} and f is periodic of period 4. find f(200)

$$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2}{x}−\mathrm{7},\:\:\mathrm{0}\:<\:{x}\:<\:\mathrm{6}}\\{\mathrm{2}^{{x}} ,\:\:\:\mathrm{7}\:<\:{x}\:<\:\mathrm{8}}\end{cases} \\ $$$$\mathrm{and}\:\mathrm{f}\:\mathrm{is}\:\mathrm{periodic}\:\mathrm{of}\:\mathrm{period}\:\mathrm{4}. \\ $$$$\mathrm{find}\:{f}\left(\mathrm{200}\right) \\ $$

Question Number 80943 Answers: 1 Comments: 0

Find equation of a plane passing through the points (x_1 , y_1 , z_1 ), (x_2 , y_2 , z_2 ) and perpendicular to the plane ax+by+cz=d

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{the} \\ $$$$\mathrm{points}\:\left({x}_{\mathrm{1}} ,\:{y}_{\mathrm{1}} ,\:{z}_{\mathrm{1}} \right),\:\left({x}_{\mathrm{2}} ,\:{y}_{\mathrm{2}} ,\:{z}_{\mathrm{2}} \right)\:\mathrm{and}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{plane}\:{ax}+{by}+{cz}={d} \\ $$

Question Number 80941 Answers: 0 Comments: 2

cos x−2cos y=−(√3) sin (x−y)=((2(√2))/3) what is sin x−2sin y ?

$$\mathrm{cos}\:{x}−\mathrm{2cos}\:{y}=−\sqrt{\mathrm{3}} \\ $$$$\mathrm{sin}\:\left({x}−{y}\right)=\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$$${what}\:{is}\:\mathrm{sin}\:{x}−\mathrm{2sin}\:{y}\:? \\ $$

Question Number 80951 Answers: 1 Comments: 3

Question Number 80930 Answers: 0 Comments: 3

Question Number 80929 Answers: 1 Comments: 5

show that cos(π/7)cos((2π)/7)cos((4π)/7)=−(1/8)

$$\mathrm{show}\:\mathrm{that} \\ $$$${cos}\frac{\pi}{\mathrm{7}}\mathrm{cos}\frac{\mathrm{2}\pi}{\mathrm{7}}\mathrm{cos}\frac{\mathrm{4}\pi}{\mathrm{7}}=−\frac{\mathrm{1}}{\mathrm{8}} \\ $$

Question Number 80927 Answers: 1 Comments: 2

Question Number 80926 Answers: 0 Comments: 2

i^i

$${i}^{{i}} \\ $$

Question Number 80925 Answers: 0 Comments: 1

∫_(−∞) ^∞ ((cos(x))/(1+x^2 )) dx =(π/e)

$$\int_{−\infty} ^{\infty} \frac{{cos}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:=\frac{\pi}{{e}} \\ $$

Question Number 80924 Answers: 1 Comments: 3

show that ∫_0 ^∞ (x^((π/5)−1) /(1+x^(2π) )) dx =φ

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\frac{\pi}{\mathrm{5}}−\mathrm{1}} }{\mathrm{1}+{x}^{\mathrm{2}\pi} }\:{dx}\:=\phi\: \\ $$

Question Number 80921 Answers: 0 Comments: 2

∫_0 ^(π/2) ((xdx)/(sin x+cos x)) = ?

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{xdx}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:=\:? \\ $$

Question Number 80917 Answers: 1 Comments: 0

((√(18−7x−x^2 ))/(2x+9)) ≥ ((√(18−7x−x^2 ))/(x+8))

$$\frac{\sqrt{\mathrm{18}−\mathrm{7}{x}−{x}^{\mathrm{2}} }}{\mathrm{2}{x}+\mathrm{9}}\:\geqslant\:\frac{\sqrt{\mathrm{18}−\mathrm{7}{x}−{x}^{\mathrm{2}} }}{{x}+\mathrm{8}} \\ $$

Question Number 80914 Answers: 0 Comments: 0

(1) Integrate F(x, y) = x^2 over the region bounded by y = x^2 , x = 2 and x = 1 (2) Integrate G(x, y) = x^2 + y^2 over the region bounded by the triangle x = y, y = 1 and y = 0

$$\left(\mathrm{1}\right) \\ $$$$\mathrm{Integrate}\:\:\mathrm{F}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:\:\:\mathrm{over}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}^{\mathrm{2}} , \\ $$$$\mathrm{x}\:\:=\:\:\mathrm{2}\:\:\mathrm{and}\:\mathrm{x}\:\:=\:\:\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{2}\right) \\ $$$$\mathrm{Integrate}\:\:\:\:\mathrm{G}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\:\:\:\mathrm{over}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{triangle}\:\:\:\:\mathrm{x}\:\:=\:\:\mathrm{y},\:\:\mathrm{y}\:\:=\:\:\mathrm{1}\:\:\mathrm{and}\:\:\mathrm{y}\:\:=\:\:\mathrm{0} \\ $$

Question Number 80912 Answers: 0 Comments: 2

Question Number 80907 Answers: 1 Comments: 0

a)∫e^x tan xdx b)∫xtan xdx

$$\left.{a}\right)\int{e}^{{x}} \mathrm{tan}\:{xdx} \\ $$$$\left.{b}\right)\int{x}\mathrm{tan}\:{xdx} \\ $$

Question Number 80900 Answers: 1 Comments: 1

Question Number 80896 Answers: 1 Comments: 0

α is a real ∈ ]0;(π/2)[. we give this (E_α ):2x^2 −2x(√2)(cosα)+cos2α=0 1. show that Δ=8sin^2 x i showed it. 2.Solve E_α in R. please help me for this question.

$$\left.\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\in\:\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[.\:\mathrm{we}\:\mathrm{give}\:\mathrm{this}\:\right. \\ $$$$\left(\mathrm{E}_{\alpha} \right):\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}\sqrt{\mathrm{2}}\left({cos}\alpha\right)+\mathrm{cos2}\alpha=\mathrm{0} \\ $$$$\mathrm{1}.\:\mathrm{show}\:\mathrm{that}\:\Delta=\mathrm{8sin}^{\mathrm{2}} {x} \\ $$$${i}\:{showed}\:{it}. \\ $$$$\mathrm{2}.{S}\mathrm{olve}\:\mathrm{E}_{\alpha} \:\mathrm{in}\:\mathbb{R}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{for}\:\mathrm{this}\:\mathrm{question}. \\ $$

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