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Question Number 150332 Answers: 0 Comments: 0

Question Number 150331 Answers: 0 Comments: 0

ultimately Q.149894 boils down to finding s_(max) , s_(min) ∀ {h−scos (θ−(π/6))}^2 +{k−ssin (θ+(π/6))}^2 =r^2

$${ultimately}\:\:{Q}.\mathrm{149894}\:\:{boils}\: \\ $$$${down}\:{to}\:{finding}\:{s}_{{max}} ,\:{s}_{{min}} \:\forall \\ $$$$\:\:\:\:\left\{{h}−{s}\mathrm{cos}\:\left(\theta−\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} \\ $$$$+\left\{{k}−{s}\mathrm{sin}\:\left(\theta+\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 150328 Answers: 0 Comments: 0

Find all the solutions to the equation: x^3 − y^3 = xy + 61

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:−\:\boldsymbol{\mathrm{y}}^{\mathrm{3}} \:=\:\boldsymbol{\mathrm{xy}}\:+\:\mathrm{61} \\ $$

Question Number 150327 Answers: 2 Comments: 0

1) 33x ≡ 48 (mod 654) 2) 5^(1000 000) ≡ x (mod 41) Find x=?

$$\left.\mathrm{1}\right)\:\mathrm{33}\boldsymbol{\mathrm{x}}\:\:\equiv\:\:\mathrm{48}\:\left(\mathrm{mod}\:\mathrm{654}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{5}^{\mathrm{1000}\:\mathrm{000}} \:\:\equiv\:\:\boldsymbol{\mathrm{x}}\:\left(\mathrm{mod}\:\mathrm{41}\right) \\ $$$$\mathrm{Find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 150326 Answers: 0 Comments: 2

Find ax^5 +by^5 if the real numbers a,b,x and y satisf the equations: ax + by = 3 ax^2 + by^2 = 7 ax^3 + by^3 = 16 ax^4 + by^4 = 42

$$\mathrm{Find}\:\:\boldsymbol{\mathrm{ax}}^{\mathrm{5}} +\boldsymbol{\mathrm{by}}^{\mathrm{5}} \:\:\mathrm{if}\:\mathrm{the}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{satisf}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{3} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{7} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{16} \\ $$$$\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{by}^{\mathrm{4}} \:=\:\mathrm{42} \\ $$

Question Number 150325 Answers: 2 Comments: 0

Solve..... 𝛗= ∫_0 ^( (π/2)) cos^( 2) (x ). ln (cot( x ))dx=? .....m.n.....

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{Solve}..... \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {cos}^{\:\mathrm{2}} \left({x}\:\right).\:{ln}\:\left({cot}\left(\:{x}\:\right)\right){dx}=?\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:.....{m}.{n}..... \\ $$

Question Number 150323 Answers: 0 Comments: 0

a pmf of a random variable Xis given as f(x)=(e^(−10) . 10^x )/x! X=0 , 1 ,2 ... find P(x<16)

$$\mathrm{a}\:\mathrm{pmf}\:\mathrm{of}\:\mathrm{a}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{Xis}\:\mathrm{given}\:\mathrm{as} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{e}^{−\mathrm{10}} .\:\mathrm{10}^{\mathrm{x}} \right)/\mathrm{x}!\:\:\mathrm{X}=\mathrm{0}\:,\:\mathrm{1}\:,\mathrm{2}\:...\:\mathrm{find}\: \\ $$$$\mathrm{P}\left(\mathrm{x}<\mathrm{16}\right) \\ $$

Question Number 150313 Answers: 2 Comments: 0

Question Number 150312 Answers: 0 Comments: 0

Find n lowest integers that divide (1^2 + 2^2 + 3^2 + …+ n^2 ) .

$${Find}\:\:{n}\:\:{lowest}\:\:{integers}\:\:{that}\:\:{divide}\:\:\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\ldots+\:{n}^{\mathrm{2}} \right)\:. \\ $$

Question Number 150308 Answers: 1 Comments: 1

Question Number 150305 Answers: 1 Comments: 1

Question Number 150303 Answers: 1 Comments: 0

If x;y;z∈[0;∞) then: 2^x +2^y +2^z +2^(x+y+z) ≥ 4^(√(xy)) +4^(√(yz)) +4^(√(zx)) +1

$$\mathrm{If}\:\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\left[\mathrm{0};\infty\right)\:\:\mathrm{then}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} +\mathrm{2}^{\boldsymbol{\mathrm{y}}} +\mathrm{2}^{\boldsymbol{\mathrm{z}}} +\mathrm{2}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}} \:\geqslant\:\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{xy}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{yz}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{zx}}}} +\mathrm{1} \\ $$

Question Number 150299 Answers: 2 Comments: 0

Given that x^2 +y^2 =73 and xy=12 , find the value of (x+y)^2

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{73}\:\mathrm{and}\:\mathrm{xy}=\mathrm{12}\:,\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \\ $$

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...

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

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