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AllQuestion and Answers: Page 130

Question Number 207381 Answers: 1 Comments: 0

Question Number 207374 Answers: 2 Comments: 0

Show that Σ_(k=0) ^n (C_n ^k )^2 =C_(2n) ^n

$${Show}\:{that}\:\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} ={C}_{\mathrm{2}{n}} ^{{n}} \\ $$

Question Number 207372 Answers: 0 Comments: 6

2 students are passing a test of n questions with the same chance to find each one Show the chance that they both don′t find a same question is ((3/4))^n

$$\mathrm{2}\:{students}\:{are}\:{passing}\: \\ $$$${a}\:{test}\:{of}\:\:{n}\:{questions}\:{with} \\ $$$${the}\:{same}\:{chance}\:{to}\:{find}\:{each}\:{one} \\ $$$${Show}\:\:{the}\:{chance}\:{that}\:{they}\:{both} \\ $$$$\:{don}'{t}\:{find}\:{a}\:{same}\:{question}\:{is}\:\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$

Question Number 207402 Answers: 1 Comments: 0

f(x) + 2f((1/x)) = 3x. f ′(x) = ?

$${f}\left({x}\right)\:+\:\mathrm{2}{f}\left(\frac{\mathrm{1}}{{x}}\right)\:=\:\mathrm{3}{x}. \\ $$$$\:{f}\:'\left({x}\right)\:=\:? \\ $$

Question Number 207362 Answers: 2 Comments: 0

Question Number 207361 Answers: 1 Comments: 0

y = ((tgx + ctgx)/8) , (0 ; (π/2)) Find: min(y) = ?

$$\mathrm{y}\:=\:\frac{\mathrm{tg}\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{ctg}\boldsymbol{\mathrm{x}}}{\mathrm{8}}\:\:\:\:\:,\:\:\:\:\:\left(\mathrm{0}\:;\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{y}\right)\:=\:? \\ $$

Question Number 207352 Answers: 1 Comments: 3

calculate: ∫_(Π/4) ^(Π/2) ⌊cot(x)⌋ dx

$${calculate}: \\ $$$$\:\int_{\frac{\Pi}{\mathrm{4}}} ^{\frac{\Pi}{\mathrm{2}}} \lfloor{cot}\left({x}\right)\rfloor\:{dx} \\ $$

Question Number 207354 Answers: 0 Comments: 4

Question Number 207359 Answers: 1 Comments: 0

∫((ln(x^2 +sin(sin(e^x ))))/( (√(x+tan(ln(x))))))dx

$$\int\frac{{ln}\left({x}^{\mathrm{2}} +{sin}\left({sin}\left({e}^{{x}} \right)\right)\right)}{\:\sqrt{{x}+{tan}\left({ln}\left({x}\right)\right)}}{dx} \\ $$

Question Number 207341 Answers: 2 Comments: 0

Question Number 207339 Answers: 2 Comments: 0

lim_(x→∞) (((x+a)^(1/x) −x^(1/x) )/((x+b)^(1/x) −x^(1/x) )) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({x}+{a}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }{\left({x}+{b}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }\:=? \\ $$

Question Number 207332 Answers: 1 Comments: 1

(a^→ ×b^→ )×(a^→ )=? how is the solution

$$\left(\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}\right)×\left(\overset{\rightarrow} {\mathrm{a}}\right)=? \\ $$$$\mathrm{how}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 207330 Answers: 1 Comments: 0

Find: 4 cos 50° + (1/(sin 20°)) = ?

$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{cos}\:\mathrm{50}°\:\:+\:\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°}\:\:=\:\:? \\ $$

Question Number 207328 Answers: 1 Comments: 0

Find: 4 sin 50° − (1/(cos 20°)) = ?

$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{sin}\:\mathrm{50}°\:−\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}°}\:\:=\:\:? \\ $$

Question Number 207327 Answers: 1 Comments: 1

(x−3) (√(x^2 −x−2)) = 0 Find: x = ?

$$\left(\mathrm{x}−\mathrm{3}\right)\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{2}}\:\:=\:\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207408 Answers: 2 Comments: 0

z = ((√3)/2) − (1/2) i find: z^(11) = ?

$$\boldsymbol{\mathrm{z}}\:\:=\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:\boldsymbol{\mathrm{i}}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{z}}^{\mathrm{11}} \:=\:? \\ $$

Question Number 207407 Answers: 0 Comments: 2

Question Number 207320 Answers: 1 Comments: 1

Question Number 207317 Answers: 2 Comments: 0

solve for y (1/(y′))+(1/(y′′))=1

$${solve}\:{for}\:{y} \\ $$$$\frac{\mathrm{1}}{{y}'}+\frac{\mathrm{1}}{{y}''}=\mathrm{1} \\ $$

Question Number 207315 Answers: 1 Comments: 0

if ab+ac+bc=2 calculate minimum of 10a^2 +10b^2 +c^2

$${if}\:{ab}+{ac}+{bc}=\mathrm{2}\: \\ $$$${calculate}\:{minimum}\:{of}\:\mathrm{10}{a}^{\mathrm{2}} +\mathrm{10}{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \\ $$

Question Number 207314 Answers: 1 Comments: 0

let f:R→R be a continuous function then show that (1) if f(x) = f(x^2 ) ∀ x ∈R then f is a constant function (2) if f(x) = f(2x+1) ∀x∈R then f is a constant function

$$\:\mathrm{let}\:\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{then} \\ $$$$\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}\left(\mathrm{x}^{\mathrm{2}} \right)\:\forall\:\mathrm{x}\:\in\mathbb{R}\:\mathrm{then}\:\mathrm{f}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant} \\ $$$$\:\:\mathrm{function} \\ $$$$\:\left(\mathrm{2}\right)\:\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}\left(\mathrm{2x}+\mathrm{1}\right)\:\forall\mathrm{x}\in\mathbb{R}\:\mathrm{then}\:\mathrm{f}\:\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\:\:\mathrm{constant}\:\mathrm{function}\: \\ $$

Question Number 207313 Answers: 0 Comments: 0

find the transfer function of the state model of the system given by x^• = determinant (((0 1 1)),((0 0 1)),((−1 −2 −3)))x+ determinant (((0 0)),((1 0)),((0 1))) and determinant ((y_1 ),(y_2 ))= determinant (((1 0 0)),((0 0 1)))x

$$\mathrm{find}\:\mathrm{the}\:\mathrm{transfer}\:\mathrm{function}\:\mathrm{of}\:\mathrm{the}\:\mathrm{state} \\ $$$$\mathrm{model}\:\mathrm{of}\:\mathrm{the}\:\mathrm{system}\:\mathrm{given}\:\mathrm{by} \\ $$$$\overset{\bullet} {\mathrm{x}}=\begin{vmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{1}}\\{−\mathrm{1}\:\:−\mathrm{2}\:\:\:−\mathrm{3}}\end{vmatrix}\mathrm{x}+\begin{vmatrix}{\mathrm{0}\:\:\:\mathrm{0}}\\{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{vmatrix} \\ $$$$\mathrm{and}\:\begin{vmatrix}{\mathrm{y}_{\mathrm{1}} }\\{\mathrm{y}_{\mathrm{2}} }\end{vmatrix}=\begin{vmatrix}{\mathrm{1}\:\:\mathrm{0}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{0}\:\:\mathrm{1}}\end{vmatrix}\mathrm{x} \\ $$

Question Number 207312 Answers: 0 Comments: 0

obtain the state model of the system whose transfer function is given by ((Y(s))/(U(s)))=(s/(15s^3 +26s+36))

$$\mathrm{obtain}\:\mathrm{the}\:\mathrm{state}\:\mathrm{model}\:\mathrm{of}\:\mathrm{the}\:\mathrm{system} \\ $$$$\mathrm{whose}\:\mathrm{transfer}\:\mathrm{function}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\frac{\mathrm{Y}\left(\mathrm{s}\right)}{\mathrm{U}\left(\mathrm{s}\right)}=\frac{\mathrm{s}}{\mathrm{15s}^{\mathrm{3}} +\mathrm{26s}+\mathrm{36}} \\ $$

Question Number 207292 Answers: 3 Comments: 1

Question Number 207287 Answers: 0 Comments: 3

Question Number 207279 Answers: 0 Comments: 1

If z = i − 1 Find z^(−100) = ?

$$\mathrm{If}\:\:\:\mathrm{z}\:=\:\boldsymbol{\mathrm{i}}\:−\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\:\boldsymbol{\mathrm{z}}^{−\mathrm{100}} \:=\:? \\ $$

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