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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

Question Number 91302    Answers: 2   Comments: 0

Question Number 91298    Answers: 1   Comments: 1

what is the particular integral of (D^2 +6D+5)y = e^(−5x )

$${what}\:{is}\:{the}\:{particular}\:{integral} \\ $$$${of}\:\left({D}^{\mathrm{2}} +\mathrm{6}{D}+\mathrm{5}\right){y}\:=\:{e}^{−\mathrm{5}{x}\:} \: \\ $$

Question Number 91297    Answers: 0   Comments: 2

Can someone please recommend a good advanced math textbook that covers precalculus?

$${Can}\:{someone}\:{please}\:{recommend} \\ $$$${a}\:{good}\:{advanced}\:{math}\:{textbook} \\ $$$${that}\:{covers}\:{precalculus}? \\ $$

Question Number 91291    Answers: 0   Comments: 3

x dy +2y dx = 2x^3 y^2 dx

$${x}\:{dy}\:+\mathrm{2}{y}\:{dx}\:=\:\mathrm{2}{x}^{\mathrm{3}} {y}^{\mathrm{2}} \:{dx} \\ $$

Question Number 91290    Answers: 0   Comments: 1

Question Number 91287    Answers: 1   Comments: 0

y′′+2y′+5y=3sin 4t

$${y}''+\mathrm{2}{y}'+\mathrm{5}{y}=\mathrm{3sin}\:\mathrm{4}{t} \\ $$

Question Number 91277    Answers: 2   Comments: 0

p=1−(1/2)+(1/3)−(1/4)+...+(1/(2003))−(1/(2004)) q=(1/(1003))+(1/(1004))+...+(1/(2004)) p^2 +q^2 =

$${p}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+...+\frac{\mathrm{1}}{\mathrm{2003}}−\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${q}=\frac{\mathrm{1}}{\mathrm{1003}}+\frac{\mathrm{1}}{\mathrm{1004}}+...+\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${p}^{\mathrm{2}} +{q}^{\mathrm{2}} \:=\: \\ $$

Question Number 91275    Answers: 0   Comments: 6

Question Number 91274    Answers: 0   Comments: 0

lim_(n→∞) n^(−n^2 ) [(n+1)(n+(1/2))....(n+(1/2^(n−1) ))]^n

$$\underset{{n}\rightarrow\infty} {{lim}n}^{−{n}^{\mathrm{2}} } \left[\left({n}+\mathrm{1}\right)\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)....\left({n}+\frac{\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}} }\right)\right]^{{n}} \\ $$

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