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AllQuestion and Answers: Page 1171

Question Number 99877    Answers: 0   Comments: 5

Question Number 99869    Answers: 2   Comments: 0

tng(𝛑/9) + 4sin(𝛑/9) =(√3)

$$\:\boldsymbol{{tng}}\frac{\boldsymbol{\pi}}{\mathrm{9}}\:\:+\:\mathrm{4}\boldsymbol{{sin}}\frac{\boldsymbol{\pi}}{\mathrm{9}}\:=\sqrt{\mathrm{3}} \\ $$

Question Number 99853    Answers: 2   Comments: 0

(1/1^2 )+(1/2^2 )+(1/3^2 )+(1/4^2 )+(1/6^2 )+.....∞=?

$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{2}} }+.....\infty=? \\ $$

Question Number 99846    Answers: 0   Comments: 1

lim_(nβ†’βˆž) (1βˆ’(1/(2!)))^(((1/(2!))βˆ’(1/(3!)))^(.........((1/(n!))βˆ’(1/((n+1)!)))) ) =?

$$\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{m}}}\left(\mathrm{1}βˆ’\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\left(\frac{\mathrm{1}}{\mathrm{2}!}βˆ’\frac{\mathrm{1}}{\mathrm{3}!}\right)^{.........\left(\frac{\mathrm{1}}{\boldsymbol{{n}}!}βˆ’\frac{\mathrm{1}}{\left(\boldsymbol{{n}}+\mathrm{1}\right)!}\right)} } =? \\ $$

Question Number 99839    Answers: 2   Comments: 4

let x_0 =1 and x_(n+1) =ln(e^x_n βˆ’x_n ) 1) prove that x_n β†’0 2)prove that Ξ£ x_n converges and ddyermine its sum

$$\mathrm{let}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1}\:\mathrm{and}\:\mathrm{x}_{\mathrm{n}+\mathrm{1}} =\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}_{\mathrm{n}} } βˆ’\mathrm{x}_{\mathrm{n}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{x}_{\mathrm{n}} \:\rightarrow\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\mathrm{prove}\:\mathrm{that}\:\Sigma\:\mathrm{x}_{\mathrm{n}} \:\mathrm{converges}\:\mathrm{and}\:\mathrm{ddyermine}\:\mathrm{its}\:\mathrm{sum} \\ $$

Question Number 99832    Answers: 0   Comments: 0

solve x^2 y^(β€²β€²) βˆ’xy^β€² +2y =x^3 e^(βˆ’x)

$$\mathrm{solve}\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{''} \:βˆ’\mathrm{xy}^{'} \:+\mathrm{2y}\:=\mathrm{x}^{\mathrm{3}} \mathrm{e}^{βˆ’\mathrm{x}} \\ $$

Question Number 99831    Answers: 0   Comments: 0

solve the ds { ((x^β€² +2y^β€² =sint)),((3x^β€² +y^β€² =te^t )) :}

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{ds}\:\:\:\begin{cases}{\mathrm{x}^{'} \:+\mathrm{2y}^{'} \:=\mathrm{sint}}\\{\mathrm{3x}^{'} +\mathrm{y}^{'} \:=\mathrm{te}^{\mathrm{t}} }\end{cases} \\ $$

Question Number 99829    Answers: 0   Comments: 0

1.Find the principal if its interest in 3month with 5(1/2)% per amount is Rs.66. 2. The length of arectangular room is double of its breadth and height is one third of the length. If the room contains 972 cubic meter of air, find the area of floor of the room.

$$\:\mathrm{1}.\mathrm{Find}\:\mathrm{the}\:\mathrm{principal}\:\mathrm{if}\:\mathrm{its}\:\mathrm{interest}\:\mathrm{in}\:\mathrm{3month}\:\mathrm{with}\:\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}\%\:\mathrm{per}\:\mathrm{amount}\:\mathrm{is}\:\mathrm{Rs}.\mathrm{66}. \\ $$$$\:\mathrm{2}.\:\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{arectangular}\:\mathrm{room}\:\mathrm{is}\:\mathrm{double}\:\mathrm{of}\:\mathrm{its}\:\mathrm{breadth}\:\mathrm{and} \\ $$$$\:\:\mathrm{height}\:\mathrm{is}\:\mathrm{one}\:\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{length}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{room}\:\mathrm{contains}\:\mathrm{972}\:\mathrm{cubic}\:\mathrm{meter}\:\mathrm{of}\:\mathrm{air}, \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{floor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{room}. \\ $$

Question Number 99828    Answers: 1   Comments: 2

let A = (((2 1)),((1 2)) ) 1) calculate A^n 2)determine cosA and sinA 3) find chA and shA

$$\mathrm{let}\:\mathrm{A}\:=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\mathrm{determine}\:\mathrm{cosA}\:\mathrm{and}\:\mathrm{sinA} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{chA}\:\mathrm{and}\:\mathrm{shA} \\ $$

Question Number 99827    Answers: 0   Comments: 0

How many days after 12/7/1941 (pearl harbour bombed) was 9/11/2001 (the september 11 terrorist attack? please help, iβ€²m having 27175days, which apparently isnβ€²t correct.

$$\mathrm{How}\:\mathrm{many}\:\mathrm{days}\:\mathrm{after}\:\mathrm{12}/\mathrm{7}/\mathrm{1941} \\ $$$$\left(\mathrm{pearl}\:\mathrm{harbour}\:\mathrm{bombed}\right)\:\mathrm{was}\:\mathrm{9}/\mathrm{11}/\mathrm{2001} \\ $$$$\left(\mathrm{the}\:\mathrm{september}\:\mathrm{11}\:\mathrm{terrorist}\:\mathrm{attack}?\right. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help},\:\mathrm{i}'\mathrm{m}\:\mathrm{having}\:\mathrm{27175days},\: \\ $$$$\mathrm{which}\:\mathrm{apparently}\:\mathrm{isn}'\mathrm{t}\:\mathrm{correct}. \\ $$

Question Number 99824    Answers: 1   Comments: 0

calculate ∫_0 ^1 xe^(βˆ’x^2 ) arctan((2/x))dx

$$\mathrm{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{xe}^{βˆ’\mathrm{x}^{\mathrm{2}} } \mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 99822    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((ch(sinx))/((x^2 +3)^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ch}\left(\mathrm{sinx}\right)}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 99820    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((x^2 dx)/((x^4 βˆ’x^2 +1)^2 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} βˆ’\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 99819    Answers: 0   Comments: 0

sove sinx y^β€² βˆ’cos(2x)y =xe^(βˆ’x)

$$\mathrm{sove}\:\:\mathrm{sinx}\:\mathrm{y}^{'} \:βˆ’\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{y}\:=\mathrm{xe}^{βˆ’\mathrm{x}} \\ $$

Question Number 99818    Answers: 2   Comments: 0

∫_0 ^1 ln(1+(1/(n^2 x^2 )))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx} \\ $$

Question Number 99807    Answers: 3   Comments: 0

Question Number 99804    Answers: 0   Comments: 3

Determine x,y ∈ Z such that 1+2^x +2^(2x+1) = y^2

$${Determine}\:{x},{y}\:\in\:\mathbb{Z}\:{such}\:{that}\: \\ $$$$\mathrm{1}+\mathrm{2}^{{x}} \:+\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} \:=\:{y}^{\mathrm{2}} \: \\ $$

Question Number 99803    Answers: 2   Comments: 0

Π_(k=1) ^∞ (1+(1/k^2 ))=? helpe me

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\right)=? \\ $$$$\mathrm{helpe}\:\mathrm{me} \\ $$

Question Number 99796    Answers: 1   Comments: 0

Question Number 99793    Answers: 0   Comments: 4

lim_(nβ†’βˆž) (1(2(3(4(5(6(....(n.)^(1/2) ..)^(1/2) )^(1/2) )^(1/2) )^(1/2) )^(1/2) )^(1/2) =?

$$\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{m}}}\:\left(\mathrm{1}\left(\mathrm{2}\left(\mathrm{3}\left(\mathrm{4}\left(\mathrm{5}\left(\mathrm{6}\left(....\left(\mathrm{n}.\right)^{\frac{\mathrm{1}}{\mathrm{2}}} ..\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =?\:\:\:\right. \\ $$

Question Number 99789    Answers: 0   Comments: 2

{ ((2^x .3^y = 6)),((3^x .4^y = 12)) :}

$$\begin{cases}{\mathrm{2}^{{x}} .\mathrm{3}^{{y}} \:=\:\mathrm{6}}\\{\mathrm{3}^{{x}} .\mathrm{4}^{{y}} \:=\:\mathrm{12}}\end{cases} \\ $$

Question Number 99779    Answers: 1   Comments: 2

Question Number 99772    Answers: 0   Comments: 13

Apk file for upcoming version with shape editing is available.

$$\mathrm{Apk}\:\mathrm{file}\:\mathrm{for}\:\mathrm{upcoming}\:\mathrm{version} \\ $$$$\mathrm{with}\:\mathrm{shape}\:\mathrm{editing}\:\mathrm{is}\:\mathrm{available}. \\ $$

Question Number 99761    Answers: 1   Comments: 2

Question Number 99766    Answers: 0   Comments: 3

my Quistion represnt these number on the number line (1)7/4 (2)βˆ’5/6

$${my}\:{Quistion} \\ $$$${represnt}\:{these}\:{number}\:\:{on}\:\:{the}\:{number}\:\:{line}\:\left(\mathrm{1}\right)\mathrm{7}/\mathrm{4}\:\left(\mathrm{2}\right)βˆ’\mathrm{5}/\mathrm{6} \\ $$

Question Number 99744    Answers: 1   Comments: 0

A wire that is highly insulated has a radius of 2.1 mm and a current of 6 Agoes through it. The material used in insulation has thickness of 2.1 mm with a thermal conductivity of 0.2 W/Km. the material used in constructing the wire has a resistivity of 4.2 Γ— 10^(βˆ’7) Ξ©m. assume the the materials reach steady state. Find the difference in temperature between the outer suface and inner surface.

$$\mathrm{A}\:\mathrm{wire}\:\mathrm{that}\:\mathrm{is}\:\mathrm{highly}\:\mathrm{insulated}\:\mathrm{has}\:\mathrm{a}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current} \\ $$$$\mathrm{of}\:\mathrm{6}\:\mathrm{Agoes}\:\mathrm{through}\:\mathrm{it}.\:\mathrm{The}\:\mathrm{material}\:\mathrm{used}\:\mathrm{in}\:\mathrm{insulation}\:\mathrm{has}\:\mathrm{thickness} \\ $$$$\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{with}\:\mathrm{a}\:\mathrm{thermal}\:\mathrm{conductivity}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{W}/\mathrm{Km}.\:\mathrm{the}\:\mathrm{material}\:\mathrm{used} \\ $$$$\mathrm{in}\:\mathrm{constructing}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{a}\:\mathrm{resistivity}\:\mathrm{of}\:\mathrm{4}.\mathrm{2}\:Γ—\:\mathrm{10}^{βˆ’\mathrm{7}} \Omega\mathrm{m}.\:\mathrm{assume}\:\mathrm{the}\: \\ $$$$\mathrm{the}\:\mathrm{materials}\:\mathrm{reach}\:\mathrm{steady}\:\mathrm{state}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{in}\:\mathrm{temperature} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{outer}\:\mathrm{suface}\:\mathrm{and}\:\mathrm{inner}\:\mathrm{surface}. \\ $$

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