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Question Number 150296 Answers: 0 Comments: 0

Question Number 150289 Answers: 1 Comments: 0

If _n C_3 − _n C_2 = 14 Find _n P_2 = ?

$$\mathrm{If}\:\:\:_{\boldsymbol{\mathrm{n}}} \mathrm{C}_{\mathrm{3}} \:−\:_{\boldsymbol{\mathrm{n}}} \mathrm{C}_{\mathrm{2}} \:=\:\mathrm{14} \\ $$$$\mathrm{Find}\:\:\:_{\boldsymbol{\mathrm{n}}} \mathrm{P}_{\mathrm{2}} \:=\:? \\ $$

Question Number 150277 Answers: 0 Comments: 2

Laplace Metodu (solution) y^(′′) + 5y^′ + 6y = cos(t) y(0) = 0 and y^′ (0) = 1

$$\mathrm{Laplace}\:\mathrm{Metodu}\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{y}^{''} \:+\:\mathrm{5y}^{'} \:+\:\mathrm{6y}\:=\:\mathrm{cos}\left(\mathrm{t}\right) \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$

Question Number 150259 Answers: 1 Comments: 0

∫_( 0) ^( ∞) ((e^(−st) (cosh(2t)−cosh(5t))dt)/t)=?

$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{e}^{−\boldsymbol{\mathrm{st}}} \left(\mathrm{cosh}\left(\mathrm{2t}\right)−\mathrm{cosh}\left(\mathrm{5t}\right)\right)\mathrm{dt}}{\mathrm{t}}=? \\ $$

Question Number 150247 Answers: 0 Comments: 11

∫_( 2) ^( 6) (x-1)(x-2)(x-3)...(x-9) dx = ? a)1 b)0 c)6! d)-2 e)4!

$$\underset{\:\mathrm{2}} {\overset{\:\mathrm{6}} {\int}}\:\left(\mathrm{x}-\mathrm{1}\right)\left(\mathrm{x}-\mathrm{2}\right)\left(\mathrm{x}-\mathrm{3}\right)...\left(\mathrm{x}-\mathrm{9}\right)\:\mathrm{dx}\:=\:? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{1}\left.\:\left.\:\:\:\:\mathrm{b}\right)\mathrm{0}\:\:\:\:\:\mathrm{c}\right)\mathrm{6}!\:\:\:\:\:\mathrm{d}\right)-\mathrm{2}\:\:\:\:\mathrm{e}\right)\mathrm{4}! \\ $$

Question Number 150231 Answers: 1 Comments: 0

Question Number 150228 Answers: 0 Comments: 1

Question Number 150224 Answers: 2 Comments: 0

Question Number 150223 Answers: 2 Comments: 0

Question Number 150222 Answers: 1 Comments: 0

Calcul des sommes A− Σ_(p=0) ^α C_n ^(2p) =.....?? avec α=E((n/2)) B− Σ_(p=0) ^β C_n ^(2p+1) =....?? avec β=E(((n−1)/2))

$${Calcul}\:{des}\:{sommes} \\ $$$${A}−\:\underset{{p}=\mathrm{0}} {\overset{\alpha} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}} =.....??\:\:\:\:\:{avec}\:\:\alpha={E}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$$${B}−\:\underset{{p}=\mathrm{0}} {\overset{\beta} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}+\mathrm{1}} =....??\:\:\:\:{avec}\:\beta={E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right) \\ $$$$ \\ $$

Question Number 150531 Answers: 0 Comments: 6

Find x;y ; x∈Q and y∈Z such that: 2020(x^2 + y^2 ) + 2019(x + y) = 2021xy

$$\mathrm{Find}\:\:\mathrm{x};\mathrm{y}\:\:;\:\:\mathrm{x}\in\mathrm{Q}\:\:\mathrm{and}\:\:\mathrm{y}\in\mathrm{Z}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\mathrm{2020}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\:+\:\mathrm{2019}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:\mathrm{2021xy} \\ $$

Question Number 150324 Answers: 0 Comments: 0

Calcul des sommes A− Σ_(p=0) ^α C_n ^(2p) =..... avec α=E((n/2)) B− Σ_(p=0) ^β C_n ^(2p+1) =..... avec β=E(((n−1)/2))

$${Calcul}\:{des}\:{sommes} \\ $$$${A}−\:\:\underset{{p}=\mathrm{0}} {\overset{\alpha} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}} =.....\:\:{avec}\:\:\alpha={E}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$$${B}−\:\underset{{p}=\mathrm{0}} {\overset{\beta} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}+\mathrm{1}} =.....\:\:{avec}\:\beta={E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right) \\ $$

Question Number 150533 Answers: 1 Comments: 0

solve... I:= ∫_(−∞) ^( ∞) e^( x−n.sinh^( 2) (x)) dx =^(??) (√(π/n)) ...m.n...

$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{solve}... \\ $$$$\:\:\mathrm{I}:=\:\int_{−\infty} ^{\:\infty} {e}^{\:{x}−{n}.{sinh}^{\:\mathrm{2}} \left({x}\right)} {dx}\:\overset{??} {=}\sqrt{\frac{\pi}{{n}}} \\ $$$$\:\:\:\:\:\:\:...{m}.{n}... \\ $$

Question Number 150202 Answers: 2 Comments: 1

lim_(x→2) (((16−4^x )/(9−3^x ))) with out lophital

$${lim}_{{x}\rightarrow\mathrm{2}} \left(\frac{\mathrm{16}−\mathrm{4}^{{x}} }{\mathrm{9}−\mathrm{3}^{{x}} }\right)\:{with}\:{out}\:{lophital} \\ $$

Question Number 150199 Answers: 0 Comments: 1

Question Number 150191 Answers: 2 Comments: 0

{ ((x - (√y) = 7)),((y + (√x) = 7)) :} ⇒ xy = ?

$$\begin{cases}{\mathrm{x}\:-\:\sqrt{\mathrm{y}}\:=\:\mathrm{7}}\\{\mathrm{y}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$

Question Number 150189 Answers: 1 Comments: 1

Solve the equation: (x - 3) (√(x^2 - x − 2)) = 0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\left(\mathrm{x}\:-\:\mathrm{3}\right)\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:−\:\mathrm{2}}\:=\:\mathrm{0} \\ $$

Question Number 150187 Answers: 2 Comments: 1

If f(x) = 2x^2 + 5 ⇒ f^( −1) (2) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{5}\:\:\Rightarrow\:\:\mathrm{f}^{\:−\mathrm{1}} \left(\mathrm{2}\right)\:=\:? \\ $$

Question Number 150186 Answers: 1 Comments: 0

If f(x) = sin^4 (3x) ⇒ f^′ ((π/(12))) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{3x}\right)\:\:\Rightarrow\:\:{f}\:^{'} \left(\frac{\pi}{\mathrm{12}}\right)\:=\:? \\ $$

Question Number 150181 Answers: 1 Comments: 0

(x−6)^3 +(x−5)^3 +(x−4)^3 =3(x−6)(x−5)(x−4) x=?

$$\:\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{5}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{3}} =\mathrm{3}\left(\mathrm{x}−\mathrm{6}\right)\left(\mathrm{x}−\mathrm{5}\right)\left(\mathrm{x}−\mathrm{4}\right) \\ $$$$\mathrm{x}=? \\ $$

Question Number 150180 Answers: 1 Comments: 0

show that derivative of Sin x/x =1

$$\mathrm{show}\:\mathrm{that}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{Sin}\:\mathrm{x}/\mathrm{x}\:=\mathrm{1} \\ $$$$ \\ $$

Question Number 150177 Answers: 1 Comments: 5

Question Number 150171 Answers: 1 Comments: 0

solve in R: (((ax−b)^3 ))^(1/7) −(((b−ax)^(−3) ))^(1/7) =((65)/8)

$${solve}\:{in}\:\mathbb{R}: \\ $$$$\sqrt[{\mathrm{7}}]{\left({ax}−{b}\right)^{\mathrm{3}} }−\sqrt[{\mathrm{7}}]{\left({b}−{ax}\right)^{−\mathrm{3}} }=\frac{\mathrm{65}}{\mathrm{8}} \\ $$

Question Number 150165 Answers: 0 Comments: 0

Question Number 150156 Answers: 2 Comments: 0

Question Number 150311 Answers: 1 Comments: 0

x,y ∈ R Find all functions that satisfy this condition : f(x+y) = f(x) ∙ f(y) − f(x ∙ y) + 1 Find all functions that satisfy this condition : f(f(x)) = f(x) + x

$${x},{y}\:\in\:\mathbb{R} \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right)\:\centerdot\:{f}\left({y}\right)\:−\:{f}\left({x}\:\centerdot\:{y}\right)\:+\:\mathrm{1} \\ $$$$ \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({f}\left({x}\right)\right)\:=\:{f}\left({x}\right)\:+\:{x} \\ $$

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