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Question Number 50987 Answers: 0 Comments: 2

(√(x + y + 9)) + (√(x − y + 8)) = 33^2 x > y x, y ∈ Z^+ (x^y + y^x ) mod (1000) = ?

$$\sqrt{{x}\:+\:{y}\:+\:\mathrm{9}}\:\:+\:\:\sqrt{{x}\:−\:{y}\:+\:\mathrm{8}}\:\:=\:\:\mathrm{33}^{\mathrm{2}} \\ $$$${x}\:>\:{y} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{Z}^{+} \\ $$$$\left({x}^{{y}} \:+\:{y}^{{x}} \right)\:\:{mod}\:\:\left(\mathrm{1000}\right)\:\:=\:\:? \\ $$

Question Number 50979 Answers: 3 Comments: 1

a)Normal to any point on the hyperbola XY=C meet the x−axis at A and tangents meets the y−axis at B.find the locus of the mid point of AB b)find the equation of assymptotes of (i)(x^2 /4)−(y^2 /5)=1 (ii)(((x−1)^2 )/(16))−(((y−3)^2 )/9)=1

$$\left.{a}\right){Normal}\:{to}\:{any}\:{point}\:{on} \\ $$$${the}\:{hyperbola}\:{XY}={C} \\ $$$${meet}\:{the}\:{x}−{axis}\:{at}\:{A} \\ $$$${and}\:{tangents}\:{meets} \\ $$$${the}\:{y}−{axis}\:{at}\:{B}.{find}\:{the} \\ $$$${locus}\:{of}\:{the}\:{mid}\:{point}\:{of}\:{AB} \\ $$$$\left.{b}\right){find}\:\:{the}\:{equation}\:{of}\: \\ $$$${assymptotes}\:{of} \\ $$$$\left({i}\right)\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\frac{{y}^{\mathrm{2}} }{\mathrm{5}}=\mathrm{1} \\ $$$$\left({ii}\right)\frac{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{16}}−\frac{\left({y}−\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{9}}=\mathrm{1} \\ $$

Question Number 50977 Answers: 3 Comments: 0

Find interms of a,b the value of c which makes the line y=mx+c a tangent to the parabola y^2 =4ax.also obtain the coordinate of the point of contact b) find the equation of tangent (x^2 /4)+(y^2 /9)=1 with gradient 2

$${Find}\:{interms}\:{of}\:\:{a},{b}\:{the} \\ $$$${value}\:{of}\:{c}\:{which}\:{makes} \\ $$$${the}\:{line}\:{y}={mx}+{c} \\ $$$${a}\:{tangent}\:{to}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{ax}.{also}\:{obtain}\:{the}\: \\ $$$${coordinate}\:{of}\:{the}\:{point}\:{of} \\ $$$${contact} \\ $$$$\left.{b}\right)\:{find}\:{the}\:{equation}\:{of}\: \\ $$$${tangent}\:\frac{{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{{y}^{\mathrm{2}} }{\mathrm{9}}=\mathrm{1}\:{with} \\ $$$${gradient}\:\mathrm{2} \\ $$

Question Number 50973 Answers: 1 Comments: 0

Question Number 50972 Answers: 1 Comments: 0

Question Number 50970 Answers: 1 Comments: 0

Given 3−2i and 1+i are the two of roots of the equation ax^4 +bx^3 +cx^3 +dx+e find the values of a,b,c,d and e

$${Given}\:\mathrm{3}−\mathrm{2}{i}\:{and}\:\mathrm{1}+{i} \\ $$$${are}\:{the}\:{two}\:{of}\:{roots}\:{of} \\ $$$${the}\:{equation} \\ $$$${ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{3}} +{dx}+{e} \\ $$$${find}\:{the}\:{values}\:{of} \\ $$$${a},{b},{c},{d}\:{and}\:{e} \\ $$

Question Number 50967 Answers: 1 Comments: 1

Question Number 50963 Answers: 2 Comments: 1

Question Number 50960 Answers: 0 Comments: 0

4 (3) 2 5 3 (?) 1 1 6 1 2 (8) ? ? 1 find numbers of each ?

$$\mathrm{4}\:\:\:\left(\mathrm{3}\right)\:\:\:\:\mathrm{2} \\ $$$$\mathrm{5}\:\:\:\:\mathrm{3}\:\:\:\left(?\right)\:\:\mathrm{1}\:\:\:\:\mathrm{1} \\ $$$$\mathrm{6}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\left(\mathrm{8}\right)\:\:\:\:?\:\:\:\:\:?\:\:\:\:\:\mathrm{1} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{each}\:\:\:? \\ $$

Question Number 50954 Answers: 1 Comments: 2

i was evaluating lim_(x→∞) ((x((x^ )^(1/x) − 1))/(log x)) and got 0 as the product. is it true, My Fellows ??

$$\mathrm{i}\:\mathrm{was}\:\mathrm{evaluating}\: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}\left(\sqrt[{{x}}]{{x}^{} }\:−\:\mathrm{1}\right)}{\mathrm{log}\:{x}} \\ $$$$\mathrm{and}\:\mathrm{got}\:\mathrm{0}\:\mathrm{as}\:\mathrm{the}\:\mathrm{product}.\:\mathrm{is}\:\mathrm{it}\:\mathrm{true},\:\mathrm{My}\:\mathrm{Fellows}\:?? \\ $$

Question Number 50952 Answers: 0 Comments: 3

Question Number 50936 Answers: 1 Comments: 1

Question Number 50925 Answers: 0 Comments: 1

factor x^3 +x^2 +x−(1/3) and x^3 +x^2 −x+(1/3) and x^3 +x^2 −x−(1/3)

$$\mathrm{factor}\:\:\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\mathrm{and} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\frac{\mathrm{1}}{\mathrm{3}}\:\:\mathrm{and} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 50932 Answers: 1 Comments: 0

Question Number 50915 Answers: 1 Comments: 0

The range of riffle bullet is 1000m when θ is the angle of projection.if the bullet is fired with the same angle from a car travelling at 36km/h towards the target show that the range will be increased by ((1000)/7).(√(tanθ)) m.

$${The}\:{range}\:{of}\:{riffle}\:{bullet} \\ $$$${is}\:\mathrm{1000}{m}\:{when}\:\theta\:{is}\:{the}\:{angle} \\ $$$${of}\:{projection}.{if}\:{the}\:{bullet} \\ $$$${is}\:{fired}\:\:{with}\:{the}\:{same}\: \\ $$$${angle}\:\:{from}\:{a}\:{car}\:{travelling} \\ $$$${at}\:\mathrm{36}{km}/{h}\:{towards}\:{the}\:{target} \\ $$$${show}\:{that}\:{the}\:{range}\:{will} \\ $$$${be}\:{increased}\:{by} \\ $$$$\frac{\mathrm{1000}}{\mathrm{7}}.\sqrt{{tan}\theta}\:{m}. \\ $$

Question Number 50914 Answers: 2 Comments: 0

prove that relative velocity is reversed by a head on collision

$${prove}\:{that}\:{relative}\:{velocity} \\ $$$${is}\:{reversed}\:{by}\:{a}\:{head}\:{on} \\ $$$${collision} \\ $$

Question Number 50913 Answers: 1 Comments: 0

A ball is dropped from height h.it strikes the ground and rises,the coefficiate of restitution being e what is the total distance it moves and the time before it comes to rest?

$${A}\:{ball}\:{is}\:{dropped}\:{from} \\ $$$${height}\:{h}.{it}\:{strikes}\:{the}\:{ground} \\ $$$${and}\:{rises},{the}\:{coefficiate} \\ $$$${of}\:{restitution}\:{being}\:\:{e} \\ $$$${what}\:{is}\:{the}\:{total}\:{distance} \\ $$$${it}\:{moves}\:\:{and}\:\:{the}\:{time}\: \\ $$$${before}\:{it}\:{comes}\:{to}\:{rest}? \\ $$$$ \\ $$$$ \\ $$

Question Number 50912 Answers: 2 Comments: 0

Show that in collision where kinetic energy is conserved linear momemtum is also conserved

$${Show}\:{that}\:{in}\:{collision} \\ $$$${where}\:{kinetic}\:{energy}\:{is} \\ $$$${conserved}\:{linear}\:{momemtum} \\ $$$${is}\:{also}\:{conserved} \\ $$

Question Number 50908 Answers: 1 Comments: 0

Given f(x)=Σ_(k=0) ^n ^n C_k sin(kx)cos((n−k)x) Find a simple form for f(x) (Your answer should be written like c(n).g(nx))

$${Given}\:{f}\left({x}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{k}} {sin}\left({kx}\right){cos}\left(\left({n}−{k}\right){x}\right) \\ $$$${Find}\:{a}\:{simple}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left({Your}\:{answer}\:{should}\:{be}\:{written}\:{like}\:{c}\left({n}\right).{g}\left({nx}\right)\right)\: \\ $$

Question Number 50898 Answers: 3 Comments: 1

Question Number 50888 Answers: 0 Comments: 2

Question Number 50890 Answers: 1 Comments: 0

Determine whether the following is true for all value of x 0≤(((x+1)^2 )/(x^2 +x+1))≤(4/3)

$${Determine}\:{whether} \\ $$$${the}\:{following}\:\:{is}\:{true}\:{for}\:{all} \\ $$$${value}\:{of}\:{x} \\ $$$$\mathrm{0}\leqslant\frac{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\leqslant\frac{\mathrm{4}}{\mathrm{3}} \\ $$

Question Number 50861 Answers: 2 Comments: 0

((n!)/((n−5)!))=20((n!)/((n−3)!)) n=? ________ please give me simple solve. thanks

$$\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{5}\right)!}=\mathrm{20}\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{3}\right)!} \\ $$$$ \\ $$$$\mathrm{n}=? \\ $$$$\_\_\_\_\_\_\_\_ \\ $$$$\mathrm{please}\:\mathrm{give}\:\mathrm{me}\:\mathrm{simple}\:\mathrm{solve}. \\ $$$$\mathrm{thanks} \\ $$

Question Number 50892 Answers: 3 Comments: 0

solve the equation tan 3θcotθ+1=0 for 0≤θ≤180 b)show that if cos 2θ is not zero then cos 2θ+sec 2θ=2[((cos^4 θ+sin^4 θ)/(cos^4 θ−sin^4 θ))] c)find the limit of ((tan (θ/3))/(3θ)) as θ→0

$${solve}\:{the}\:{equation} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta{cot}\theta+\mathrm{1}=\mathrm{0}\:{for} \\ $$$$\mathrm{0}\leqslant\theta\leqslant\mathrm{180} \\ $$$$\left.{b}\right){show}\:{that}\:{if}\:\mathrm{cos}\:\mathrm{2}\theta\:{is}\:{not}\:{zero} \\ $$$${then} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{sec}\:\mathrm{2}\theta=\mathrm{2}\left[\frac{\mathrm{cos}\:^{\mathrm{4}} \theta+\mathrm{sin}\:^{\mathrm{4}} \theta}{\mathrm{cos}\:^{\mathrm{4}} \theta−\mathrm{sin}\:^{\mathrm{4}} \theta}\right] \\ $$$$\left.{c}\right){find}\:{the}\:{limit}\:{of} \\ $$$$\frac{\mathrm{tan}\:\frac{\theta}{\mathrm{3}}}{\mathrm{3}\theta}\:{as}\:\theta\rightarrow\mathrm{0} \\ $$$$ \\ $$

Question Number 50856 Answers: 1 Comments: 0

show that Σ_(x=0) ^n xp(x)=np given that p(x)=^n C_x p^x q^(n−x)

$${show}\:{that} \\ $$$$\underset{\mathrm{x}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}{xp}\left({x}\right)={np}\:{given}\: \\ $$$${that}\:{p}\left({x}\right)=^{\mathrm{n}} {C}_{\mathrm{x}} {p}^{{x}} {q}^{{n}−{x}} \\ $$

Question Number 50855 Answers: 1 Comments: 0

For the random variable x show that a)Var(x)=E^2 (x)−[E(x)]^2 b)Var(ax+b)=a^2 Var(x)

$${F}\mathrm{or}\:{the}\:{random}\:{variable} \\ $$$${x}\:{show}\:{that} \\ $$$$\left.{a}\right){Var}\left({x}\right)={E}^{\mathrm{2}} \left({x}\right)−\left[{E}\left({x}\right)\right]^{\mathrm{2}} \\ $$$$\left.{b}\right){Var}\left({ax}+{b}\right)={a}^{\mathrm{2}} {Var}\left({x}\right) \\ $$$$ \\ $$

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