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Question Number 13081    Answers: 2   Comments: 0

{ ((x+y+z=[1]_5 )),((xy=[2]_5 )),((yz=[1]_5 )) :} Solve system on Z_5

$$\begin{cases}{{x}+{y}+{z}=\left[\mathrm{1}\right]_{\mathrm{5}} }\\{{xy}=\left[\mathrm{2}\right]_{\mathrm{5}} }\\{{yz}=\left[\mathrm{1}\right]_{\mathrm{5}} }\end{cases} \\ $$$${Solve}\:{system}\:{on}\:\mathbb{Z}_{\mathrm{5}} \\ $$

Question Number 13075    Answers: 0   Comments: 5

S(x) is the sum of 49 terms of AP The first term is (1/2)x^3 and the difference is (7 − x) If S(x) maximum, the value of 10^(th) term is ...

$${S}\left({x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{49}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{AP} \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{3}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{difference} \\ $$$$\mathrm{is}\:\left(\mathrm{7}\:−\:{x}\right) \\ $$$$\mathrm{If}\:{S}\left({x}\right)\:\mathrm{maximum},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{10}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:... \\ $$

Question Number 13059    Answers: 2   Comments: 0

please help for ∫_(−3π ) ^( 3π) sin^(2009) x dx

$$\mathrm{please}\:\mathrm{help}\:\mathrm{for} \\ $$$$\int_{−\mathrm{3}\pi\:} ^{\:\:\:\mathrm{3}\pi} \mathrm{sin}^{\mathrm{2009}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 13054    Answers: 1   Comments: 0

An object is placed between a converging lens and a plane mirror. Explain how two real images of the object may be produced by the system. If the focal length of the lens is 15cm and the object is 20cm from both the lens and the mirror.Calculate the distance of the two images from the lens.. pls help me with this....

$$\mathrm{An}\:\mathrm{object}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{between}\:\mathrm{a}\: \\ $$$$\mathrm{converging}\:\mathrm{lens}\:\mathrm{and}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{mirror}. \\ $$$$\mathrm{Explain}\:\mathrm{how}\:\mathrm{two}\:\mathrm{real}\:\mathrm{images}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{object}\:\mathrm{may}\:\mathrm{be}\:\mathrm{produced}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{system}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{focal}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lens}\:\mathrm{is}\:\mathrm{15cm} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{object}\:\mathrm{is}\:\mathrm{20cm}\:\mathrm{from}\:\mathrm{both}\: \\ $$$$\mathrm{the}\:\mathrm{lens}\:\mathrm{and}\:\mathrm{the}\:\mathrm{mirror}.\mathrm{Calculate} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{images}\: \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{lens}.. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{pls}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{this}....\: \\ $$

Question Number 13049    Answers: 1   Comments: 0

Two charges q_1 = 10 μC and q_2 = 5 μC are placed on the axis at A (10, 0) cm and (20, 0) cm respectively. Determine a position between the two charges where the electric field intensity is 0.

$$\mathrm{Two}\:\mathrm{charges}\:\mathrm{q}_{\mathrm{1}} \:=\:\mathrm{10}\:\mu\mathrm{C}\:\mathrm{and}\:\:\mathrm{q}_{\mathrm{2}} \:=\:\mathrm{5}\:\mu\mathrm{C}\:\:\mathrm{are}\:\mathrm{placed}\:\mathrm{on}\:\mathrm{the}\:\mathrm{axis}\:\mathrm{at}\:\mathrm{A}\:\left(\mathrm{10},\:\mathrm{0}\right)\:\mathrm{cm} \\ $$$$\mathrm{and}\:\left(\mathrm{20},\:\mathrm{0}\right)\:\mathrm{cm}\:\:\mathrm{respectively}.\:\mathrm{Determine}\:\mathrm{a}\:\mathrm{position}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two}\:\mathrm{charges} \\ $$$$\mathrm{where}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{field}\:\mathrm{intensity}\:\mathrm{is}\:\mathrm{0}.\: \\ $$

Question Number 13068    Answers: 2   Comments: 0

If y = (x)^(1/3) Find (dy/dx) from the first principle

$$\mathrm{If}\:\:\:\mathrm{y}\:=\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}\:\:\:\:\:\mathrm{Find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle} \\ $$

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

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