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Question Number 41912    Answers: 2   Comments: 0

The estimated time for Abu and Ali to repair a faulty car is six hours. If Abu used 10 hours to repair the car, how many hours will Ali use to repair the car?

$$\mathrm{The}\:\mathrm{estimated}\:\mathrm{time}\:\mathrm{for}\:\mathrm{Abu}\:\mathrm{and}\:\mathrm{Ali}\:\mathrm{to}\:\mathrm{repair}\:\mathrm{a} \\ $$$$\mathrm{faulty}\:\mathrm{car}\:\mathrm{is}\:\mathrm{six}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{Abu}\:\mathrm{used}\:\mathrm{10}\:\mathrm{hours}\:\mathrm{to} \\ $$$$\mathrm{repair}\:\mathrm{the}\:\mathrm{car},\:\mathrm{how}\:\mathrm{many}\:\mathrm{hours}\:\mathrm{will}\:\mathrm{Ali}\:\mathrm{use}\:\mathrm{to}\:\mathrm{repair} \\ $$$$\mathrm{the}\:\mathrm{car}? \\ $$

Question Number 41911    Answers: 2   Comments: 5

h(x)=(√(sin^4 x+cos^4 x−2msinxcosx)) Find all the values of the parameter m for the funtion denined on R

$${h}\left({x}\right)=\sqrt{{sin}^{\mathrm{4}} {x}+{cos}^{\mathrm{4}} {x}−\mathrm{2}{msinxcosx}} \\ $$$${Find}\:{all}\:{the}\:{values}\:{of}\:{the}\:{parameter}\:{m}\:{for}\:{the}\:{funtion}\:{denined}\:{on}\:{R} \\ $$$$ \\ $$

Question Number 41906    Answers: 0   Comments: 1

A concave lens of focal length 60cm is made of material whose refractive index for red light is 1.641 and refractive index for blue light is 1.659.That for white light is 1.65.It is combined with a convex lens of dispersive power 0.0173 to form an achromatic doublet. Calculate the focal length of the achromatic lens.

$${A}\:{concave}\:{lens}\:{of}\:{focal}\:{length}\:\mathrm{60}{cm} \\ $$$${is}\:{made}\:{of}\:{material}\:{whose} \\ $$$${refractive}\:{index}\:{for}\:{red}\:{light}\:{is} \\ $$$$\mathrm{1}.\mathrm{641}\:{and}\:{refractive}\:{index}\:{for}\:{blue} \\ $$$${light}\:{is}\:\mathrm{1}.\mathrm{659}.{That}\:{for}\:{white}\:{light} \\ $$$${is}\:\mathrm{1}.\mathrm{65}.{It}\:{is}\:{combined}\:{with}\:{a}\:{convex} \\ $$$${lens}\:{of}\:{dispersive}\:{power}\:\mathrm{0}.\mathrm{0173}\:{to} \\ $$$${form}\:{an}\:{achromatic}\:{doublet}. \\ $$$${Calculate}\:{the}\:{focal}\:{length}\:{of}\:{the} \\ $$$${achromatic}\:{lens}. \\ $$

Question Number 41962    Answers: 1   Comments: 1

A student holding a 324Hz tuning fork approaches a wall at a speed of 6ms^(−1) .The speed of sound in air is 336ms^(−1) .What frequency will the student detect from waves omitted from the fork and waves coming from the wall?

$${A}\:{student}\:{holding}\:{a}\:\mathrm{324}{Hz}\:{tuning} \\ $$$${fork}\:{approaches}\:{a}\:{wall}\:{at}\:{a}\:{speed} \\ $$$${of}\:\mathrm{6}{ms}^{−\mathrm{1}} .{The}\:{speed}\:{of}\:{sound}\:{in}\:{air} \\ $$$${is}\:\mathrm{336}{ms}^{−\mathrm{1}} .{What}\:{frequency}\:{will} \\ $$$${the}\:{student}\:{detect}\:{from}\:{waves} \\ $$$${omitted}\:{from}\:{the}\:{fork}\:{and}\:{waves} \\ $$$${coming}\:{from}\:{the}\:{wall}? \\ $$

Question Number 41902    Answers: 1   Comments: 0

tan3θ tan2θ =1 find the general^(solution......)

$$\mathrm{tan3}\theta\:\mathrm{tan2}\theta\:=\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:^{\mathrm{solution}......} \\ $$

Question Number 41921    Answers: 2   Comments: 0

Find x : 625^(x − 5) = 200((√x))^3

$$\mathrm{Find}\:\mathrm{x}\::\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\left(\sqrt{\mathrm{x}}\right)^{\mathrm{3}} \\ $$

Question Number 41896    Answers: 2   Comments: 1

∫_(−1/2) ^(1/2) [ (((x+1)/(x−1)))^2 +(((x−1)/(x+1)))^2 −2]^(1/2) dx =

$$\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\:\left[\:\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{\mathrm{2}} −\mathrm{2}\right]^{\mathrm{1}/\mathrm{2}} {dx}\:= \\ $$

Question Number 41895    Answers: 1   Comments: 1

(√3)sin3x−cos3x+2sin((9x)/4)=4

$$\sqrt{\mathrm{3}}{sin}\mathrm{3}{x}−{cos}\mathrm{3}{x}+\mathrm{2}{sin}\frac{\mathrm{9}{x}}{\mathrm{4}}=\mathrm{4} \\ $$

Question Number 41888    Answers: 0   Comments: 5

The length of mercury column in a mercury-in-glass thermometer is 4cm at triple point.What is the length of the column when the scale indicates temperature of 560K.

$${The}\:{length}\:{of}\:{mercury}\:{column}\:{in} \\ $$$${a}\:{mercury}-{in}-{glass}\:{thermometer} \\ $$$${is}\:\mathrm{4}{cm}\:{at}\:{triple}\:{point}.{What}\:{is}\:{the} \\ $$$${length}\:{of}\:{the}\:{column}\:{when}\:{the} \\ $$$${scale}\:{indicates}\:{temperature}\:{of} \\ $$$$\mathrm{560}{K}. \\ $$

Question Number 41887    Answers: 1   Comments: 0

x+(√y)+xy=82 (√x)+y+(√(xy))=16 Find x and y by khaled.k

$$\mathrm{x}+\sqrt{\mathrm{y}}+\mathrm{xy}=\mathrm{82} \\ $$$$\sqrt{\mathrm{x}}+\mathrm{y}+\sqrt{\mathrm{xy}}=\mathrm{16} \\ $$$$\mathrm{Find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{by}\:\mathrm{khaled}.\mathrm{k} \\ $$

Question Number 41879    Answers: 1   Comments: 0

If a fraction is added to its denominator , it reduces to (1/2) and when the same fraction added to numerator, it also reduces to (2/3) (a) what is the fraction (b) find the square root such that the result of the fraction is less than 1

$$\mathrm{If}\:\mathrm{a}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{its}\:\mathrm{denominator}\:,\:\:\mathrm{it}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{same}\:\mathrm{fraction}\:\mathrm{added}\:\mathrm{to}\:\mathrm{numerator},\:\mathrm{it}\:\mathrm{also}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{fraction} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{1} \\ $$$$ \\ $$

Question Number 41878    Answers: 1   Comments: 0

(√3)sin3x−cos3x+2sin((9x)/4)=2

$$\sqrt{\mathrm{3}}{sin}\mathrm{3}{x}−{cos}\mathrm{3}{x}+\mathrm{2}{sin}\frac{\mathrm{9}{x}}{\mathrm{4}}=\mathrm{2} \\ $$

Question Number 41877    Answers: 1   Comments: 0

The tens digit of a two digit number is 3 greater than the units digit. When the digits are reversed, the number is reduced by 27. what is the number ?

$$\mathrm{The}\:\mathrm{tens}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{3}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{reversed},\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reduced}\:\mathrm{by}\:\mathrm{27}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:? \\ $$

Question Number 41870    Answers: 0   Comments: 0

Question Number 41869    Answers: 0   Comments: 0

Question Number 41868    Answers: 0   Comments: 0

Question Number 41867    Answers: 0   Comments: 0

Question Number 41866    Answers: 1   Comments: 0

Question Number 41860    Answers: 0   Comments: 2

(1,2,3,........100)are given number find the value of Σ(1×2)

$$\left(\mathrm{1},\mathrm{2},\mathrm{3},........\mathrm{100}\right){are}\:{given}\:{number} \\ $$$${find}\:{the}\:{value}\:{of}\:\Sigma\left(\mathrm{1}×\mathrm{2}\right) \\ $$

Question Number 41858    Answers: 0   Comments: 3

i have fever...so brain activity got reduced...

$${i}\:{have}\:{fever}...{so}\:{brain}\:{activity}\:{got}\:{reduced}... \\ $$

Question Number 41856    Answers: 1   Comments: 0

Question Number 41855    Answers: 0   Comments: 1

lim_(x→+∞ ) ((n!)/(ln (1+n!))) find the limit

$$\underset{{x}\rightarrow+\infty\:\:} {\mathrm{lim}}\frac{\mathrm{n}!}{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{n}!\right)} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit} \\ $$

Question Number 41854    Answers: 0   Comments: 0

1)calculate ∫_0 ^1 ln(1+x+x^2 +x^3 )dx 2)then find the value of ∫_0 ^1 ln( 1−x^5 ) dx 3) find the value of Σ_(n=1) ^∞ (1/(n(5n+1))) .

$$\left.\mathrm{1}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \right){dx} \\ $$$$\left.\mathrm{2}\right){then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\:\mathrm{1}−{x}^{\mathrm{5}} \right)\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}\left(\mathrm{5}{n}+\mathrm{1}\right)}\:. \\ $$$$ \\ $$$$ \\ $$

Question Number 41851    Answers: 0   Comments: 2

Question Number 41847    Answers: 1   Comments: 0

let f(x) = ∫_0 ^(π/4) (dt/(x +tan(t))) 1) find anoher expression off (x) 2) calculate ∫_0 ^(π/4) (dt/(2+tan(t))) and A(θ) = ∫_0 ^(π/4) (dt/(sinθ+tant)) 3) calculate ∫_0 ^(π/4) (dt/((1+tant)^2 ))

$${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\frac{{dt}}{{x}\:+{tan}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{anoher}\:{expression}\:{off}\:\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dt}}{\mathrm{2}+{tan}\left({t}\right)}\:\:\:{and}\:\:{A}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{{sin}\theta+{tant}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{tant}\right)^{\mathrm{2}} } \\ $$

Question Number 41846    Answers: 1   Comments: 0

find ∫ (dx/((√(1+x^2 )) +(√(1−x^2 ))))

$${find}\:\:\int\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:\:+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$

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