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Question Number 13067    Answers: 0   Comments: 4

Question Number 13040    Answers: 1   Comments: 0

which is heavier,HOT water or COLD water? pls give explanation Thanks

$$\mathrm{which}\:\mathrm{is}\:\mathrm{heavier},\mathrm{HOT}\:\mathrm{water}\:\mathrm{or}\: \\ $$$$\mathrm{COLD}\:\mathrm{water}?\:\:\mathrm{pls}\:\mathrm{give}\:\mathrm{explanation} \\ $$$$ \\ $$$$\mathrm{Thanks} \\ $$

Question Number 13034    Answers: 0   Comments: 4

MrW1 Before we concluded that: Φ=Σ_(x=0) ^m Σ_(y=0) ^n (1−sgn(x−x′)) If you do: Σ_(x=0) ^1 Σ_(y=0) ^1 (1−sgn(x−x′)) =Σ_(x=0) ^1 Σ_(y=0) ^1 (1−sgn(x−((LCM(x,y))/y))) =(1−sgn(0−((LCM(0,0))/0)))+(1−sgn(1−((LCM(1,0))/0)) +(1−sgn(0−((LCM(0,1))/1)))+(1−sgn(1−((LCM(1,1))/1)) =(1−sgn(−((LCM(0,0))/0)))+(1−sgn(1−(0/0))) +(1−sgn(−(0/1)))+(1−sgn(1−(1/1))) =????

$$\mathrm{MrW1} \\ $$$$\: \\ $$$$\mathrm{Before}\:\mathrm{we}\:\mathrm{concluded}\:\mathrm{that}: \\ $$$$\Phi=\underset{{x}=\mathrm{0}} {\overset{{m}} {\sum}}\underset{{y}=\mathrm{0}} {\overset{{n}} {\sum}}\left(\mathrm{1}−\mathrm{sgn}\left({x}−{x}'\right)\right) \\ $$$$\: \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{do}: \\ $$$$\underset{{x}=\mathrm{0}} {\overset{\mathrm{1}} {\sum}}\underset{{y}=\mathrm{0}} {\overset{\mathrm{1}} {\sum}}\left(\mathrm{1}−\mathrm{sgn}\left({x}−{x}'\right)\right) \\ $$$$=\underset{{x}=\mathrm{0}} {\overset{\mathrm{1}} {\sum}}\underset{{y}=\mathrm{0}} {\overset{\mathrm{1}} {\sum}}\left(\mathrm{1}−\mathrm{sgn}\left({x}−\frac{\mathrm{LCM}\left({x},{y}\right)}{{y}}\right)\right) \\ $$$$=\left(\mathrm{1}−\mathrm{sgn}\left(\mathrm{0}−\frac{\mathrm{LCM}\left(\mathrm{0},\mathrm{0}\right)}{\mathrm{0}}\right)\right)+\left(\mathrm{1}−\mathrm{sgn}\left(\mathrm{1}−\frac{\mathrm{LCM}\left(\mathrm{1},\mathrm{0}\right)}{\mathrm{0}}\right)\right. \\ $$$$+\left(\mathrm{1}−\mathrm{sgn}\left(\mathrm{0}−\frac{\mathrm{LCM}\left(\mathrm{0},\mathrm{1}\right)}{\mathrm{1}}\right)\right)+\left(\mathrm{1}−\mathrm{sgn}\left(\mathrm{1}−\frac{\mathrm{LCM}\left(\mathrm{1},\mathrm{1}\right)}{\mathrm{1}}\right)\right. \\ $$$$\: \\ $$$$=\left(\mathrm{1}−\mathrm{sgn}\left(−\frac{\mathrm{LCM}\left(\mathrm{0},\mathrm{0}\right)}{\mathrm{0}}\right)\right)+\left(\mathrm{1}−\mathrm{sgn}\left(\mathrm{1}−\frac{\mathrm{0}}{\mathrm{0}}\right)\right) \\ $$$$+\left(\mathrm{1}−\mathrm{sgn}\left(−\frac{\mathrm{0}}{\mathrm{1}}\right)\right)+\left(\mathrm{1}−\mathrm{sgn}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}}\right)\right) \\ $$$$\: \\ $$$$=???? \\ $$

Question Number 13031    Answers: 1   Comments: 0

MrW1 Going off of Q12883 How many unique angles angles in Z^3 ? What about Z^n ?

$$\mathrm{MrW1} \\ $$$$ \\ $$$$\mathrm{Going}\:\mathrm{off}\:\mathrm{of}\:\mathrm{Q12883} \\ $$$$\: \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{unique}\:\mathrm{angles}\:\mathrm{angles}\:\mathrm{in}\:\mathbb{Z}^{\mathrm{3}} ? \\ $$$$\mathrm{What}\:\mathrm{about}\:\mathbb{Z}^{{n}} ? \\ $$

Question Number 13030    Answers: 0   Comments: 1

Question Number 13029    Answers: 1   Comments: 1

Question Number 13025    Answers: 1   Comments: 1

Question Number 13012    Answers: 0   Comments: 2

Sir. MRV please i need the cubic equation formular. my phone has fault and i just restore it. please help me re send it. i really appreciate your effort sir. God bless you sir.

$${Sir}.\:{MRV}\:\:{please}\:\mathrm{i}\:\mathrm{need}\:{the}\:\mathrm{cubic}\:\mathrm{equation}\:\mathrm{formular}.\:\:\mathrm{my}\:\mathrm{phone}\:\mathrm{has}\:\mathrm{fault} \\ $$$$\mathrm{and}\:\mathrm{i}\:\mathrm{just}\:\mathrm{restore}\:\mathrm{it}.\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{re}\:\mathrm{send}\:\mathrm{it}.\:\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{effort} \\ $$$$\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Question Number 13011    Answers: 1   Comments: 0

lim_(x→∞) [5^x + 5^(3x) ]^(1/x) = ? please help

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\left[\mathrm{5}^{\mathrm{x}} \:+\:\mathrm{5}^{\mathrm{3x}} \right]^{\frac{\mathrm{1}}{\mathrm{x}}} \:=\:? \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 13010    Answers: 1   Comments: 0

Question Number 13005    Answers: 1   Comments: 0

using De Moivre theorem solve the equation (x+1)^5 +(x−1)^5 =0

$${using}\:{De}\:{Moivre}\:{theorem}\:{solve}\:{the}\:{equation}\:\left({x}+\mathrm{1}\right)^{\mathrm{5}} +\left({x}−\mathrm{1}\right)^{\mathrm{5}} =\mathrm{0} \\ $$

Question Number 13004    Answers: 0   Comments: 0

If ∫f(x)dx=g(x) ,then why ∫_b ^a f(x)dx=g(a)−g(b)???

$${If}\:\int{f}\left({x}\right){dx}={g}\left({x}\right)\:,{then}\:{why} \\ $$$$\int_{{b}} ^{{a}} {f}\left({x}\right){dx}={g}\left({a}\right)−{g}\left({b}\right)??? \\ $$

Question Number 12998    Answers: 1   Comments: 0

((a +_− (√(2a.1.1)))/2)

$$\frac{{a}\:\underset{−} {+}\sqrt{\mathrm{2}{a}.\mathrm{1}.\mathrm{1}}}{\mathrm{2}} \\ $$

Question Number 12995    Answers: 0   Comments: 0

If a, b, c are in GP and a−b, c−a, b−c are in HP, then a+4b+c is equal to

$$\mathrm{If}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:\:{a}−{b},\:{c}−{a},\:{b}−{c}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{HP},\:\mathrm{then}\:{a}+\mathrm{4}{b}+{c}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 12968    Answers: 1   Comments: 0

(x+3)^2 +(y−5)^2 =45 A(0;11) of the circle to the point of trying to find the angular coefficient.

$$\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{y}}−\mathrm{5}\right)^{\mathrm{2}} =\mathrm{45}\:\:\:\boldsymbol{\mathrm{A}}\left(\mathrm{0};\mathrm{11}\right) \\ $$$$\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{circle}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{point}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{trying}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{angular}}\:\:\boldsymbol{\mathrm{coefficient}}. \\ $$

Question Number 13000    Answers: 0   Comments: 3

∫ sin^4 x cos^3 x dx

$$\int\:\mathrm{sin}^{\mathrm{4}} \:{x}\:\mathrm{cos}^{\mathrm{3}} \:{x}\:{dx} \\ $$

Question Number 13002    Answers: 1   Comments: 0

3^((x − 3)(x − y − 2)) = 1 5^((x^2 − 2xy + y^2 + x − y − 3/2)) = (√5) Find the value of x and y

$$\mathrm{3}^{\left({x}\:−\:\mathrm{3}\right)\left({x}\:−\:{y}\:−\:\mathrm{2}\right)} \:=\:\mathrm{1} \\ $$$$\mathrm{5}^{\left({x}^{\mathrm{2}} \:−\:\mathrm{2}{xy}\:+\:{y}^{\mathrm{2}} \:+\:{x}\:−\:{y}\:−\:\mathrm{3}/\mathrm{2}\right)} \:=\:\sqrt{\mathrm{5}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y} \\ $$

Question Number 12946    Answers: 1   Comments: 0

a_n =(√(3a_(n−1) +2)) a_1 =1 lim_(n→∞) a_n =?

$${a}_{{n}} =\sqrt{\mathrm{3}{a}_{{n}−\mathrm{1}} +\mathrm{2}}\:\:\:{a}_{\mathrm{1}} =\mathrm{1} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}} =? \\ $$

Question Number 12933    Answers: 2   Comments: 9

Question Number 12930    Answers: 1   Comments: 0

Question Number 12929    Answers: 0   Comments: 0

Question Number 12928    Answers: 1   Comments: 0

Question Number 12927    Answers: 0   Comments: 1

Σcos ((1/n))

$$\Sigma\mathrm{cos}\:\left(\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 12926    Answers: 1   Comments: 0

∫_( 0) ^(π/2) log ∣tan x+cot x∣ dx =

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{log}\:\mid\mathrm{tan}\:{x}+\mathrm{cot}\:{x}\mid\:{dx}\:= \\ $$

Question Number 12962    Answers: 1   Comments: 0

Question Number 12919    Answers: 0   Comments: 0

The value of the integral ∫_( 0) ^1 e^x^2 dx lies in the interval

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{e}^{{x}^{\mathrm{2}} } {dx}\:\:\mathrm{lies} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$

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