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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