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Question Number 47302 Answers: 1 Comments: 0

A train which travels at a uniform speed due to mechanical fault after traveling for an hour goes at 3/5 th of the original speed and reaches the destination 2 hours late.If the fault occured after traveling another 50 miles the train would have reached 40 minutes earlier. What is the distance between the two stations ?

$${A}\:{train}\:{which}\:{travels}\:{at}\:{a}\:{uniform}\:{speed}\:{due}\:{to}\:{mechanical}\: \\ $$$${fault}\:{after}\:{traveling}\:{for}\:{an}\:{hour}\:{goes}\:{at}\:\mathrm{3}/\mathrm{5}\:{th}\:{of}\:{the}\:{original}\: \\ $$$${speed}\:{and}\:{reaches}\:{the}\:{destination}\:\mathrm{2}\:{hours}\:{late}.{If}\:{the}\:{fault} \\ $$$${occured}\:{after}\:{traveling}\:{another}\:\mathrm{50}\:{miles}\:{the}\:{train}\:{would}\:{have} \\ $$$${reached}\:\mathrm{40}\:{minutes}\:{earlier}.\:{What}\:{is}\:{the}\:{distance}\:{between}\:{the}\: \\ $$$${two}\:{stations}\:? \\ $$

Question Number 47301 Answers: 1 Comments: 0

If the equation x^2 +px+q =0 has roots a and b where p, q are non−zero constants. Then

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} +{px}+{q}\:=\mathrm{0}\:\mathrm{has}\:\mathrm{roots} \\ $$$${a}\:\mathrm{and}\:{b}\:\mathrm{where}\:{p},\:{q}\:\mathrm{are}\:\mathrm{non}−\mathrm{zero}\: \\ $$$$\mathrm{constants}.\:\mathrm{Then} \\ $$

Question Number 47295 Answers: 0 Comments: 6

calculate f(α) =∫_(−∞) ^(+∞) (dx/(x^2 +2x cosα +1)) 2) calculate g(α)=∫_(−∞) ^(+∞) ((sinα)/((x^2 +2x cosα+1)^2 ))dx 3) find f^((n)) (α) with n integr natural . 4) calculate ∫_(−∞) ^(+∞) (dx/(x^2 +x +1)) and ∫_(−∞) ^(+∞) (dx/((x^2 +x+1)^2 ))

$${calculate}\:{f}\left(\alpha\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+\mathrm{2}{x}\:{cos}\alpha\:+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left(\alpha\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{sin}\alpha}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}\:{cos}\alpha+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{f}^{\left({n}\right)} \left(\alpha\right)\:{with}\:{n}\:{integr}\:{natural}\:. \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}}\:{and}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 47291 Answers: 1 Comments: 0

solve for x∈C: ∣x−(3/4)∣×∣x+(5/4)∣=3

$$\mathrm{solve}\:\mathrm{for}\:{x}\in\mathbb{C}: \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3} \\ $$

Question Number 47283 Answers: 0 Comments: 1

A stone tied to a string is made to resolve in a horizontal circle of radius 4m with another speed of 2rads^(−1) .With what tangential velocity will the stone be off the circle if the string cuts?

$${A}\:{stone}\:{tied}\:{to}\:{a}\:{string}\:{is}\:{made}\:{to} \\ $$$${resolve}\:{in}\:{a}\:{horizontal}\:{circle}\:{of} \\ $$$${radius}\:\mathrm{4}{m}\:{with}\:{another}\:{speed}\:{of} \\ $$$$\mathrm{2}{rads}^{−\mathrm{1}} .{With}\:{what}\:{tangential} \\ $$$${velocity}\:{will}\:{the}\:{stone}\:{be}\:{off}\:{the} \\ $$$${circle}\:{if}\:{the}\:{string}\:{cuts}? \\ $$

Question Number 47282 Answers: 2 Comments: 0

Question Number 47311 Answers: 0 Comments: 1

Question Number 47280 Answers: 0 Comments: 0

A geometric progression bas three terms a ,b ,c whose sum is 42.If 6 is added to each of the firs two term and 3 to the third ,a new G.P. result whose first term is the same as n. Find a,band?c.

$${A}\:{geometric}\:{progression}\:{bas}\:{three} \\ $$$${terms}\:{a}\:,{b}\:,{c}\:{whose}\:{sum}\:{is}\:\mathrm{42}.{If}\:\mathrm{6} \\ $$$${is}\:{added}\:{to}\:{each}\:{of}\:{the}\:{firs}\:{two}\:{term} \\ $$$${and}\:\mathrm{3}\:{to}\:{the}\:{third}\:,{a}\:{new}\:{G}.{P}.\:{result} \\ $$$${whose}\:{first}\:{term}\:{is}\:{the}\:{same}\:{as}\:{n}. \\ $$$${Find}\:{a},{band}?{c}. \\ $$

Question Number 47272 Answers: 2 Comments: 1

Question Number 47259 Answers: 0 Comments: 0

∫_0 ^1 ((tan^(−1) ((x/(x+1))))/(tan^(−1) (((1−2x^2 +2x)/2))))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}+\mathrm{1}}\right)}{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \left(\frac{\mathrm{1}−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 47289 Answers: 0 Comments: 4

Pls can Q47194 be solved by using the cosine rule?If possible please show me with the required diagram. Thanks in advance.

$${Pls}\:{can}\:{Q}\mathrm{47194}\:{be}\:{solved}\:{by}\:{using} \\ $$$${the}\:{cosine}\:{rule}?{If}\:{possible}\:{please} \\ $$$${show}\:{me}\:{with}\:{the}\:{required}\:{diagram}. \\ $$$${Thanks}\:{in}\:{advance}. \\ $$

Question Number 47250 Answers: 1 Comments: 0

Question Number 47248 Answers: 0 Comments: 1

calculate ∫_(−1) ^1 ((ln(x+2))/((x+4)^2 −1))dx

$${calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}+\mathrm{2}\right)}{\left({x}+\mathrm{4}\right)^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$

Question Number 47243 Answers: 1 Comments: 0

Question Number 47239 Answers: 1 Comments: 1

((1.8×10^6 )/(tan(89.9999°))) ∼ π (upto 9 decimal places) can i have some explanations how it is worked out ? Thank you!

$$\frac{\mathrm{1}.\mathrm{8}×\mathrm{10}^{\mathrm{6}} }{{tan}\left(\mathrm{89}.\mathrm{9999}°\right)}\:\sim\:\pi\:\left({upto}\:\mathrm{9}\:{decimal}\:{places}\right) \\ $$$${can}\:{i}\:{have}\:{some}\:{explanations}\:{how}\:{it}\:{is}\:{worked}\:{out}\:? \\ $$$${Thank}\:{you}! \\ $$

Question Number 47266 Answers: 1 Comments: 1

Question Number 47235 Answers: 0 Comments: 0

the force acting on a particle P of mass 2kg is (2ti +4j)N. P is initially at rest at point with position vector (i+2j). Find the velocity of P when t=2 and the position vector when t=2.

$${the}\:{force}\:{acting}\:{on}\:{a}\:{particle}\:{P}\:{of}\:{mass}\:\:\mathrm{2}{kg}\:{is}\:\left(\mathrm{2}{ti}\:+\mathrm{4}{j}\right){N}. \\ $$$${P}\:{is}\:{initially}\:{at}\:{rest}\:{at}\:{point}\:{with}\:{position}\:{vector}\:\left({i}+\mathrm{2}{j}\right). \\ $$$${Find}\:{the}\:{velocity}\:{of}\:{P}\:{when}\:{t}=\mathrm{2}\:{and}\:{the}\:{position}\:{vector}\: \\ $$$${when}\:{t}=\mathrm{2}. \\ $$

Question Number 47234 Answers: 0 Comments: 0

the force acting on a particle P of mass 2kg is (2ti +4j)N. P is initially at rest at point with position vector (i+2j). Find the velocity of P when t=2 and the position vector when t=2.

Question Number 47233 Answers: 0 Comments: 0

the force acting on a particle P of mass 2kg is (2ti +4j)N. P is initially at rest at point with position vector (i+2j). Find the velocity of P when t=2 and the position vector when t=2.

Question Number 47224 Answers: 3 Comments: 3

Could you please help me for this question : Solve for x : ∣ 3x + 2 ∣ + ∣ 7x − 5 ∣ = 20 Thank you

$$\mathrm{Could}\:\mathrm{you}\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{for}\:\mathrm{this}\:\mathrm{question}\:: \\ $$$$ \\ $$$$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}}\:: \\ $$$$ \\ $$$$\:\mid\:\mathrm{3}{x}\:+\:\mathrm{2}\:\mid\:\:+\:\:\mid\:\mathrm{7}{x}\:−\:\mathrm{5}\:\mid\:\:=\:\:\mathrm{20} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$$$ \\ $$

Question Number 47217 Answers: 0 Comments: 1

Question Number 47216 Answers: 0 Comments: 1

Question Number 47199 Answers: 0 Comments: 0

S_n = [4 − (1/(n^2 )) , 6 + (1/n) ], find ∩_(n = 1) ^∞ S_n and ∪_(n = 1) ^∞ S_n

$$\mathrm{S}_{\mathrm{n}} \:\:=\:\:\left[\mathrm{4}\:−\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \:}\:,\:\:\:\:\:\:\:\:\mathrm{6}\:+\:\frac{\mathrm{1}}{\mathrm{n}}\:\right],\:\:\:\mathrm{find}\:\:\:\:\:\:\:\:\:\:\:\cap_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\mathrm{S}_{\mathrm{n}} \:\:\:\:\:\:\mathrm{and}\:\:\:\:\cup_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\:\mathrm{S}_{\mathrm{n}} \\ $$

Question Number 47195 Answers: 1 Comments: 0

Find the volume of the pyramid which is folded from a trangular paper with sides a, b and c.

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{pyramid}\:{which} \\ $$$${is}\:{folded}\:{from}\:{a}\:{trangular}\:{paper}\:{with} \\ $$$${sides}\:\boldsymbol{{a}},\:\boldsymbol{{b}}\:{and}\:\boldsymbol{{c}}. \\ $$

Question Number 47194 Answers: 1 Comments: 4

The velocity of a ship Q relqtive to a ship P is 10km/h in a direction N45^. E.If the velocity of P is 20km/h in a direction N60^. W.Find the actual velocity of Q in magnitude and direction.

$${The}\:{velocity}\:{of}\:{a}\:{ship}\:{Q}\:{relqtive}\:{to} \\ $$$${a}\:{ship}\:{P}\:\:{is}\:\mathrm{10}{km}/{h}\:{in}\:{a}\:{direction} \\ $$$${N}\mathrm{45}^{.} {E}.{If}\:{the}\:{velocity}\:{of}\:{P}\:\:{is}\:\mathrm{20}{km}/{h} \\ $$$${in}\:{a}\:{direction}\:{N}\mathrm{60}^{.} {W}.{Find}\:{the} \\ $$$${actual}\:{velocity}\:{of}\:{Q}\:{in}\:{magnitude} \\ $$$${and}\:{direction}. \\ $$

Question Number 47190 Answers: 1 Comments: 0

find the angel between the surface x^2 +y^2 +z^2 and 3x^2 −y^2 +2z=1 at (1,−2,1)

$${find}\:{the}\:{angel}\:{between}\:{the}\:{surface}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:\:{and}\:\mathrm{3}{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\mathrm{2}{z}=\mathrm{1}\:{at}\:\left(\mathrm{1},−\mathrm{2},\mathrm{1}\right) \\ $$

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