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Question Number 91439    Answers: 1   Comments: 2

solve 2x^(99) +3x^(98) +2x^(97) +3x^(96) +.....2x+3=0 in R

$${solve}\:\mathrm{2}{x}^{\mathrm{99}} +\mathrm{3}{x}^{\mathrm{98}} +\mathrm{2}{x}^{\mathrm{97}} +\mathrm{3}{x}^{\mathrm{96}} +.....\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\:{in}\:\mathbb{R} \\ $$

Question Number 91671    Answers: 0   Comments: 2

show that (x)^(1/(ln(x))) =e

$${show}\:{that} \\ $$$$\sqrt[{{ln}\left({x}\right)}]{{x}}={e} \\ $$

Question Number 91419    Answers: 0   Comments: 1

lim_(x→0) (1/(sin^4 x))(sin ((x/(1+x)))−((sin x)/(1+sin x)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{4}} {x}}\left(\mathrm{sin}\:\left(\frac{{x}}{\mathrm{1}+{x}}\right)−\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\right) \\ $$

Question Number 91417    Answers: 0   Comments: 1

y′+2y=e^(−x)

$${y}'+\mathrm{2}{y}={e}^{−{x}} \\ $$

Question Number 91422    Answers: 0   Comments: 0

(dy/dx) = ((x^2 +y^2 )/(x^2 −y^2 ))

$$\frac{{dy}}{{dx}}\:=\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$

Question Number 91399    Answers: 2   Comments: 13

Question Number 91395    Answers: 0   Comments: 0

∫_0 ^π ((∣x∣sin^2 x)/(1+2∣cos x∣sin x))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mid{x}\mid\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{2}\mid\mathrm{cos}\:{x}\mid\mathrm{sin}\:{x}}{dx} \\ $$

Question Number 91390    Answers: 1   Comments: 3

ABCDEF is a 6 digit number, ABC and DEF are 3 digit numbers. find ABCDEF satisfying: 1) ABCDEF=1×ABC×DEF 2) ABCDEF=2×ABC×DEF 3) ABCDEF=3×ABC×DEF 4) ABCDEF=4×ABC×DEF 5) ABCDEF=5×ABC×DEF 6) ABCDEF=6×ABC×DEF 7) ABCDEF=7×ABC×DEF 8) ABCDEF=8×ABC×DEF 9) ABCDEF=9×ABC×DEF

$${ABCDEF}\:{is}\:{a}\:\mathrm{6}\:{digit}\:{number}, \\ $$$${ABC}\:{and}\:{DEF}\:{are}\:\mathrm{3}\:{digit}\:{numbers}. \\ $$$${find}\:{ABCDEF}\:\:{satisfying}: \\ $$$$\left.\mathrm{1}\right)\:\:\:{ABCDEF}=\mathrm{1}×{ABC}×{DEF} \\ $$$$\left.\mathrm{2}\right)\:\:\:{ABCDEF}=\mathrm{2}×{ABC}×{DEF} \\ $$$$\left.\mathrm{3}\right)\:\:\:{ABCDEF}=\mathrm{3}×{ABC}×{DEF} \\ $$$$\left.\mathrm{4}\right)\:\:\:{ABCDEF}=\mathrm{4}×{ABC}×{DEF} \\ $$$$\left.\mathrm{5}\right)\:\:\:{ABCDEF}=\mathrm{5}×{ABC}×{DEF} \\ $$$$\left.\mathrm{6}\right)\:\:\:{ABCDEF}=\mathrm{6}×{ABC}×{DEF} \\ $$$$\left.\mathrm{7}\right)\:\:\:{ABCDEF}=\mathrm{7}×{ABC}×{DEF} \\ $$$$\left.\mathrm{8}\right)\:\:\:{ABCDEF}=\mathrm{8}×{ABC}×{DEF} \\ $$$$\left.\mathrm{9}\right)\:\:\:{ABCDEF}=\mathrm{9}×{ABC}×{DEF} \\ $$

Question Number 91421    Answers: 2   Comments: 2

∫_1 ^3 (1/(x(√(3x^2 +2x−1))))dx

$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{1}}{{x}\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}{dx} \\ $$

Question Number 91384    Answers: 0   Comments: 4

particular integral y′′+3y′+2y = 4cos^2 x

$${particular}\:{integral}\: \\ $$$${y}''+\mathrm{3}{y}'+\mathrm{2}{y}\:=\:\mathrm{4cos}\:^{\mathrm{2}} {x} \\ $$

Question Number 91378    Answers: 1   Comments: 6

Question Number 91377    Answers: 0   Comments: 1

Question Number 91375    Answers: 0   Comments: 3

x4+2x3−5x2+6x+2/x2−2x+2^

$${x}\mathrm{4}+\mathrm{2}{x}\mathrm{3}−\mathrm{5}{x}\mathrm{2}+\mathrm{6}{x}+\mathrm{2}/{x}\mathrm{2}−\mathrm{2}{x}+\mathrm{2}^{} \\ $$

Question Number 91374    Answers: 0   Comments: 0

A car of mass 700 kg has maximum power P ,at all times, there is a non gravitational R to the motion of the car. the car moves along an inclined of angle θ where 10 sinθ = 1. The maximum speed of the car up the plane is is half the value of the speed down the plane. (a) find the value of R. on level road the car has speed of 20 ms^(−1) . (b) find the value of P.

$$\mathrm{A}\:\mathrm{car}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{700}\:\mathrm{kg}\:\mathrm{has}\:\mathrm{maximum}\:\mathrm{power}\:{P}\:\:,\mathrm{at}\:\mathrm{all}\:\mathrm{times}, \\ $$$$\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{non}\:\mathrm{gravitational}\:{R}\:\mathrm{to}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}. \\ $$$$\mathrm{the}\:\mathrm{car}\:\mathrm{moves}\:\mathrm{along}\:\mathrm{an}\:\mathrm{inclined}\:\mathrm{of}\:\mathrm{angle}\:\theta\:\mathrm{where}\:\mathrm{10}\:\mathrm{sin}\theta\:=\:\mathrm{1}.\:\mathrm{The} \\ $$$$\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{up}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{speed}\:\mathrm{down}\:\mathrm{the}\:\mathrm{plane}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{R}. \\ $$$$\:\mathrm{on}\:\mathrm{level}\:\mathrm{road}\:\mathrm{the}\:\mathrm{car}\:\mathrm{has}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{20}\:\mathrm{ms}^{−\mathrm{1}} . \\ $$$$\left(\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{P}. \\ $$

Question Number 91371    Answers: 0   Comments: 1

what is the particular integral (D^2 +D+1)y=e^x sin x

$${what}\:{is}\:{the}\:{particular}\: \\ $$$${integral}\:\left({D}^{\mathrm{2}} +{D}+\mathrm{1}\right){y}={e}^{{x}} \mathrm{sin}\:{x} \\ $$

Question Number 91362    Answers: 1   Comments: 3

Question Number 91354    Answers: 0   Comments: 3

ABCDEF = 3 × ABC × DEF ABCDEF is 6 digits number. ABC, DEF are 3 digits number . What is ABCDEF ?

$${ABCDEF}\:\:=\:\:\mathrm{3}\:×\:{ABC}\:×\:{DEF} \\ $$$${ABCDEF}\:\:{is}\:\:\mathrm{6}\:\:{digits}\:\:{number}. \\ $$$${ABC},\:{DEF}\:\:{are}\:\:\mathrm{3}\:\:{digits}\:\:{number}\:. \\ $$$${What}\:\:{is}\:\:{ABCDEF}\:\:? \\ $$

Question Number 91353    Answers: 1   Comments: 0

(dy/dx) = e^(3x−y^2 )

$$\frac{{dy}}{{dx}}\:=\:{e}^{\mathrm{3}{x}−{y}^{\mathrm{2}} } \: \\ $$

Question Number 91336    Answers: 0   Comments: 9

How many eleven digits palindrome numbers can be formed by 0, 2, 3, 4, and 8 ? Zero in the middle of order always .

$${How}\:\:{many}\:\:{eleven}\:\:{digits}\:\:{palindrome}\:\:{numbers}\:\:{can}\:\:{be} \\ $$$${formed}\:\:{by}\:\:\mathrm{0},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\:{and}\:\:\mathrm{8}\:? \\ $$$${Zero}\:\:{in}\:\:{the}\:{middle}\:\:{of}\:\:{order}\:\:{always}\:. \\ $$

Question Number 91329    Answers: 0   Comments: 3

Solve the differential equation: (d^2 y/dx^2 ) − x^2 (dy/dx)+xy = x

$$\:\mathrm{S}\boldsymbol{\mathrm{olve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}+\boldsymbol{\mathrm{xy}}\:=\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 91328    Answers: 0   Comments: 9

Find the sum (9/(1+(√2)))+((10−⌊(√2)⌋)/((√2)+(√3)))+((10−⌊(√3)⌋)/((√3)+(√4)))+...+((10−⌊(√(99))⌋)/((√(99))+(√(100)))) ⌊x⌋=the greatest integer function

$${Find}\:{the}\:{sum} \\ $$$$\frac{\mathrm{9}}{\mathrm{1}+\sqrt{\mathrm{2}}}+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{2}}\rfloor}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{3}}\rfloor}{\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+...+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{99}}\rfloor}{\sqrt{\mathrm{99}}+\sqrt{\mathrm{100}}} \\ $$$$\lfloor{x}\rfloor={the}\:{greatest}\:{integer}\:{function} \\ $$

Question Number 91326    Answers: 2   Comments: 1

Question Number 91321    Answers: 0   Comments: 3

1)find eigen values and corresponding eigen vector of the matrix A= [((cos(θ)),(−sin(θ))),((sin(θ)),( cos(θ))) ] 2)solve 6y^2 dx−x(y+2x^2 )dy=0

$$\left.\mathrm{1}\right){find}\:{eigen}\:{values}\:{and}\:{corresponding} \\ $$$${eigen}\:{vector}\:{of}\:{the}\:{matrix} \\ $$$$ \\ $$$${A}=\begin{bmatrix}{{cos}\left(\theta\right)}&{−{sin}\left(\theta\right)}\\{{sin}\left(\theta\right)}&{\:\:\:\:\:{cos}\left(\theta\right)}\end{bmatrix} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){solve} \\ $$$$ \\ $$$$\mathrm{6}{y}^{\mathrm{2}} {dx}−{x}\left({y}+\mathrm{2}{x}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$

Question Number 91310    Answers: 0   Comments: 0

show that ∫_0 ^(π/2) cot (x) ln(sec(x)) dx=(π^2 /(24))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cot}\:\left({x}\right)\:{ln}\left({sec}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{24}} \\ $$

Question Number 91308    Answers: 0   Comments: 2

∫ (x^2 /(x^4 −x^2 −2)) dx ?

$$\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}\:{dx}\:? \\ $$

Question Number 91303    Answers: 0   Comments: 3

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