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Question Number 26454    Answers: 0   Comments: 0

Question Number 26452    Answers: 1   Comments: 0

∫(√(tanx))

$$\int\sqrt{{tanx}} \\ $$

Question Number 26450    Answers: 2   Comments: 5

A man of mass M is standing on a platform of mass m_1 holding a string passing over a system of ideal pulleys. Another mass m_2 is hanging as shown (m_2 = 20 kg, m_1 = 10 kg, g = 10 m/s^2 ) Force exerted by man on string to accelerate upwards

$$\mathrm{A}\:\mathrm{man}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{is}\:\mathrm{standing}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{platform}\:\mathrm{of}\:\mathrm{mass}\:{m}_{\mathrm{1}} \:\mathrm{holding}\:\mathrm{a}\:\mathrm{string} \\ $$$$\mathrm{passing}\:\mathrm{over}\:\mathrm{a}\:\mathrm{system}\:\mathrm{of}\:\mathrm{ideal}\:\mathrm{pulleys}. \\ $$$$\mathrm{Another}\:\mathrm{mass}\:{m}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{hanging}\:\mathrm{as}\:\mathrm{shown} \\ $$$$\left({m}_{\mathrm{2}} \:=\:\mathrm{20}\:\mathrm{kg},\:{m}_{\mathrm{1}} \:=\:\mathrm{10}\:\mathrm{kg},\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right) \\ $$$$\mathrm{Force}\:\mathrm{exerted}\:\mathrm{by}\:\mathrm{man}\:\mathrm{on}\:\mathrm{string}\:\mathrm{to} \\ $$$$\mathrm{accelerate}\:\mathrm{upwards} \\ $$

Question Number 26449    Answers: 1   Comments: 0

Transform the equation 5x^2 + 4xy + 2y^2 − 2x + 4y + 4 = 0 into one without xy, x and y terms.

$${Transform}\:{the}\:{equation}\:\mathrm{5}{x}^{\mathrm{2}} \:+\:\mathrm{4}{xy} \\ $$$$+\:\mathrm{2}{y}^{\mathrm{2}} \:−\:\mathrm{2}{x}\:+\:\mathrm{4}{y}\:+\:\mathrm{4}\:=\:\mathrm{0}\:{into}\:{one} \\ $$$${without}\:{xy},\:{x}\:{and}\:{y}\:{terms}. \\ $$

Question Number 26447    Answers: 0   Comments: 1

Question Number 26446    Answers: 1   Comments: 0

Question Number 26442    Answers: 0   Comments: 1

find the lateral surface area of cuboid = L=13m 12m and 10m

$${find}\:{the}\:{lateral}\:{surface}\:{area}\:{of}\:{cuboid}\:= \\ $$$${L}=\mathrm{13}{m}\:\mathrm{12}{m}\:{and}\:\mathrm{10}{m} \\ $$

Question Number 26438    Answers: 1   Comments: 0

Question Number 26425    Answers: 0   Comments: 0

A body is projected vertically upward with an initial velocity of u. Another Another body is projected with the same initial velocity, t seconds after the first. If T is the time when the two bodies meet, and g the acceleration due to gravity, Show that T = ((2u + gt)/(2g))

$$\mathrm{A}\:\mathrm{body}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{vertically}\:\mathrm{upward}\:\mathrm{with}\:\mathrm{an}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{u}.\:\mathrm{Another} \\ $$$$\mathrm{Another}\:\mathrm{body}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\mathrm{initial}\:\mathrm{velocity},\:\mathrm{t}\:\mathrm{seconds}\:\mathrm{after} \\ $$$$\mathrm{the}\:\mathrm{first}.\:\mathrm{If}\:\:\mathrm{T}\:\mathrm{is}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{the}\:\mathrm{two}\:\mathrm{bodies}\:\mathrm{meet},\:\mathrm{and}\:\mathrm{g}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{due}\:\mathrm{to}\:\mathrm{gravity},\:\mathrm{Show}\:\mathrm{that}\:\:\:\boldsymbol{\mathrm{T}}\:=\:\frac{\mathrm{2u}\:+\:\mathrm{gt}}{\mathrm{2g}} \\ $$

Question Number 26424    Answers: 0   Comments: 0

The front of a train 80m long passes a signal at a speed of 72km/hr. If the rear of the train passes the signal 5s later, Find (a) The magnitude of the acceleration of the train. (b) The speed at which the rear of the train passes the signal.

$$\mathrm{The}\:\mathrm{front}\:\mathrm{of}\:\mathrm{a}\:\mathrm{train}\:\mathrm{80m}\:\mathrm{long}\:\mathrm{passes}\:\mathrm{a}\:\mathrm{signal}\:\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{72km}/\mathrm{hr}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{rear}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}\:\mathrm{passes}\:\mathrm{the}\:\mathrm{signal}\:\mathrm{5s}\:\mathrm{later},\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{speed}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{rear}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}\:\mathrm{passes}\:\mathrm{the}\:\mathrm{signal}. \\ $$

Question Number 26405    Answers: 1   Comments: 0

Question Number 26403    Answers: 0   Comments: 5

developp the function f(x)=/x/ 2π periodic in fourier serie .(f even)

$${developp}\:{the}\:{function}\:{f}\left({x}\right)=/{x}/\:\mathrm{2}\pi \\ $$$${periodic}\:{in}\:{fourier}\:{serie}\:.\left({f}\:{even}\right) \\ $$

Question Number 26402    Answers: 1   Comments: 2

find the nature of the serie Σ_(n=0) ^∝ ((n!)/(1+2^n )) .

$${find}\:{the}\:{nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \frac{{n}!}{\mathrm{1}+\mathrm{2}^{{n}} }\:\:. \\ $$

Question Number 26401    Answers: 1   Comments: 1

find the sum of Σ_(n=1) ^∝ (1/(n 2^n )) .

$${find}\:{the}\:{sum}\:{of}\:\: \\ $$$$\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}\:\:\mathrm{2}^{{n}} }\:\:. \\ $$

Question Number 26400    Answers: 1   Comments: 0

find the sequence (u_n ) wich verify u_n −2 u_(n−1) +1= 2^n

$${find}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{wich}\:{verify}\:{u}_{{n}} \:−\mathrm{2}\:{u}_{{n}−\mathrm{1}} \:+\mathrm{1}=\:\mathrm{2}^{{n}} \\ $$

Question Number 26399    Answers: 2   Comments: 0

calculate ∫∫ _D cos(x^2 +y^2 )dxdy with D=C(o.(√(π/2))).

$${calculate}\:\:\int\int\:_{{D}} {cos}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}\:\:\:{with}\:\:{D}={C}\left({o}.\sqrt{\frac{\pi}{\mathrm{2}}}\right). \\ $$

Question Number 26398    Answers: 2   Comments: 2

find the value of ∫∫_D x^2 y dxdy on the domain D={(x.y)∈R^2 / x^2 +y^2 −2x≤0 and y≥0}

$${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:{x}^{\mathrm{2}} {y}\:{dxdy}\:\:\:{on}\:{the}\:{domain} \\ $$$${D}=\left\{\left({x}.{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:−\mathrm{2}{x}\leqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\} \\ $$

Question Number 26397    Answers: 2   Comments: 1

find ∫ (dx/(x(√(1+x^2 )))) and calculate ∫_1 ^3 (dx/(x(√(1+x^2 ))))

$${find}\:\int\:\:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{and}\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$

Question Number 26396    Answers: 1   Comments: 1

find the value of ∫_0 ^(1 ) (dx/(x^2 +2x +5)) .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}\:+\mathrm{5}}\:. \\ $$

Question Number 26395    Answers: 1   Comments: 0

find ∫ (dx/(x(√(x^2 +x−1))))

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

Question Number 26382    Answers: 0   Comments: 1

Question Number 26381    Answers: 0   Comments: 9

Question Number 26380    Answers: 0   Comments: 0

Question Number 26389    Answers: 0   Comments: 1

Question Number 26368    Answers: 0   Comments: 1

y=a^(arctg(√x)) derivative ?

$${y}={a}^{\mathrm{arc}{tg}\sqrt{{x}}} \\ $$$${derivative}\:? \\ $$

Question Number 26365    Answers: 0   Comments: 1

y=log_a (x^2 −16)

$${y}=\mathrm{log}_{{a}} \left({x}^{\mathrm{2}} −\mathrm{16}\right) \\ $$

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