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Question Number 28027 Answers: 1 Comments: 0

Question Number 36365 Answers: 1 Comments: 2

Question Number 36366 Answers: 3 Comments: 0

Question Number 28015 Answers: 1 Comments: 1

Question Number 28006 Answers: 0 Comments: 1

∫_0 ^∞ (ln x)^(−3) dx

$$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{ln}\:{x}\right)^{−\mathrm{3}} {dx} \\ $$

Question Number 27999 Answers: 0 Comments: 1

find I_(n,m) = ∫_0 ^1 x^n (1−x)^m dx with (n,m)∈N^★^2 and calculate Σ_(n=0) ^∝ I_(n,m) .

$${find}\:\:{I}_{{n},{m}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \:\left(\mathrm{1}−{x}\right)^{{m}} \:{dx}\:{with} \\ $$$$\left({n},{m}\right)\in{N}^{\bigstar^{\mathrm{2}} } \:{and}\:{calculate}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \:{I}_{{n},{m}} . \\ $$

Question Number 27997 Answers: 1 Comments: 3

Question Number 27996 Answers: 1 Comments: 0

p,q are two natural number and ((p^6 +2p^4 +4p^2 )/(p^9 −8p^3 ))−(1/(4q))=(5/(6q)), then find the minimum possible value of p+q

$$\mathrm{p},\mathrm{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{and}\: \\ $$$$\:\frac{\mathrm{p}^{\mathrm{6}} +\mathrm{2p}^{\mathrm{4}} +\mathrm{4p}^{\mathrm{2}} }{\mathrm{p}^{\mathrm{9}} −\mathrm{8p}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{4q}}=\frac{\mathrm{5}}{\mathrm{6q}}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}+\mathrm{q} \\ $$

Question Number 27986 Answers: 0 Comments: 1

Prove that the angular momentum H_G ^ of a rigid body about its mass center is given by : H_x =I_x ^ ω_x −I_(xy) ^ ω_y −I_(xz) ^ ω_z H_y =−I_(yx) ^ ω_x +I_y ^ ω_y −I_(yz) ^ ω_z H_z =−I_(zx) ^ ω_x −I_(zy) ^ ω_y +I_z ^ ω_z where I_x ^ =∫(y^2 +z^2 )dm I_(xy) ^ =∫xy dm ...and so on..

$${Prove}\:{that}\:{the}\:{angular}\:{momentum} \\ $$$$\bar {\boldsymbol{{H}}}_{{G}} \:{of}\:{a}\:{rigid}\:{body}\:{about}\:{its}\:{mass} \\ $$$${center}\:{is}\:{given}\:{by}\:: \\ $$$${H}_{{x}} =\bar {{I}}_{{x}} \omega_{{x}} −\bar {{I}}_{{xy}} \omega_{{y}} −\bar {{I}}_{{xz}} \omega_{{z}} \\ $$$${H}_{{y}} =−\bar {{I}}_{{yx}} \omega_{{x}} +\bar {{I}}_{{y}} \omega_{{y}} −\bar {{I}}_{{yz}} \omega_{{z}} \\ $$$${H}_{{z}} =−\bar {{I}}_{{zx}} \omega_{{x}} −\bar {{I}}_{{zy}} \omega_{{y}} +\bar {{I}}_{{z}} \omega_{{z}} \\ $$$$\:\:\:\:{where}\:\:\bar {{I}}_{{x}} =\int\left({y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right){dm} \\ $$$$\:\:\:\:\:\:\bar {{I}}_{{xy}} =\int{xy}\:{dm}\:...{and}\:{so}\:{on}.. \\ $$

Question Number 27983 Answers: 2 Comments: 0

1) find two factors of 1000001 other than 1 and 1000001 2)(x^2 −5x+5)^((x^2 +2x−24)) =1 what is the value of the product of the solutions?

$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{two}\:\:\mathrm{factors}\:\mathrm{of}\:\mathrm{1000001}\:\mathrm{other}\:\mathrm{than}\:\mathrm{1}\:\mathrm{and}\:\mathrm{1000001} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{5}\right)^{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{24}\right)} =\mathrm{1}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solutions}? \\ $$

Question Number 28012 Answers: 1 Comments: 1

1,4,5,16,17,20....... what is the 68th term in this sequnce?

$$\mathrm{1},\mathrm{4},\mathrm{5},\mathrm{16},\mathrm{17},\mathrm{20}.......\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{68th}\:\mathrm{term}\:\mathrm{in}\:\mathrm{this}\:\mathrm{sequnce}? \\ $$

Question Number 27977 Answers: 1 Comments: 0

∣2x+1∣≤2

$$\mid\mathrm{2}{x}+\mathrm{1}\mid\leqslant\mathrm{2} \\ $$

Question Number 27976 Answers: 1 Comments: 1

solve ((2x)/(x^2 +1))<((3x+1)/(2(x^2 +1)))

$${solve} \\ $$$$ \\ $$$$\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}<\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$ \\ $$

Question Number 27975 Answers: 1 Comments: 0

solve the inequality (1/(x^2 +x+1))>0

$${solve}\:{the}\:{inequality} \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}>\mathrm{0} \\ $$

Question Number 27974 Answers: 0 Comments: 1

let put f(t)=∫_0 ^∞ ((e^(−ax) − e^(−bx) )/x^2 ) e^(−tx^2 ) dx with t≥0 and a>0 and b>0 find a integral form of f(t).

$${let}\:{put}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{ax}} \:−\:{e}^{−{bx}} }{{x}^{\mathrm{2}} }\:{e}^{−{tx}^{\mathrm{2}} } \:{dx} \\ $$$${with}\:{t}\geqslant\mathrm{0}\:\:{and}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$${find}\:{a}\:{integral}\:{form}\:{of}\:{f}\left({t}\right). \\ $$

Question Number 27958 Answers: 1 Comments: 0

For α∈R, cosαcosx+siny≥sinx, ∀x∈R, then find the sum of the possible values of sinα+siny.

$${For}\:\alpha\in{R},\:{cos}\alpha{cosx}+{siny}\geqslant{sinx},\:\forall{x}\in{R}, \\ $$$${then}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{possible}\:{values} \\ $$$${of}\:{sin}\alpha+{siny}. \\ $$

Question Number 27959 Answers: 0 Comments: 6

Question Number 27954 Answers: 0 Comments: 1

Question Number 27951 Answers: 0 Comments: 0

Use the trapezoidal rule with 5 ordinates to evaluate ∫_( 0) ^( 0.8) e^x^2 dx

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{trapezoidal}\:\mathrm{rule}\:\mathrm{with}\:\mathrm{5}\:\mathrm{ordinates}\:\mathrm{to}\:\mathrm{evaluate}\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{0}.\mathrm{8}} \:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx} \\ $$

Question Number 27950 Answers: 0 Comments: 0

Find by the trapezoidal rule the approximate value of ∫_( 0) ^( 1) (dx/(1 + x^2 )). Use ordinates spaced at equal interval of width h = 0.1

$$\mathrm{Find}\:\mathrm{by}\:\mathrm{the}\:\mathrm{trapezoidal}\:\mathrm{rule}\:\mathrm{the}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{of}\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }.\:\:\:\mathrm{Use} \\ $$$$\mathrm{ordinates}\:\mathrm{spaced}\:\mathrm{at}\:\mathrm{equal}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{width}\:\:\mathrm{h}\:=\:\mathrm{0}.\mathrm{1} \\ $$

Question Number 27961 Answers: 0 Comments: 0

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

$${A}\:\mathrm{and}\:{B}\:\mathrm{play}\:\mathrm{a}\:\mathrm{game}\:\mathrm{where}\:\mathrm{each}\:\mathrm{is} \\ $$$$\mathrm{asked}\:\mathrm{to}\:\mathrm{select}\:\mathrm{a}\:\mathrm{number}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{25}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{two}\:\mathrm{numbers}\:\mathrm{match},\:\mathrm{both}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{win}\:\mathrm{a}\:\mathrm{prize}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{they} \\ $$$$\mathrm{will}\:\mathrm{not}\:\mathrm{win}\:\mathrm{a}\:\mathrm{prize}\:\mathrm{in}\:\mathrm{a}\:\mathrm{single}\:\mathrm{trial}\:\mathrm{is} \\ $$

Question Number 27948 Answers: 0 Comments: 0

what is relation between intensity of diffraction pattern .slit width?

$${what}\:{is}\:{relation}\:{between}\: \\ $$$${intensity}\:{of}\:{diffraction}\: \\ $$$${pattern}\:.{slit}\:{width}? \\ $$

Question Number 27946 Answers: 1 Comments: 0

Q.N− Find the coefficint of x^4 in the expansion of (1+3x+10x^2 )(x+(1/x))^(10)

Question Number 27944 Answers: 0 Comments: 0

Did anybody give Silverzone iOM of class 11?

$${Did}\:{anybody}\:{give}\:{Silverzone}\:{iOM}\:{of} \\ $$$${class}\:\mathrm{11}? \\ $$

Question Number 27942 Answers: 1 Comments: 1

Question Number 27939 Answers: 0 Comments: 1

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