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Question Number 51841    Answers: 0   Comments: 2

Question Number 51840    Answers: 2   Comments: 0

solve (dy/(dx )) + ((2y)/(3x )) = (x/(√y))

$${solve} \\ $$$$\frac{{dy}}{{dx}\:}\:+\:\frac{\mathrm{2}{y}}{\mathrm{3}{x}\:}\:=\:\frac{{x}}{\sqrt{{y}}} \\ $$

Question Number 51837    Answers: 1   Comments: 1

Question Number 51834    Answers: 0   Comments: 1

calculatef(a)= ∫_0 ^∞ ((ln(1+at^2 ))/(1+t^4 ))dt with a>0. 2)find the value of ∫_0 ^∞ ((ln(3+t^2 ))/(1+t^4 ))dt.

$${calculatef}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{1}+{at}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:\:{with}\:{a}>\mathrm{0}. \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{3}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$

Question Number 51825    Answers: 1   Comments: 3

find f(α)=∫_0 ^1 ln(1+e^(−α) x)dx with α≥0

$${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{e}^{−\alpha} {x}\right){dx}\:\:{with}\:\alpha\geqslant\mathrm{0} \\ $$

Question Number 51824    Answers: 1   Comments: 0

find ∫ (dx/(cosx +cos(2x)+cos(3x)))

$${find}\:\int\:\:\:\frac{{dx}}{{cosx}\:+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right)} \\ $$

Question Number 51818    Answers: 0   Comments: 0

Find the relation between the ecentric angles of the point which are at the end of focal chord

$${Find}\:{the}\:{relation}\:{between} \\ $$$${the}\:{ecentric}\:{angles} \\ $$$${of}\:{the}\:{point}\:\:{which}\:{are} \\ $$$${at}\:{the}\:{end}\:{of}\:{focal}\:{chord} \\ $$

Question Number 51817    Answers: 0   Comments: 0

The earth moves arround the sun in an elliptical orbit with the sun at one of its foci.the eccentricity (1/3).the shortest distance from the earth to sun is 3000000km.Find the furthest distance of the earth from the sun.

$${The}\:{earth}\:{moves}\:{arround} \\ $$$${the}\:{sun}\:{in}\:{an}\:{elliptical} \\ $$$${orbit}\:{with}\:{the}\:{sun}\:{at} \\ $$$${one}\:{of}\:{its}\:{foci}.{the}\:{eccentricity} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}.{the}\:{shortest}\:{distance} \\ $$$${from}\:{the}\:{earth}\:{to}\:{sun}\: \\ $$$${is}\:\mathrm{3000000}{km}.{Find}\:{the} \\ $$$${furthest}\:{distance}\:{of}\:{the} \\ $$$${earth}\:{from}\:{the}\:{sun}. \\ $$

Question Number 51812    Answers: 0   Comments: 4

Question Number 51805    Answers: 2   Comments: 3

Question Number 51798    Answers: 0   Comments: 3

Question Number 51779    Answers: 0   Comments: 3

Q= In how many ways 8 students can be divided into two equal groups? Ans= ((8!)/(2!×(4!)^2 )) here why two factorial is divided? we do not do the same incase of distributing 52 cards equally among 4 persons. pls explain...

$${Q}=\:\:{In}\:{how}\:{many}\:{ways}\:\mathrm{8}\:{students}\:{can}\:{be}\:{divided}\:{into}\:{two}\:{equal}\:{groups}? \\ $$$$ \\ $$$${Ans}=\:\:\:\:\frac{\mathrm{8}!}{\mathrm{2}!×\left(\mathrm{4}!\right)^{\mathrm{2}} }\:\:\: \\ $$$$ \\ $$$${here}\:{why}\:{two}\:{factorial}\:{is}\:{divided}? \\ $$$${we}\:{do}\:{not}\:{do}\:{the}\:{same}\:{incase}\:{of}\:{distributing}\:\mathrm{52}\:{cards}\:{equally}\:{among}\:\mathrm{4}\:{persons}. \\ $$$$ \\ $$$${pls}\:{explain}... \\ $$

Question Number 51774    Answers: 1   Comments: 4

Question Number 51768    Answers: 1   Comments: 2

Question Number 51772    Answers: 2   Comments: 0

x^3 +12x+12=0 Express your answer in surd form

$$\mathrm{x}^{\mathrm{3}} +\mathrm{12x}+\mathrm{12}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Express}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form} \\ $$$$ \\ $$

Question Number 51733    Answers: 2   Comments: 3

Question Number 51729    Answers: 1   Comments: 0

81^(1/4) × 9^(3/2) × 27^(4/3) = _____

$$\mathrm{81}^{\frac{\mathrm{1}}{\mathrm{4}}} ×\:\mathrm{9}^{\frac{\mathrm{3}}{\mathrm{2}}} ×\:\mathrm{27}^{\frac{\mathrm{4}}{\mathrm{3}}} =\:\_\_\_\_\_ \\ $$

Question Number 51728    Answers: 0   Comments: 5

Question Number 51721    Answers: 1   Comments: 0

Find the range of value of x given that: ∣x + i∣ ≥ (1/x)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{given}\:\mathrm{that}:\:\:\:\:\:\mid\mathrm{x}\:+\:\mathrm{i}\mid\:\geqslant\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 51720    Answers: 0   Comments: 0

Question Number 51712    Answers: 0   Comments: 9

Question Number 51700    Answers: 1   Comments: 1

Question Number 51694    Answers: 1   Comments: 0

Question Number 51691    Answers: 1   Comments: 0

Question Number 51710    Answers: 1   Comments: 0

solve the equation y = xy′+ (y′)^2

$${solve}\:{the}\:{equation} \\ $$$${y}\:=\:{xy}'+\:\left({y}'\right)^{\mathrm{2}} \\ $$

Question Number 51709    Answers: 2   Comments: 0

y′′=2y(y′) solve the equation

$${y}''=\mathrm{2}{y}\left({y}'\right) \\ $$$$ \\ $$$${solve}\:{the}\:{equation} \\ $$

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