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Question Number 175008    Answers: 0   Comments: 2

Find The Centroid Coordinate If Trapezoid With B_1 =4, B_2 =3 And Height=5 With Positions Like This

$${Find}\:{The}\:{Centroid}\:{Coordinate}\: \\ $$$${If}\:{Trapezoid}\:{With}\:{B}_{\mathrm{1}} =\mathrm{4},\:{B}_{\mathrm{2}} =\mathrm{3} \\ $$$${And}\:{Height}=\mathrm{5}\:{With}\:{Positions}\: \\ $$$${Like}\:{This} \\ $$

Question Number 175023    Answers: 0   Comments: 0

𝚺_(n=0) ^∞ (((βˆ’1)^n )/(7+6n))[𝛙^((0)) (((9+6n)/2))βˆ’π›™^((0)) (((7+6n)/2))]

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(βˆ’\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{7}+\mathrm{6}\boldsymbol{\mathrm{n}}}\left[\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\frac{\mathrm{9}+\mathrm{6}\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right)βˆ’\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\frac{\mathrm{7}+\mathrm{6}\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right)\right] \\ $$

Question Number 175004    Answers: 0   Comments: 1

Question Number 175000    Answers: 1   Comments: 1

Question Number 174983    Answers: 0   Comments: 3

Question Number 174982    Answers: 2   Comments: 0

Question Number 174981    Answers: 0   Comments: 1

Question Number 174975    Answers: 1   Comments: 0

Question Number 174974    Answers: 1   Comments: 0

Question Number 174965    Answers: 1   Comments: 0

∫ ((x+sin x)/(1+cos x)) dx =?

$$\:\:\:\:\:\:\int\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$

Question Number 174963    Answers: 3   Comments: 1

Question Number 174960    Answers: 1   Comments: 0

solve for all x ⌊x^2 βŒ‹ βˆ’ ⌊xβŒ‹^2 = 100

$${solve}\:{for}\:{all}\:{x}\: \\ $$$$\lfloor{x}^{\mathrm{2}} \rfloor\:βˆ’\:\lfloor{x}\rfloor^{\mathrm{2}} \:=\:\mathrm{100} \\ $$

Question Number 174951    Answers: 1   Comments: 0

lim_(nβ†’βˆž) (1/n)[1+(√2)+^3 (√3)+...^n (√n)]

$$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\left[\mathrm{1}+\sqrt{\mathrm{2}}+^{\mathrm{3}} \sqrt{\mathrm{3}}+...^{{n}} \sqrt{{n}}\right] \\ $$

Question Number 174950    Answers: 1   Comments: 0

Have you seen this method of solving quadratic problem? x^2 βˆ’xβˆ’12=0 yβ€²=Β±(√(b^2 βˆ’4ac))

$$\mathrm{Have}\:\mathrm{you}\:\mathrm{seen}\:\mathrm{this}\:\mathrm{method}\:\mathrm{of}\:\mathrm{solving} \\ $$$$\mathrm{quadratic}\:\mathrm{problem}? \\ $$$$\mathrm{x}^{\mathrm{2}} βˆ’\mathrm{x}βˆ’\mathrm{12}=\mathrm{0} \\ $$$$\mathrm{y}'=\pm\sqrt{\mathrm{b}^{\mathrm{2}} βˆ’\mathrm{4ac}} \\ $$

Question Number 174933    Answers: 1   Comments: 0

Question Number 174928    Answers: 3   Comments: 0

How many digits does 1000^(1000) have? Mastermind

$$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{does}\:\mathrm{1000}^{\mathrm{1000}} \:\mathrm{have}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174915    Answers: 1   Comments: 0

Find the value of a for which the limit lim_(xβ†’0) ((sin (ax)βˆ’arctan xβˆ’x)/(x^3 +x^4 )) is finite and then evaluate the limit

$$\:{Find}\:{the}\:{value}\:{of}\:{a}\:{for}\:{which}\: \\ $$$$\:{the}\:{limit}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({ax}\right)βˆ’\mathrm{arctan}\:{x}βˆ’{x}}{{x}^{\mathrm{3}} +{x}^{\mathrm{4}} } \\ $$$${is}\:{finite}\:{and}\:{then}\:{evaluate}\:{the}\:{limit} \\ $$

Question Number 174939    Answers: 1   Comments: 0

sum of the all proper factors of 360 ?

$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{all}\:\mathrm{proper}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{360}\:? \\ $$

Question Number 174938    Answers: 0   Comments: 0

let u_n = ∫_0 ^1 x^n artan(nx)dx 1)lim u_n ? 2)nature of Σ u_n 3) calculate u_n 4)equivalent of u_n ?

$${let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} {artan}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right){lim}\:{u}_{{n}} ? \\ $$$$\left.\mathrm{2}\right){nature}\:{of}\:\Sigma\:{u}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{u}_{{n}} \\ $$$$\left.\mathrm{4}\right){equivalent}\:{of}\:{u}_{{n}} ? \\ $$

Question Number 174940    Answers: 0   Comments: 1

f(x)=(log3^x βˆ’2log3).(x^2 βˆ’1) let

$${f}\left({x}\right)=\left({log}\mathrm{3}^{{x}} βˆ’\mathrm{2}{log}\mathrm{3}\right).\left({x}^{\mathrm{2}} βˆ’\mathrm{1}\right) \\ $$$${let} \\ $$

Question Number 174902    Answers: 1   Comments: 0

Question Number 174896    Answers: 0   Comments: 0

prove that ∫_(βˆ’βˆž) ^( ∞) ((x csch((x/2)))/(x^2 +Ο€^2 ))dx=Ο€βˆ’2

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{βˆ’\infty} ^{\:\infty} \frac{\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{csch}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\pi^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=\piβˆ’\mathrm{2} \\ $$

Question Number 174888    Answers: 1   Comments: 0

Question Number 174884    Answers: 1   Comments: 0

Question Number 174883    Answers: 2   Comments: 0

lim_(nβ†’βˆž) ∫_0 ^1 e^x^2 sin(nx)dx

$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } \mathrm{sin}\left({nx}\right){dx}\: \\ $$

Question Number 174879    Answers: 0   Comments: 7

Q : (an E lementary to abstract algebra ) prove that the order of an element in” quotient group ” (Q , βŠ•)/(Z , βŠ•) is finite. Notice: (Q , βŠ•)/(Z , βŠ•) = { (a/b) + Z ∣ a,b ∈ Z , b β‰ 0 } ≻ Source: John B .F raleigh book β‰Ί

$$ \\ $$$$\:\:\:\boldsymbol{\mathrm{Q}}\::\:\left(\boldsymbol{{an}}\:\:\mathscr{E}\:\boldsymbol{{lementary}}\:\boldsymbol{{to}}\:\boldsymbol{{abstract}}\:\boldsymbol{{algebra}}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\:\boldsymbol{{order}}\:\:\boldsymbol{{of}}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{an}}\:\:\boldsymbol{{element}}\:\:\boldsymbol{{in}}''\:\boldsymbol{{quotient}}\:\boldsymbol{{group}}\:''\:\left(\mathbb{Q}\:,\:\oplus\right)/\left(\mathbb{Z}\:,\:\oplus\right)\:\boldsymbol{{is}}\:\boldsymbol{{finite}}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Notice}}:\:\:\left(\mathbb{Q}\:,\:\oplus\right)/\left(\mathbb{Z}\:,\:\oplus\right)\:=\:\left\{\:\frac{\boldsymbol{{a}}}{\boldsymbol{{b}}}\:+\:\mathbb{Z}\:\mid\:\:\boldsymbol{{a}},\boldsymbol{{b}}\:\in\:\mathbb{Z}\:,\:\boldsymbol{{b}}\:\neq\mathrm{0}\:\right\}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ\:\boldsymbol{{Source}}:\:\boldsymbol{{John}}\:\boldsymbol{{B}}\:.\boldsymbol{{F}}\:\boldsymbol{{raleigh}}\:\boldsymbol{{book}}\:\prec\:\:\:\: \\ $$$$ \\ $$

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