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AllQuestion and Answers: Page 1570

Question Number 42340    Answers: 2   Comments: 3

Question Number 42320    Answers: 1   Comments: 3

Question Number 42316    Answers: 1   Comments: 2

Question Number 42315    Answers: 2   Comments: 0

the point (2,−1) is reflected in the line x=4 find the image point.

$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{point}}\:\left(\mathrm{2},−\mathrm{1}\right)\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{reflected}}\: \\ $$$$\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{line}}\:\:\boldsymbol{{x}}=\mathrm{4}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{image}}\:\boldsymbol{\mathrm{point}}. \\ $$

Question Number 42314    Answers: 0   Comments: 1

Question Number 42528    Answers: 1   Comments: 0

Solve : ((p+2)/(2p+1)) = ((q+2p)/(2q+p)) = ((1+2q)/(2+q)) = λ. Find (p,q) ?

$$\mathrm{Solve}\:: \\ $$$$\frac{\mathrm{p}+\mathrm{2}}{\mathrm{2p}+\mathrm{1}}\:=\:\frac{\mathrm{q}+\mathrm{2p}}{\mathrm{2q}+\mathrm{p}}\:=\:\frac{\mathrm{1}+\mathrm{2q}}{\mathrm{2}+\mathrm{q}}\:=\:\lambda. \\ $$$$\mathrm{Find}\:\left(\mathrm{p},\mathrm{q}\right)\:? \\ $$

Question Number 42299    Answers: 1   Comments: 0

The set X and Y have five elementseach . Given that ΣX=25,ΣY=55,ΣX^2 =165 and ΣY^2 =765 and a linear Function y= px + q tranforms the set X into the set Y,where p and q are positive constants. a) Find the mean and Variance of X and Y hence,or otherwise , b)find the values of p and q.

$${The}\:{set}\:{X}\:{and}\:{Y}\:{have}\:{five}\:{elementseach}\:. \\ $$$${Given}\:{that}\:\Sigma{X}=\mathrm{25},\Sigma{Y}=\mathrm{55},\Sigma{X}^{\mathrm{2}} =\mathrm{165}\:{and}\:\Sigma{Y}^{\mathrm{2}} =\mathrm{765} \\ $$$${and}\:{a}\:{linear}\:{Function}\:{y}=\:{px}\:+\:{q}\:\:{tranforms}\:{the}\:{set}\:{X}\:{into}\:{the}\:{set}\: \\ $$$${Y},{where}\:{p}\:{and}\:{q}\:{are}\:{positive}\:{constants}. \\ $$$$\left.{a}\right)\:{Find}\:{the}\:{mean}\:{and}\:{Variance}\:{of}\:{X}\:{and}\:{Y} \\ $$$${hence},{or}\:{otherwise}\:, \\ $$$$\left.{b}\right){find}\:{the}\:{values}\:{of}\:{p}\:{and}\:{q}. \\ $$

Question Number 42296    Answers: 1   Comments: 1

solve in Z^2 2x+3y =7

$${solve}\:{in}\:{Z}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{2}{x}+\mathrm{3}{y}\:=\mathrm{7} \\ $$

Question Number 42291    Answers: 1   Comments: 0

y = ((1080 − 19x)/(49)) (x,y ∈ Z) Find (x,y)

$${y}\:=\:\frac{\mathrm{1080}\:−\:\mathrm{19}{x}}{\mathrm{49}}\:\:\:\:\:\:\:\:\left({x},{y}\:\in\:\mathbb{Z}\right) \\ $$$$\mathrm{Find}\:\left({x},{y}\right) \\ $$

Question Number 42289    Answers: 1   Comments: 1

log(x+y)=1 log_2 x+log_4 y^2 =4

$$\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{log}}_{\mathrm{2}} \boldsymbol{{x}}+\boldsymbol{\mathrm{log}}_{\mathrm{4}} \boldsymbol{{y}}^{\mathrm{2}} =\mathrm{4} \\ $$

Question Number 42287    Answers: 1   Comments: 0

Your family will be attending a family reunion at a particular beach resort. To avoid hassle, you consider renting a car that charges a flat rate of P2 000 plus P150 per kilometer. Write a piecewise function that model the situation.

$${Your}\:{family}\:{will}\:{be}\:{attending}\:{a}\: \\ $$$${family}\:{reunion}\:{at}\:{a}\:{particular}\:{beach} \\ $$$${resort}.\:{To}\:{avoid}\:{hassle},\:{you}\:{consider} \\ $$$${renting}\:{a}\:{car}\:{that}\:{charges}\:{a}\:{flat}\:{rate} \\ $$$${of}\:{P}\mathrm{2}\:\mathrm{000}\:{plus}\:{P}\mathrm{150}\:{per}\:{kilometer}.\: \\ $$$${Write}\:{a}\:{piecewise}\:{function}\:{that}\: \\ $$$${model}\:{the}\:{situation}. \\ $$

Question Number 42285    Answers: 0   Comments: 2

let S_p =Σ_(n=0) ^∞ cos(((nπ)/p)) and W_p =Σ_(n=0) ^∞ sin(((nπ)/p)) with p natural integr not0 1) find a simple form of S_p and W_p 2) find the value of Σ_(n=0) ^∞ cos(((nπ)/3)) and Σ_(n=0) ^∞ sin(((nπ)/3)) 3) find the value of Σ_(n=0) ^∞ cos(((nπ)/5)) and Σ_(n=0) ^∞ sin(((nπ)/5)) 4) calculate A =Σ_(n=0) ^∞ cos^2 (((nπ)/3)) and B =Σ_(n=0) ^∞ sin^2 (((nπ)/3)) .

$${let}\:\:{S}_{{p}} =\sum_{{n}=\mathrm{0}} ^{\infty} \:\:{cos}\left(\frac{{n}\pi}{{p}}\right)\:\:{and}\:\:{W}_{{p}} \:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}\left(\frac{{n}\pi}{{p}}\right)\:{with}\:{p}\:{natural}\:{integr}\:{not}\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{S}_{{p}} \:{and}\:{W}_{{p}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{cos}\left(\frac{{n}\pi}{\mathrm{3}}\right)\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}\left(\frac{{n}\pi}{\mathrm{3}}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{cos}\left(\frac{{n}\pi}{\mathrm{5}}\right)\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}\left(\frac{{n}\pi}{\mathrm{5}}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:{A}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{cos}^{\mathrm{2}} \left(\frac{{n}\pi}{\mathrm{3}}\right)\:{and}\:{B}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}^{\mathrm{2}} \left(\frac{{n}\pi}{\mathrm{3}}\right)\:. \\ $$

Question Number 42304    Answers: 0   Comments: 1

solve in Z^3 x+2y +3z =12 .

$${solve}\:{in}\:{Z}^{\mathrm{3}} \:\:\:\:{x}+\mathrm{2}{y}\:+\mathrm{3}{z}\:=\mathrm{12}\:\:. \\ $$

Question Number 42278    Answers: 0   Comments: 1

Question Number 42266    Answers: 0   Comments: 1

find the value of Σ_(n =0) ^∞ (1/(n^2 +1)) and Σ_(n=0) ^∞ (((−1)^n )/(n^2 +1)) .

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}\:=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\mathrm{1}}\:\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \:+\mathrm{1}}\:. \\ $$

Question Number 42264    Answers: 1   Comments: 0

Thd local barangay recieved a budget of 150000 to provide medical check−ups for the children in the barangay. Write an equation representing the relationship of the alloted money per child.

$${Thd}\:{local}\:{barangay}\:{recieved}\:{a}\:{budget}\:{of}\:\mathrm{150000}\:{to}\:{provide}\:{medical}\:{check}−{ups}\:{for}\:{the}\:{children}\:{in}\:{the}\:{barangay}.\:{Write}\:{an}\:{equation}\:{representing}\:{the}\:{relationship}\:{of}\:{the}\:{alloted}\:{money}\:{per}\:{child}. \\ $$

Question Number 42262    Answers: 1   Comments: 0

Heat is supplied at a rate of 500W to a pressure cooker containing water and fitted with a safety valve.Steam escape such that water is lost at 12g/min.If the heat is supplied at 900W,water is lost at 20g/min.Calculate the specific latent heat of steam.

$${Heat}\:{is}\:{supplied}\:{at}\:{a}\:{rate}\:{of}\:\mathrm{500}{W} \\ $$$${to}\:{a}\:{pressure}\:{cooker}\:{containing} \\ $$$${water}\:{and}\:{fitted}\:{with}\:{a}\:{safety}\: \\ $$$${valve}.{Steam}\:{escape}\:{such}\:{that}\: \\ $$$${water}\:{is}\:{lost}\:{at}\:\mathrm{12}{g}/{min}.{If}\:{the} \\ $$$${heat}\:{is}\:{supplied}\:{at}\:\mathrm{900}{W},{water}\:{is} \\ $$$${lost}\:{at}\:\mathrm{20}{g}/{min}.{Calculate}\:{the} \\ $$$${specific}\:{latent}\:{heat}\:{of}\:{steam}. \\ $$$$ \\ $$

Question Number 42261    Answers: 1   Comments: 1

How much sweat must evaporate from the surface of 150kg of human body to be able to cool the human by 2°C.(assume C=3.35J/g/K for human and L=2.5mJ/kg for water at body temperature)

$${How}\:{much}\:{sweat}\:{must}\:{evaporate} \\ $$$${from}\:{the}\:{surface}\:{of}\:\mathrm{150}{kg}\:{of}\:{human} \\ $$$${body}\:{to}\:{be}\:{able}\:{to}\:{cool}\:{the}\:{human} \\ $$$${by}\:\mathrm{2}°{C}.\left({assume}\:{C}=\mathrm{3}.\mathrm{35}{J}/{g}/{K}\:{for}\right. \\ $$$${human}\:{and}\:{L}=\mathrm{2}.\mathrm{5}{mJ}/{kg}\:{for} \\ $$$$\left.{water}\:{at}\:{body}\:{temperature}\right) \\ $$

Question Number 42260    Answers: 0   Comments: 2

let f(a) = ∫_(−∞) ^(+∞) cos(ax^2 )dx with a>0 1) calculate f(a) interms of a ) calculate ∫_(−∞) ^(+∞) cos(2x^2 )dx 3) find the value of ∫_(−∞) ^(+∞) cos(x^2 +x+1)dx .

$${let}\:{f}\left({a}\right)\:=\:\int_{−\infty} ^{+\infty} \:{cos}\left({ax}^{\mathrm{2}} \right){dx}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right)\:{interms}\:{of}\:{a} \\ $$$$\left.\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:{cos}\left(\mathrm{2}{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:{cos}\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right){dx}\:. \\ $$

Question Number 42305    Answers: 0   Comments: 6

let f(x) = ∫_(−∞) ^(+∞) ((cos(xt))/((t−i)^2 )) dt 1) let R =Re(f(x)) and I =Im(f(x)) extract R and I 2) calculate R and I 3) conclude the value of f(x) 4) calculate ∫_(−∞) ^(+∞) ((cos(2t))/((t−i)^2 ))dt 5) let u_n = ∫_(−∞) ^(+∞) ((cos((t/n)))/((t−i)^2 ))dt (n natral integer not o) find lim_(n→+∞) u_n and study the convergence of Σu_n

$${let}\:{f}\left({x}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({xt}\right)}{\left({t}−{i}\right)^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{let}\:{R}\:={Re}\left({f}\left({x}\right)\right)\:{and}\:{I}\:={Im}\left({f}\left({x}\right)\right)\:{extract}\:{R}\:{and}\:{I} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{R}\:{and}\:{I} \\ $$$$\left.\mathrm{3}\right)\:{conclude}\:{the}\:{value}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{t}\right)}{\left({t}−{i}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{5}\right)\:{let}\:{u}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\frac{{t}}{{n}}\right)}{\left({t}−{i}\right)^{\mathrm{2}} }{dt}\:\:\:\:\left({n}\:{natral}\:{integer}\:{not}\:{o}\right) \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} \:\:\:\:{and}\:\:{study}\:{the}\:{convergence}\:{of}\:\Sigma{u}_{{n}} \\ $$

Question Number 42228    Answers: 1   Comments: 0

Solve : 2x^2 ydx −2y^4 dx+2x^3 dy+3xy^3 dy=0.

$$\mathrm{Solve}\:: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} {ydx}\:−\mathrm{2}{y}^{\mathrm{4}} {dx}+\mathrm{2}{x}^{\mathrm{3}} {dy}+\mathrm{3}{xy}^{\mathrm{3}} {dy}=\mathrm{0}. \\ $$

Question Number 42224    Answers: 0   Comments: 5

a + b + c = 180 a,b,c ∈ N number of triplets possible (a,b,c) for the above equation are ? ( the order of a,b,c doesn′t matter)

$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{180}\: \\ $$$${a},{b},{c}\:\in\:\mathbb{N} \\ $$$${number}\:{of}\:{triplets}\:{possible} \\ $$$$\left({a},{b},{c}\right)\:{for}\:{the}\:{above} \\ $$$${equation}\:{are}\:? \\ $$$$\left(\:{the}\:{order}\:{of}\:{a},{b},{c}\:\:{doesn}'{t}\right. \\ $$$$\left.{matter}\right) \\ $$

Question Number 42222    Answers: 1   Comments: 0

let f(x) =e^(−∣x∣) , 2π periodic even developp f at fourier serie .

$${let}\:{f}\left({x}\right)\:={e}^{−\mid{x}\mid} \:,\:\:\mathrm{2}\pi\:{periodic}\:{even}\:\:{developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$

Question Number 42221    Answers: 1   Comments: 0

Solve: (dt/dx) = (2/(x+t)) .

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dt}}{\mathrm{d}{x}}\:=\:\frac{\mathrm{2}}{{x}+\mathrm{t}}\:. \\ $$

Question Number 42215    Answers: 0   Comments: 3

Number of straight lines which satisfy the differential equation (dy/dx) + x((dy/dx))^2 − y =0 is ?

$$\mathrm{Number}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{{dx}}\:+\:{x}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −\:{y}\:=\mathrm{0}\:{is}\:? \\ $$

Question Number 42207    Answers: 1   Comments: 0

Find the equation of tangent and normal to the curve y given by y = x^3 + 3x^2 + 7 .

$${Find}\:{the}\:{equation}\:{of}\:{tangent}\:{and}\:{normal}\:{to}\:\:{the}\:{curve}\:{y} \\ $$$${given}\:{by}\:\:\:{y}\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{7}\:. \\ $$

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