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Question Number 150840 Answers: 1 Comments: 0

∫_( 0) ^( ∞) ((arctan(x))/(x(x^2 +x+1))) dx = ?

$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$

Question Number 150839 Answers: 2 Comments: 0

e^x + y = x^2 y^2 find the expression for (dy/dx)

$$\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{for}\:\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$

Question Number 150838 Answers: 1 Comments: 0

Question Number 150828 Answers: 2 Comments: 0

∫_0 ^( ∞) (( sin^( 2) (x ))/(x(√x))) dx=^? (√π)

$$ \\ $$$$\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{2}} \left({x}\:\right)}{{x}\sqrt{{x}}}\:{dx}\overset{?} {=}\:\sqrt{\pi} \\ $$

Question Number 150827 Answers: 0 Comments: 0

Question Number 150807 Answers: 5 Comments: 0

For matris solution: { ((2x - 3y = 8)),((x + 5y = - 9)) :}

$$\mathrm{For}\:\mathrm{matris}\:\mathrm{solution}: \\ $$$$\begin{cases}{\mathrm{2x}\:-\:\mathrm{3y}\:=\:\mathrm{8}}\\{\mathrm{x}\:+\:\mathrm{5y}\:=\:-\:\mathrm{9}}\end{cases} \\ $$

Question Number 150946 Answers: 0 Comments: 0

Question Number 150944 Answers: 4 Comments: 3

Question Number 150804 Answers: 1 Comments: 0

Question Number 150794 Answers: 0 Comments: 0

Question Number 150793 Answers: 0 Comments: 2

(R−r)^2 + R^2 = (R + r)^2 ⇔ R^2 + r^2 −2rR + R^2 = R^2 + r^2 +2rR ⇒ R^2 = 4rR ⇒ r = (R/4) = 1cm A_S = πr^2 = π×1cm^2 = πcm^2

$$\left({R}−{r}\right)^{\mathrm{2}} \:+\:{R}^{\mathrm{2}} \:=\:\left({R}\:+\:{r}\right)^{\mathrm{2}} \:\Leftrightarrow \\ $$$${R}^{\mathrm{2}} \:+\:{r}^{\mathrm{2}} −\mathrm{2}{rR}\:+\:{R}^{\mathrm{2}} \:=\:{R}^{\mathrm{2}} \:+\:{r}^{\mathrm{2}} \:+\mathrm{2}{rR}\:\Rightarrow \\ $$$${R}^{\mathrm{2}} \:=\:\mathrm{4}{rR}\:\Rightarrow\:{r}\:=\:\frac{{R}}{\mathrm{4}}\:=\:\mathrm{1}{cm} \\ $$$$\mathscr{A}_{{S}} \:=\:\pi{r}^{\mathrm{2}} \:=\:\pi×\mathrm{1}{cm}^{\mathrm{2}} \:=\:\pi{cm}^{\mathrm{2}} \\ $$

Question Number 150789 Answers: 1 Comments: 0

Question Number 150786 Answers: 1 Comments: 0

Question Number 150801 Answers: 0 Comments: 5

Question Number 150797 Answers: 2 Comments: 0

x;y∈N ((18^((x^2 + y^2 )/2) )/9^(xy) ) = 2592 ⇒ find xy=?

$$\mathrm{x};\mathrm{y}\in\mathbb{N} \\ $$$$\frac{\mathrm{18}^{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} }{\mathrm{2}}} }{\mathrm{9}^{\boldsymbol{\mathrm{xy}}} }\:=\:\mathrm{2592}\:\:\Rightarrow\:\mathrm{find}\:\:\boldsymbol{\mathrm{xy}}=? \\ $$

Question Number 150769 Answers: 1 Comments: 0

((1^3 +2^3 +3^3 +4^3 +...+x^3 )/(1∙4+2∙7+3∙10+...+x(3x+1))) = 2021 find x=?

$$\frac{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\mathrm{4}^{\mathrm{3}} +...+\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\mathrm{1}\centerdot\mathrm{4}+\mathrm{2}\centerdot\mathrm{7}+\mathrm{3}\centerdot\mathrm{10}+...+\boldsymbol{\mathrm{x}}\left(\mathrm{3}\boldsymbol{\mathrm{x}}+\mathrm{1}\right)}\:=\:\mathrm{2021} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 150761 Answers: 6 Comments: 0

Question Number 150783 Answers: 0 Comments: 0

The current in the windings on a toroid is 2A. There are 400turns and the mean circumferential length is 40cm. With the aid of a search coil and charge measuring instrument,the magnetic field is found to be 1.0T. calculate: i)magnetic intensity ii)magnetization iii)the equivalent surface current

$$\mathrm{The}\:\mathrm{current}\:\mathrm{in}\:\mathrm{the}\:\mathrm{windings}\:\mathrm{on}\:\mathrm{a}\:\mathrm{toroid} \\ $$$$\mathrm{is}\:\mathrm{2A}.\:\mathrm{There}\:\mathrm{are}\:\mathrm{400turns}\:\mathrm{and}\:\mathrm{the}\:\mathrm{mean} \\ $$$$\mathrm{circumferential}\:\mathrm{length}\:\mathrm{is}\:\mathrm{40cm}.\:\mathrm{With} \\ $$$$\mathrm{the}\:\mathrm{aid}\:\mathrm{of}\:\mathrm{a}\:\mathrm{search}\:\mathrm{coil}\:\mathrm{and}\:\mathrm{charge} \\ $$$$\mathrm{measuring}\:\mathrm{instrument},\mathrm{the}\:\mathrm{magnetic} \\ $$$$\mathrm{field}\:\mathrm{is}\:\mathrm{found}\:\mathrm{to}\:\mathrm{be}\:\mathrm{1}.\mathrm{0T}.\:\mathrm{calculate}: \\ $$$$\left.\mathrm{i}\left.\right)\mathrm{magnetic}\:\mathrm{intensity}\:\mathrm{ii}\right)\mathrm{magnetization} \\ $$$$\left.\mathrm{iii}\right)\mathrm{the}\:\mathrm{equivalent}\:\mathrm{surface}\:\mathrm{current} \\ $$$$ \\ $$$$ \\ $$

Question Number 150759 Answers: 1 Comments: 0

lim_(x→0) ((log(e+x)−1)/x)=? please help..

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{log}\left({e}+{x}\right)−\mathrm{1}}{{x}}=? \\ $$$${please}\:{help}.. \\ $$

Question Number 150752 Answers: 1 Comments: 2

x^3 +3x+12=0 solve real number help

$$\mathrm{x}^{\mathrm{3}} +\mathrm{3x}+\mathrm{12}=\mathrm{0}\:\:\mathrm{solve}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\mathrm{help} \\ $$

Question Number 150749 Answers: 0 Comments: 0

Prove That :: I := ∫_0 ^( ∞) ((( sin (x ).cos (x ))^( 4) )/(x . (√x) ))dx=(1/(32)) (2 (√2) −1 )(√( π)) ....■ ..m.n..

$$ \\ $$$$\:\:\mathrm{Prove}\:\:\:\mathrm{That}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathcal{I}\::=\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left(\:{sin}\:\left({x}\:\right).{cos}\:\left({x}\:\right)\right)^{\:\mathrm{4}} }{{x}\:.\:\sqrt{{x}}\:}{dx}=\frac{\mathrm{1}}{\mathrm{32}}\:\left(\mathrm{2}\:\sqrt{\mathrm{2}}\:−\mathrm{1}\:\right)\sqrt{\:\pi}\:....\blacksquare\:\: \\ $$$$\:\:\:..{m}.{n}..\:\: \\ $$

Question Number 150747 Answers: 2 Comments: 0

prove :: Ω:=∫_0 ^( ∞) e^(−(√x)) .ln ((( x))^(1/4) )=^? 1−γ m.n..

$$ \\ $$$${prove}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} {e}^{−\sqrt{{x}}} .{ln}\:\left(\sqrt[{\mathrm{4}}]{\:{x}}\:\right)\overset{?} {=}\:\mathrm{1}−\gamma \\ $$$$\:{m}.{n}.. \\ $$

Question Number 150746 Answers: 2 Comments: 0

Find the smallest positive integer n so that (1^2 + 2^2 + 3^2 + … + n^2 ) is divided by n .

$${Find}\:\:{the}\:\:{smallest}\:\:{positive}\:\:{integer}\:\:{n}\:\:{so}\:\:{that}\:\:\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\ldots\:+\:{n}^{\mathrm{2}} \right)\:\:{is}\:\:{divided}\:\:{by}\:\:{n}\:. \\ $$

Question Number 150742 Answers: 0 Comments: 0

Question Number 150738 Answers: 1 Comments: 2

A point P(x, y) moves such that its perpendicular distance from the line 12x + 5y − 1 = 0 is always 3 units. Find the equation that describes the locus precisely.

$$\mathrm{A}\:\mathrm{point}\:\mathrm{P}\left({x},\:{y}\right)\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{perpendicular}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{12}{x}\:+\:\mathrm{5}{y}\:−\:\mathrm{1}\:=\:\:\mathrm{0}\:\mathrm{is}\:\mathrm{always}\:\mathrm{3}\:{units}.\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{that}\:\mathrm{describes}\:\mathrm{the}\: \\ $$$$\mathrm{locus}\:\mathrm{precisely}. \\ $$

Question Number 150737 Answers: 0 Comments: 0

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