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Question Number 91465 Answers: 1 Comments: 1

Question Number 91460 Answers: 1 Comments: 0

one of the conditions of the inflection point is inflection tangent. what is inflection tangent?

$${one}\:{of}\:{the}\:{conditions}\:{of}\:{the}\:{inflection} \\ $$$${point}\:{is}\:{inflection}\:{tangent}. \\ $$$${what}\:{is}\:{inflection}\:{tangent}? \\ $$

Question Number 91452 Answers: 2 Comments: 1

((−1))^(1/4) =?

$$\:\:\:\sqrt[{\mathrm{4}}]{−\mathrm{1}}\:=? \\ $$

Question Number 91448 Answers: 0 Comments: 3

prove that 1+x^(111) +x^(222) +x^(333) +x^(444) divides 1+ x^(111) +x^(222) +x^(333) +.......+x^(999)

$${prove}\:{that}\:\mathrm{1}+{x}^{\mathrm{111}} +{x}^{\mathrm{222}} +{x}^{\mathrm{333}} +{x}^{\mathrm{444}} \:\:{divides}\:\mathrm{1}+\:{x}^{\mathrm{111}} +{x}^{\mathrm{222}} +{x}^{\mathrm{333}} +.......+{x}^{\mathrm{999}} \\ $$

Question Number 91446 Answers: 0 Comments: 1

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

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

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

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