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Question Number 192397 Answers: 1 Comments: 0

Let f:D(f)⊆R^n →R^m let ′a′ be an interior point of Dom(f) and let ′u′ be any vector in R^n , when is a vector v∈R^m called the directional derivative of f at ′a′ along the line determine by u ? help!

$$\mathrm{Let}\:\mathrm{f}:\mathrm{D}\left(\mathrm{f}\right)\subseteq\mathbb{R}^{\mathrm{n}} \rightarrow\mathbb{R}^{\mathrm{m}} \\ $$$$\mathrm{let}\:'\mathrm{a}'\:\mathrm{be}\:\mathrm{an}\:\mathrm{interior}\:\mathrm{point}\:\mathrm{of}\:\mathrm{Dom}\left(\mathrm{f}\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:'\mathrm{u}'\:\mathrm{be}\:\mathrm{any}\:\mathrm{vector}\:\mathrm{in}\:\mathbb{R}^{\mathrm{n}} ,\:\mathrm{when} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{v}\in\mathbb{R}^{\mathrm{m}} \:\mathrm{called}\:\mathrm{the}\:\mathrm{directional} \\ $$$$\mathrm{derivative}\:\mathrm{of}\:\mathrm{f}\:\mathrm{at}\:'\mathrm{a}'\:\mathrm{along}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{determine}\:\mathrm{by}\:\mathrm{u}\:? \\ $$$$ \\ $$$$\mathrm{help}! \\ $$

Question Number 192396 Answers: 1 Comments: 0

Question Number 192390 Answers: 1 Comments: 0

Give the function: x^2 −7x−8=0 have two roots x_(1 ) and x_2 No solving the function Find: x_1 ^3 +x_2 +2023

$${Give}\:{the}\:{function}: \\ $$$${x}^{\mathrm{2}} −\mathrm{7}{x}−\mathrm{8}=\mathrm{0} \\ $$$${have}\:{two}\:{roots}\:{x}_{\mathrm{1}\:} {and}\:{x}_{\mathrm{2}} \\ $$$${No}\:{solving}\:{the}\:{function}\: \\ $$$${Find}:\:{x}_{\mathrm{1}} ^{\mathrm{3}} +{x}_{\mathrm{2}} +\mathrm{2023} \\ $$

Question Number 192388 Answers: 1 Comments: 0

Question Number 192387 Answers: 1 Comments: 0

Simplify (√(2(1+(√(4+(((2017^4 −1)/(2017^2 )))^2 ))))) is ....

$$\:\mathrm{Simplify}\: \\ $$$$\:\sqrt{\mathrm{2}\left(\mathrm{1}+\sqrt{\mathrm{4}+\left(\frac{\mathrm{2017}^{\mathrm{4}} −\mathrm{1}}{\mathrm{2017}^{\mathrm{2}} }\right)^{\mathrm{2}} }\right)}\: \\ $$$$\:\mathrm{is}\:....\: \\ $$

Question Number 192377 Answers: 1 Comments: 0

The probability density function f(x) of a variable x is given by f(x)= { ((kxsin πx 0≤x≤1)),((0 for all value of x)) :} Show that k=π and deduce that mean and the variance of the distribution are (1−(4/π^2 )) and (2/π^2 )(1−(8/π^2 ))

$${The}\:{probability}\:{density}\:{function}\:{f}\left({x}\right) \\ $$$$\:{of}\:{a}\:{variable}\:{x}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({x}\right)=\begin{cases}{{kx}\mathrm{sin}\:\pi{x}\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{\mathrm{0}\:{for}\:{all}\:{value}\:{of}\:{x}}\end{cases} \\ $$$${Show}\:{that}\:{k}=\pi\:\:{and}\:{deduce}\:{that}\:{mean}\: \\ $$$${and}\:{the}\:{variance}\:{of}\:{the}\:{distribution}\:{are} \\ $$$$\left(\mathrm{1}−\frac{\mathrm{4}}{\pi^{\mathrm{2}} }\right)\:{and}\:\frac{\mathrm{2}}{\pi^{\mathrm{2}} }\left(\mathrm{1}−\frac{\mathrm{8}}{\pi^{\mathrm{2}} }\right) \\ $$

Question Number 192376 Answers: 0 Comments: 0

Find the first four moment of the binomial distribution

$${Find}\:{the}\:{first}\:{four}\:{moment}\:{of}\:{the} \\ $$$${binomial}\:{distribution} \\ $$$$ \\ $$

Question Number 192375 Answers: 1 Comments: 0

Show that E(Z)=0 and Var(Z)=1 where Z is the standard normal variable

$${Show}\:{that}\:{E}\left({Z}\right)=\mathrm{0}\:\:\:{and}\:{Var}\left({Z}\right)=\mathrm{1}\:{where} \\ $$$${Z}\:{is}\:{the}\:{standard}\:{normal}\:{variable} \\ $$

Question Number 192374 Answers: 3 Comments: 1

why “ 200!<100^(200) ” ?

$${why}\:\:\:``\:\mathrm{200}!<\mathrm{100}^{\mathrm{200}} \:''\:? \\ $$

Question Number 192370 Answers: 2 Comments: 0

Solve the equation x^4 − 2x^3 + 4x^2 + 6x − 21 = 0, Given that the sum of two of its roots is zero

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\:\:\mathrm{x}^{\mathrm{4}} \:\:−\:\:\mathrm{2x}^{\mathrm{3}} \:\:+\:\:\mathrm{4x}^{\mathrm{2}} \:\:+\:\:\mathrm{6x}\:\:\:−\:\:\mathrm{21}\:\:\:=\:\:\:\mathrm{0},\:\: \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{of}\:\mathrm{its}\:\mathrm{roots}\:\mathrm{is}\:\mathrm{zero} \\ $$

Question Number 192367 Answers: 1 Comments: 0

Question Number 192363 Answers: 0 Comments: 0

Solve for x x_i −x+(2cx−cb)(y_i +cx^2 −cbx)=0 the following is true for this equaition i)c>0 ii)b>0 iii)there is only one real solution

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}_{{i}} −{x}+\left(\mathrm{2}{cx}−{cb}\right)\left({y}_{{i}} +{cx}^{\mathrm{2}} −{cbx}\right)=\mathrm{0} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true}\:\mathrm{for}\:\mathrm{this}\:\mathrm{equaition} \\ $$$$\left.{i}\right)\mathrm{c}>\mathrm{0} \\ $$$$\left.{ii}\right)\mathrm{b}>\mathrm{0} \\ $$$$\left.{iii}\right)\mathrm{there}\:\mathrm{is}\:\mathrm{only}\:\mathrm{one}\:\mathrm{real}\:\mathrm{solution} \\ $$

Question Number 192343 Answers: 1 Comments: 0

Find minimum value of y=((1−sin^2 x)/(2 tan^2 x))

$$\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\mathrm{y}=\frac{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{2}\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\: \\ $$

Question Number 192342 Answers: 1 Comments: 0

1) Compute in S_a , a^(−1) ba where a=(1 2)(1 3 5), b=(1 5 7 1) 2) Given permutation α = (1 2)(3 4), β = (1 3)(5 6). Find a permutation x∈S_6 ∃αx = β. help!

$$\left.\mathrm{1}\right)\:\mathrm{Compute}\:\mathrm{in}\:\mathrm{S}_{\mathrm{a}} \:,\:\mathrm{a}^{−\mathrm{1}} \mathrm{ba}\:\:\mathrm{where}\: \\ $$$$\mathrm{a}=\left(\mathrm{1}\:\mathrm{2}\right)\left(\mathrm{1}\:\mathrm{3}\:\mathrm{5}\right),\:\mathrm{b}=\left(\mathrm{1}\:\mathrm{5}\:\mathrm{7}\:\mathrm{1}\right) \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Given}\:\mathrm{permutation}\:\alpha\:=\:\left(\mathrm{1}\:\mathrm{2}\right)\left(\mathrm{3}\:\mathrm{4}\right), \\ $$$$\beta\:=\:\left(\mathrm{1}\:\mathrm{3}\right)\left(\mathrm{5}\:\mathrm{6}\right).\:\mathrm{Find}\:\mathrm{a}\:\mathrm{permutation} \\ $$$$\mathrm{x}\in\mathrm{S}_{\mathrm{6}} \:\exists\alpha\mathrm{x}\:=\:\beta. \\ $$$$ \\ $$$$\mathrm{help}! \\ $$

Question Number 192341 Answers: 1 Comments: 0

1) Find the sign of odd or even (or pality) of permutation θ=(1 2 3 4 5 6 7 8) 2) prove that any permutation θ:S→S where S is a finite set can be written as a product of disjoint cycle help!

$$\left.\mathrm{1}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sign}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{or}\:\mathrm{even}\:\left(\mathrm{or}\:\mathrm{pality}\right) \\ $$$$\mathrm{of}\:\mathrm{permutation}\:\theta=\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:\mathrm{4}\:\mathrm{5}\:\mathrm{6}\:\mathrm{7}\:\mathrm{8}\right) \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{permutation} \\ $$$$\theta:\mathrm{S}\rightarrow\mathrm{S}\:\mathrm{where}\:\mathrm{S}\:\mathrm{is}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{set}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{written}\:\mathrm{as}\:\mathrm{a}\:\mathrm{product}\:\mathrm{of}\:\mathrm{disjoint} \\ $$$$\mathrm{cycle} \\ $$$$ \\ $$$$\mathrm{help}! \\ $$

Question Number 192340 Answers: 1 Comments: 0

Prove that the order of any permuta− tion θ is the least common multiple of the length of its disjoint cycles. hi

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{any}\:\mathrm{permuta}− \\ $$$$\mathrm{tion}\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{least}\:\mathrm{common}\:\mathrm{multiple} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{its}\:\mathrm{disjoint}\:\mathrm{cycles}. \\ $$$$ \\ $$$$\:\mathrm{hi} \\ $$

Question Number 192339 Answers: 1 Comments: 0

Express as the product of disjoint cycle the permutation a) θ(1)=4 θ(2)=6 θ(1)=5 θ(4)=1 θ(5)=3 θ(6)=2 b) (1 6 3)(1 3 5 7)(6 7)(1 2 3 4 5) c) (1 2 3 4 5)(6 7)(1 3 5 7) Find the order of each of them help!

$$\mathrm{Express}\:\mathrm{as}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{disjoint}\: \\ $$$$\mathrm{cycle}\:\mathrm{the}\:\mathrm{permutation} \\ $$$$\left.\mathrm{a}\right)\:\theta\left(\mathrm{1}\right)=\mathrm{4}\:\:\theta\left(\mathrm{2}\right)=\mathrm{6}\:\:\theta\left(\mathrm{1}\right)=\mathrm{5}\:\:\theta\left(\mathrm{4}\right)=\mathrm{1} \\ $$$$\theta\left(\mathrm{5}\right)=\mathrm{3}\:\:\theta\left(\mathrm{6}\right)=\mathrm{2} \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\left(\mathrm{1}\:\mathrm{6}\:\mathrm{3}\right)\left(\mathrm{1}\:\mathrm{3}\:\mathrm{5}\:\mathrm{7}\right)\left(\mathrm{6}\:\mathrm{7}\right)\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:\mathrm{4}\:\mathrm{5}\right) \\ $$$$ \\ $$$$\left.\mathrm{c}\right)\:\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:\mathrm{4}\:\mathrm{5}\right)\left(\mathrm{6}\:\mathrm{7}\right)\left(\mathrm{1}\:\mathrm{3}\:\mathrm{5}\:\mathrm{7}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{them} \\ $$$$ \\ $$$$\mathrm{help}! \\ $$

Question Number 192338 Answers: 2 Comments: 0

y= ((((lim_(h→0) (((x+h)^3 −x^3 )/h))(Σ_(n=0) ^∞ (x^(n+1) /(n+1))))/(∫_0 ^( x) lnt dt))) (dy/dx)?

$${y}=\:\left(\frac{\left(\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+{h}\right)^{\mathrm{3}} −{x}^{\mathrm{3}} }{{h}}\right)\left(\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\right)}{\int_{\mathrm{0}} ^{\:{x}} {lnt}\:{dt}}\right) \\ $$$$ \\ $$$$\frac{{dy}}{{dx}}? \\ $$

Question Number 192336 Answers: 1 Comments: 0