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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)

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

Question Number 50849 Answers: 3 Comments: 0

solve for z in the form x+iy if tanz=0.5

$$\mathrm{solve}\:{for}\:{z}\:\:{in}\:{the}\:{form}\:\:{x}+{iy}\: \\ $$$${if}\:{tanz}=\mathrm{0}.\mathrm{5}\: \\ $$

Question Number 50835 Answers: 1 Comments: 1

Question Number 50834 Answers: 0 Comments: 4

Question Number 50829 Answers: 2 Comments: 1

Question Number 50825 Answers: 1 Comments: 0

x^4 =ax^2 +by^2 y^4 =bx^2 +ay^2 solve for x, y. [a ,b∈ R; a, b≠0]

Question Number 50820 Answers: 1 Comments: 1

Question Number 51822 Answers: 1 Comments: 0

If p and q are the length of perpendicular from the origin to the lines xcos θ−ysin θ=kcos2θ and xsec θ+ycosec θ=k respectively prove that p^2 +4q^2 =k^2

$${If}\:\:{p}\:{and}\:{q}\:\:{are}\:{the}\:{length} \\ $$$${of}\:{perpendicular}\:{from} \\ $$$${the}\:{origin}\:{to}\:{the}\:{lines} \\ $$$${x}\mathrm{cos}\:\theta−{y}\mathrm{sin}\:\:\theta={kcos}\mathrm{2}\theta \\ $$$${and}\:{x}\mathrm{sec}\:\theta+{y}\mathrm{cosec}\:\theta={k} \\ $$$${respectively} \\ $$$${prove}\:{that} \\ $$$${p}^{\mathrm{2}} +\mathrm{4}{q}^{\mathrm{2}} ={k}^{\mathrm{2}} \\ $$

Question Number 50818 Answers: 1 Comments: 0

If a right angled triangle has same area and double perimeter as that of a circle of unit radius, find the mutually perpendicular sides of the triangle.

$${If}\:{a}\:{right}\:{angled}\:{triangle}\:{has} \\ $$$${same}\:{area}\:{and}\:{double}\:{perimeter} \\ $$$${as}\:{that}\:{of}\:{a}\:{circle}\:{of}\:{unit}\:{radius}, \\ $$$${find}\:{the}\:{mutually}\:{perpendicular} \\ $$$${sides}\:{of}\:{the}\:{triangle}. \\ $$

Question Number 51823 Answers: 0 Comments: 0

Give a proof for : Σ_(n=1) ^k (Π_(n′=0) ^m ( n+n′)) = ((Π_(x=0) ^(m+1) (k+x))/(m+2)) In other terms : (it is the same) Σ_(n=1) ^k n(n+1)(n+2) ... (n+m) = (( k(k+1)(k+2) ... (k+m)(k+m+1) )/(m + 2)) Thank you !!!

$$ \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{Give}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{proof}}\:\boldsymbol{\mathrm{for}}\:: \\ $$$$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\:\left(\underset{{n}'=\mathrm{0}} {\overset{{m}} {\prod}}\left(\:{n}+\mathrm{n}'\right)\right)\:\:=\:\:\frac{\underset{{x}=\mathrm{0}} {\overset{{m}+\mathrm{1}} {\prod}}\left({k}+{x}\right)}{{m}+\mathrm{2}}\: \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{In}\:\mathrm{other}\:\mathrm{terms}\::\:\left({it}\:{is}\:{the}\:{same}\right) \\ $$$$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\:...\:\left({n}+{m}\right) \\ $$$$\:=\:\frac{\:{k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)\:...\:\left({k}+{m}\right)\left({k}+{m}+\mathrm{1}\right)\:}{{m}\:+\:\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:!!! \\ $$

Question Number 50811 Answers: 1 Comments: 2

Question Number 50808 Answers: 2 Comments: 0

Question Number 50806 Answers: 2 Comments: 0

Determine the fourth roots of − 16 , giving the results in polar form and in exponential form Answers: (√2) (1 + j) , (√2) (− 1 + j) , (√2) (− 1 − j), (√2)(1 − j)

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{roots}\:\mathrm{of}\:\:−\:\mathrm{16}\:,\:\:\mathrm{giving}\:\mathrm{the}\:\mathrm{results}\:\mathrm{in}\:\mathrm{polar} \\ $$$$\mathrm{form}\:\mathrm{and}\:\mathrm{in}\:\mathrm{exponential}\:\mathrm{form} \\ $$$$\boldsymbol{\mathrm{Answers}}:\:\:\:\:\:\sqrt{\mathrm{2}}\:\left(\mathrm{1}\:+\:\boldsymbol{\mathrm{j}}\right)\:,\:\:\sqrt{\mathrm{2}}\:\left(−\:\mathrm{1}\:+\:\boldsymbol{\mathrm{j}}\right)\:,\:\:\:\:\:\sqrt{\mathrm{2}}\:\left(−\:\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\right),\:\:\:\:\sqrt{\mathrm{2}}\left(\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\right) \\ $$

Question Number 50802 Answers: 2 Comments: 2