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AllQuestion and Answers: Page 1265

Question Number 87952 Answers: 1 Comments: 5

Question Number 87944 Answers: 0 Comments: 1

y ′ = ((2xy)/(y^2 −x^2 ))

$$\mathrm{y}\:'\:=\:\frac{\mathrm{2xy}}{\mathrm{y}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 87930 Answers: 0 Comments: 0

Question Number 87927 Answers: 1 Comments: 2

x+(√y) = 7 (√x) + y = 11 find x+y

$$\mathrm{x}+\sqrt{\mathrm{y}}\:=\:\mathrm{7} \\ $$$$\sqrt{\mathrm{x}}\:+\:\mathrm{y}\:=\:\mathrm{11} \\ $$$$\mathrm{find}\:\mathrm{x}+\mathrm{y}\: \\ $$

Question Number 87939 Answers: 0 Comments: 9

Question Number 87933 Answers: 0 Comments: 10

how many terms are there in (x^2 +x+1)^(11) ?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{there} \\ $$$$\mathrm{in}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{11}} \:? \\ $$

Question Number 87935 Answers: 1 Comments: 0

A man buys a hen at 9$ and sells it at 11$. He buys the same hen later on at 12$ and sells it now at 14$. What is his total benefit ?

$${A}\:{man}\:{buys}\:{a}\:{hen}\:{at}\:\mathrm{9\$}\:{and}\:{sells}\:{it}\:{at}\:\mathrm{11\$}.\:{He}\:{buys} \\ $$$${the}\:{same}\:{hen}\:{later}\:{on}\:{at}\:\mathrm{12\$}\:{and}\:{sells}\:{it}\:{now} \\ $$$${at}\:\mathrm{14\$}.\:{What}\:{is}\:{his}\:{total}\:{benefit}\:? \\ $$

Question Number 87920 Answers: 0 Comments: 1

Question Number 87918 Answers: 0 Comments: 1

Question Number 87911 Answers: 0 Comments: 3

Question Number 87910 Answers: 0 Comments: 0

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Question Number 87905 Answers: 1 Comments: 1

y′ = 2^y

$$\mathrm{y}'\:=\:\mathrm{2}^{\mathrm{y}} \\ $$

Question Number 87904 Answers: 2 Comments: 2

y ′′ −3y′ +2y = 10sin x + 2cos 2x

$$\mathrm{y}\:''\:−\mathrm{3y}'\:+\mathrm{2y}\:=\:\mathrm{10sin}\:\mathrm{x}\:+\:\mathrm{2cos}\:\mathrm{2x} \\ $$

Question Number 87903 Answers: 0 Comments: 0

find ∫_0 ^∞ ∫_0 ^∞ ((arctan(xy))/((x+y)^2 ))dxdy

$${find}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({xy}\right)}{\left({x}+{y}\right)^{\mathrm{2}} }{dxdy} \\ $$

Question Number 87902 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ∫_0 ^∞ (e^(−(x^2 +y^2 )) /((x+y)^2 ))dxdy

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} }{\left({x}+{y}\right)^{\mathrm{2}} }{dxdy} \\ $$

Question Number 87901 Answers: 0 Comments: 0

calculate ∫∫_([0,1]^2 ) ((arctan(x+y))/(x+y))dxdy

$${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{arctan}\left({x}+{y}\right)}{{x}+{y}}{dxdy} \\ $$

Question Number 87893 Answers: 1 Comments: 0

∫ (√((sin x)/(sin x−cos x))) dx

$$\int\:\sqrt{\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}}\:\:\mathrm{dx}\: \\ $$

Question Number 87886 Answers: 1 Comments: 2

Question Number 87884 Answers: 1 Comments: 0

Question Number 87881 Answers: 1 Comments: 1

∫_(−∞) ^( +∞) (1/x) dx =

$$\:\int_{−\infty} ^{\:+\infty} \frac{\mathrm{1}}{{x}}\:{dx}\:=\: \\ $$

Question Number 87878 Answers: 1 Comments: 0

posons (1+2(√3))^n =a_n +b_n (√3) montre que pgcd(a_n ;b_n )=1

$${posons}\: \\ $$$$\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} =\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} +\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \sqrt{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{montre}}\:\boldsymbol{\mathrm{que}}\:\boldsymbol{\mathrm{pgcd}}\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{{b}}_{\boldsymbol{{n}}} \right)=\mathrm{1} \\ $$

Question Number 87877 Answers: 0 Comments: 0

posons (1+2(√3))^n =a_n +b_n (√3) montre que pgcd(a_n ;b_n )=1

Question Number 87876 Answers: 0 Comments: 1

prove that Γ(z)=∫_0 ^∞ e^(−x) x^(z−1) dx,Re(z)>0

$${prove}\:{that} \\ $$$$\Gamma\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \:{x}^{{z}−\mathrm{1}} \:{dx},{Re}\left({z}\right)>\mathrm{0} \\ $$

Question Number 87870 Answers: 0 Comments: 0

x amd y are imtegers. how many possible solitions do the eqiation has x^2 −10y^2 = ±1

$$\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{amd}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{imtegers}}. \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{solitions}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{eqiation}}\:\boldsymbol{\mathrm{has}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{10}\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:=\:\pm\mathrm{1} \\ $$

Question Number 87862 Answers: 0 Comments: 3

Evaluate ∫_(−1) ^1 (1/(x−1)) dx

$$\mathrm{Evaluate}\:\:\:\:\overset{\mathrm{1}} {\int}_{−\mathrm{1}} \frac{\mathrm{1}}{{x}−\mathrm{1}}\:{dx}\: \\ $$

Question Number 87861 Answers: 0 Comments: 4

∫_0 ^(π/4) tanh 2x dx

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\mathrm{tanh}\:\mathrm{2}{x}\:{dx} \\ $$

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