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Question Number 25677 Answers: 0 Comments: 0

let 0<x<1 find the value of F(x) = ∫ ln (1+x cost)dt fromt=0 to t=pi

$${let}\:\mathrm{0}<{x}<\mathrm{1}\:\:{find}\:{the}\:{value}\:{of}\:{F}\left({x}\right)\:=\:\int\:\mathrm{ln}\:\left(\mathrm{1}+{x}\:{cost}\right){dt}\:{fromt}=\mathrm{0}\:{to}\:{t}={pi} \\ $$

Question Number 25676 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ sin(x^ n )/x^ 2 + 1 dx

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\boldsymbol{{sin}}\left(\hat {\boldsymbol{{x}}}{n}\:\right)/\hat {{x}}\mathrm{2}\:+\:\mathrm{1}\:{dx} \\ $$

Question Number 25675 Answers: 1 Comments: 1

Question Number 25667 Answers: 0 Comments: 2

Deepak srarts a work and work for 12 days and find he has ompleted 10% less work which he had to finish in order to complete the work in 24 days,^ so he ask Rahman to join him to finish the work on time . If Rahman work half day only for the remaining days. Find the efficiency of Rahman is what percent less then the efficiency of Deepak ?

$$\mathrm{Deepak}\:\mathrm{srarts}\:\mathrm{a}\:\mathrm{work}\:\mathrm{and}\:\mathrm{work}\:\mathrm{for}\:\mathrm{12} \\ $$$$\mathrm{days}\:\mathrm{and}\:\mathrm{find}\:\mathrm{he}\:\mathrm{has}\:\mathrm{ompleted}\:\mathrm{10\%}\: \\ $$$$\mathrm{less}\:\mathrm{work}\:\mathrm{which}\:\mathrm{he}\:\mathrm{had}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{in}\: \\ $$$$\mathrm{order}\:\mathrm{to}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{24}\:\mathrm{days}\bar {,} \\ $$$$\mathrm{so}\:\mathrm{he}\:\mathrm{ask}\:\mathrm{Rahman}\:\mathrm{to}\:\mathrm{join}\:\mathrm{him}\:\mathrm{to}\:\mathrm{finish} \\ $$$$\mathrm{the}\:\mathrm{work}\:\mathrm{on}\:\mathrm{time}\:.\:\mathrm{If}\:\mathrm{Rahman}\:\mathrm{work}\: \\ $$$$\mathrm{half}\:\mathrm{day}\:\mathrm{only}\:\mathrm{for}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{days}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of}\:\mathrm{Rahman}\:\mathrm{is}\:\mathrm{what} \\ $$$$\mathrm{percent}\:\mathrm{less}\:\mathrm{then}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of} \\ $$$$\mathrm{Deepak}\:? \\ $$

Question Number 27181 Answers: 0 Comments: 1

find the value of ∫_0 ^(∝ ) ((ln(1+t^2 ))/(1−t^2 )) dt

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\propto\:} \frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}−{t}^{\mathrm{2}} }\:{dt} \\ $$

Question Number 27180 Answers: 0 Comments: 1

find the value of ∫∫_D (x^2 /y^2 ) dxdy with D ={(x ,y)∈R^2 / 1≤x≤2 and (1/x)≤y≤ x }.

$${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:\:\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:{dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x}\:,{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:{and}\:\:\frac{\mathrm{1}}{{x}}\leqslant{y}\leqslant\:{x}\:\:\right\}. \\ $$

Question Number 25660 Answers: 0 Comments: 1

Question Number 25656 Answers: 0 Comments: 3

trace the curve y^2 (x+1)=x^2 (3−x) clearly stating all the properties used for tracing.

$${trace}\:{the}\:{curve}\: \\ $$$${y}^{\mathrm{2}} \left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \left(\mathrm{3}−{x}\right) \\ $$$${clearly}\:{stating}\:{all}\:{the}\:{properties}\:{used} \\ $$$${for}\:{tracing}. \\ $$

Question Number 25655 Answers: 0 Comments: 0

use lagranges mean value theorem to prove that x<sin^(−1) x<(x/(√(1−x^2 ))),0<x<1.

$${use}\:{lagranges}\:{mean}\:{value}\:{theorem}\:{to} \\ $$$${prove}\:{that}\: \\ $$$${x}<{sin}^{−\mathrm{1}} {x}<\frac{{x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }},\mathrm{0}<{x}<\mathrm{1}. \\ $$

Question Number 25718 Answers: 0 Comments: 8

Question Number 25723 Answers: 0 Comments: 0

Given a_1 , a_2 , ..., a_n are non−negative integers and satisfy (1/2^a_1 ) + (1/2^a_2 ) + ... + (1/2^a_n ) = (1/3^a_1 ) + (2/3^a_2 ) + ... + (n/3^a_n ) = 1 If n is positive integer, find all possible solution of n

$$\mathrm{Given}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:...,\:{a}_{{n}} \:\mathrm{are}\:\mathrm{non}−\mathrm{negative} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{satisfy} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} } }\:=\:\frac{\mathrm{1}}{\mathrm{3}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{2}}{\mathrm{3}^{{a}_{\mathrm{2}} } }\:+\:...\:+\:\frac{{n}}{\mathrm{3}^{{a}_{{n}} } }\:=\:\mathrm{1}\: \\ $$$$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solution} \\ $$$$\mathrm{of}\:{n}\: \\ $$

Question Number 25638 Answers: 0 Comments: 1

Question Number 25635 Answers: 0 Comments: 1

let f be the function defined on [−1,1] by f(x)={ { ((−1,if x is rational)),((1,if x is irrational.)) :} find U(P,f) and L(P,f).f is integrable or not ?

$${let}\:{f}\:{be}\:{the}\:{function}\:{defined}\:{on} \\ $$$$\left[−\mathrm{1},\mathrm{1}\right]\:{by} \\ $$$${f}\left({x}\right)=\left\{\begin{cases}{−\mathrm{1},{if}\:{x}\:{is}\:{rational}}\\{\mathrm{1},{if}\:{x}\:{is}\:{irrational}.}\end{cases}\right. \\ $$$${find}\:{U}\left({P},{f}\right)\:{and}\:{L}\left({P},{f}\right).{f}\:{is}\:{integrable} \\ $$$${or}\:{not}\:? \\ $$

Question Number 25634 Answers: 1 Comments: 0

find the equation of the tangent to the curve (√x)+(√y)=(√a) at any point (x,y)on it.

$${find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\: \\ $$$${the}\:{curve}\:\sqrt{{x}}+\sqrt{{y}}=\sqrt{{a}}\:{at}\:{any}\:{point} \\ $$$$\left({x},{y}\right){on}\:{it}. \\ $$

Question Number 25630 Answers: 1 Comments: 0

Question Number 25628 Answers: 0 Comments: 0

Question Number 25623 Answers: 1 Comments: 0

solve for A and B if 2A+B [((6 3)),((6 −2)) ] and 3A+2B [((1 0)),((0 5)) ]

$${solve}\:{for}\:{A}\:{and}\:{B}\:{if}\:\mathrm{2}{A}+{B}\:\begin{bmatrix}{\mathrm{6}\:\:\:\mathrm{3}}\\{\mathrm{6}\:\:−\mathrm{2}}\end{bmatrix} \\ $$$${and}\:\mathrm{3}{A}+\mathrm{2}{B}\:\begin{bmatrix}{\mathrm{1}\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\mathrm{5}}\end{bmatrix} \\ $$

Question Number 25619 Answers: 1 Comments: 0

Question Number 25618 Answers: 1 Comments: 0

∫_6 ^5 f(x)dx

$$\underset{\mathrm{6}} {\overset{\mathrm{5}} {\int}}{f}\left({x}\right){dx} \\ $$$$ \\ $$

Question Number 26950 Answers: 0 Comments: 3

∫_0 ^1 ((6x^2 − x − 1)/(6x^2 − 5x + 1)) dx

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{6}{x}^{\mathrm{2}} \:−\:{x}\:−\:\mathrm{1}}{\mathrm{6}{x}^{\mathrm{2}} \:−\:\mathrm{5}{x}\:+\:\mathrm{1}}\:{dx} \\ $$

Question Number 25609 Answers: 0 Comments: 4

Question Number 25605 Answers: 1 Comments: 4

Question Number 25602 Answers: 1 Comments: 1

Question Number 25600 Answers: 1 Comments: 0

A block pulled along a horizontal floo by a horizontal rope. The tension in the rope is 500N and the blocks moves at a constant speed of 2.75ms^(−1.) Find the work done by the tension in 40s and also find the power applied by the tension. GUYS PLS HELP

$$\mathrm{A}\:\mathrm{block}\:\mathrm{pulled}\:\mathrm{along}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{floo} \\ $$$$\mathrm{by}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{rope}. \\ $$$$\mathrm{The}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{is}\:\mathrm{500N}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{blocks}\:\mathrm{moves}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{2}.\mathrm{75ms}^{−\mathrm{1}.} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{work}\:\mathrm{done}\:\mathrm{by}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{40s} \\ $$$$\mathrm{and}\:\mathrm{also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{power}\:\mathrm{applied}\:\mathrm{by}\:\mathrm{the}\:\mathrm{tension}. \\ $$$$\mathrm{GUYS}\:\mathrm{PLS}\:\mathrm{HELP} \\ $$

Question Number 25593 Answers: 1 Comments: 0

if : log_6 ^(45) =x , log_(18) ^(24) =y then : log _(12)^(25) =?(in terms of x,y)

$$\boldsymbol{{if}}\:\::\:\:\:\boldsymbol{{log}}_{\mathrm{6}} ^{\mathrm{45}} =\boldsymbol{{x}}\:\:,\:\:\:\boldsymbol{{log}}_{\mathrm{18}} ^{\mathrm{24}} =\boldsymbol{{y}} \\ $$$$\boldsymbol{{then}}\::\:\:\:\boldsymbol{{log}}\:_{\mathrm{12}} ^{\mathrm{25}} \:=?\left(\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x},\mathrm{y}\right) \\ $$

Question Number 25611 Answers: 0 Comments: 0

if cosh(u+iv)=x+iy , show that (x^2 /(cosh^2 u))+(y^2 /(sinh^2 u))=1 and (x^2 /(cosh^2 v))−(y^2 /(sinh^2 v))=1 where sinhx and coshx hhyperbolcfunction

$${if}\:{cosh}\left({u}+{iv}\right)={x}+{iy}\:,\:{show}\:{that} \\ $$$$\frac{{x}^{\mathrm{2}} }{{cosh}^{\mathrm{2}} {u}}+\frac{{y}^{\mathrm{2}} }{{sinh}^{\mathrm{2}} {u}}=\mathrm{1}\:\:{and}\:\:\frac{{x}^{\mathrm{2}} }{{cosh}^{\mathrm{2}} {v}}−\frac{{y}^{\mathrm{2}} }{{sinh}^{\mathrm{2}} {v}}=\mathrm{1} \\ $$$$ \\ $$$${where}\:\:\:\:{sinhx}\:{and}\:{coshx}\:\:\:\:{hhyperbolcfunction} \\ $$

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