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Question Number 115771 Answers: 2 Comments: 0

y′′−y′−2y=e^(2x) .cos^2 x

$${y}''−{y}'−\mathrm{2}{y}={e}^{\mathrm{2}{x}} .\mathrm{cos}\:^{\mathrm{2}} {x} \\ $$

Question Number 115769 Answers: 1 Comments: 0

There are 3 teachers and 6 students who will sit on the 9 available seats. many arrangements they sit if each teacher is flanked by 2 students

$${There}\:{are}\:\mathrm{3}\:{teachers}\:{and}\:\mathrm{6}\:{students} \\ $$$${who}\:{will}\:{sit}\:{on}\:{the}\:\mathrm{9}\:{available}\:{seats}.\:{many} \\ $$$${arrangements}\:{they}\:{sit}\:{if}\:{each}\: \\ $$$${teacher}\:{is}\:{flanked}\:{by}\:\mathrm{2}\:{students} \\ $$

Question Number 115765 Answers: 1 Comments: 3

Show that sin (α + β) = sin α cos β + cos α sin β.

$$\: \\ $$$$\:\:\:\mathrm{Show}\:\mathrm{that}\:\mathrm{sin}\:\left(\alpha\:+\:\beta\right)\:=\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta\:+\:\mathrm{cos}\:\alpha\:\mathrm{sin}\:\beta. \\ $$

Question Number 115761 Answers: 2 Comments: 1

.... advanced calculus... ... evaluate ... Ψ= ∫_(−∞) ^( +∞) ((x/(2+2^(−x) +2^x )))^2 dx =??? m.n.july 70

$$\:\:\:\:\:\:....\:\:\:{advanced}\:\:{calculus}...\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:...\:\:\:{evaluate}\:...\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\:\int_{−\infty} ^{\:+\infty} \left(\frac{{x}}{\mathrm{2}+\mathrm{2}^{−{x}} +\mathrm{2}^{{x}} }\right)^{\mathrm{2}} {dx}\:=??? \\ $$$$\:{m}.{n}.{july}\:\mathrm{70} \\ $$$$ \\ $$

Question Number 115830 Answers: 0 Comments: 1

create the differention equation from x^2 +y^2 +2ax+2by+c=0

$${create}\:{the}\:{differention}\:{equation}\:{from} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{ax}+\mathrm{2}{by}+{c}=\mathrm{0} \\ $$

Question Number 115829 Answers: 1 Comments: 0

prove that (y−c)^2 =cx its solution of the differention equation 4xy^(′′) +2xy^′ −y=0 (m.o)

$${prove}\:{that}\:\left({y}−{c}\right)^{\mathrm{2}} ={cx}\:{its}\:{solution}\:{of}\:{the}\:{differention}\:{equation}\:\mathrm{4}{xy}^{''} +\mathrm{2}{xy}^{'} −{y}=\mathrm{0} \\ $$$$\left({m}.{o}\right) \\ $$

Question Number 115750 Answers: 4 Comments: 0

Question Number 115743 Answers: 3 Comments: 0

∫ e^(ax) .sin bx dx =? by complex number

$$\int\:{e}^{{ax}} .\mathrm{sin}\:{bx}\:{dx}\:=? \\ $$$${by}\:{complex}\:{number} \\ $$

Question Number 115742 Answers: 1 Comments: 0

what the cooefficient of x^(10) from (1+x)×(1+2x^2 )×(1+3x^3 )×...×(1+2020x^(2020) )

$${what}\:{the}\:{cooefficient}\:{of}\:{x}^{\mathrm{10}} \:{from} \\ $$$$\left(\mathrm{1}+{x}\right)×\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)×\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right)×...×\left(\mathrm{1}+\mathrm{2020}{x}^{\mathrm{2020}} \right) \\ $$

Question Number 115736 Answers: 2 Comments: 0

Question Number 115733 Answers: 3 Comments: 0

Given xy =(1/3) for x,y∈R find min value of (4/x^6 )+(9/y^6 )

$${Given}\:{xy}\:=\frac{\mathrm{1}}{\mathrm{3}}\:{for}\:{x},{y}\in\mathbb{R}\: \\ $$$${find}\:{min}\:{value}\:{of}\:\frac{\mathrm{4}}{{x}^{\mathrm{6}} }+\frac{\mathrm{9}}{{y}^{\mathrm{6}} } \\ $$

Question Number 115732 Answers: 0 Comments: 1

Question Number 115725 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((lnx)/((x^(2 ) +x+2)^2 ))dx

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

Question Number 115721 Answers: 2 Comments: 4

(D^2 −6D+9)y = (e^(3x) /x^2 )

$$\left({D}^{\mathrm{2}} −\mathrm{6}{D}+\mathrm{9}\right){y}\:=\:\frac{{e}^{\mathrm{3}{x}} }{{x}^{\mathrm{2}} } \\ $$

Question Number 115714 Answers: 0 Comments: 1

Question Number 115706 Answers: 1 Comments: 3

the area of a square, A(t) is increased at a rate equal to its perimeter write a differential equation that A(t) satisfy , starting from (dA/dt) =

$$\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square},\:{A}\left({t}\right)\:\mathrm{is}\:\mathrm{increased} \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{its}\:\mathrm{perimeter} \\ $$$$\mathrm{write}\:\mathrm{a}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{that}\:{A}\left({t}\right) \\ $$$$\mathrm{satisfy}\:,\:\mathrm{starting}\:\mathrm{from}\:\frac{{dA}}{{dt}}\:= \\ $$

Question Number 115705 Answers: 1 Comments: 0

... nice math ... find :: Φ=∫_0 ^( ∞) (sin(x)−cos(x) )ln(x)dx=???

$$\:\:\:\:\:...\:{nice}\:\:\:{math}\:... \\ $$$$ \\ $$$$\:\:\:\:{find}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\Phi=\int_{\mathrm{0}} ^{\:\infty} \left({sin}\left({x}\right)−{cos}\left({x}\right)\:\right){ln}\left({x}\right){dx}=??? \\ $$$$ \\ $$

Question Number 115711 Answers: 2 Comments: 0

Find the value of x:- x^x =𝛑

$${Find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{x}}:- \\ $$$$\boldsymbol{{x}}^{\boldsymbol{{x}}} =\boldsymbol{\pi} \\ $$

Question Number 115696 Answers: 0 Comments: 4

e^x =logx

$$\mathrm{e}^{\mathrm{x}} =\mathrm{logx} \\ $$

Question Number 115695 Answers: 2 Comments: 0

The product of all the solutions of the equation ∣(x−2)^2 ∣−3∣x−2∣+2=0 is

$$\mathrm{The}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\:\mid\left({x}−\mathrm{2}\right)^{\mathrm{2}} \mid−\mathrm{3}\mid{x}−\mathrm{2}\mid+\mathrm{2}=\mathrm{0}\:\:\mathrm{is} \\ $$

Question Number 115689 Answers: 1 Comments: 0

Question Number 115685 Answers: 1 Comments: 0

If α, β, γ, δ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k, then the value of 4 sin (α/2)+3 sin (β/2)+2 sin (γ/2)+sin (δ/2) is equal to

$$\mathrm{If}\:\:\alpha,\:\beta,\:\gamma,\:\delta\:\:\mathrm{are}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\: \\ $$$$\mathrm{angles}\:\mathrm{in}\:\mathrm{ascending}\:\mathrm{order}\:\mathrm{of} \\ $$$$\mathrm{magnitude}\:\mathrm{which}\:\mathrm{have}\:\mathrm{their}\:\mathrm{sines}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{quantity}\:{k},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{4}\:\mathrm{sin}\:\frac{\alpha}{\mathrm{2}}+\mathrm{3}\:\mathrm{sin}\:\frac{\beta}{\mathrm{2}}+\mathrm{2}\:\mathrm{sin}\:\frac{\gamma}{\mathrm{2}}+\mathrm{sin}\:\frac{\delta}{\mathrm{2}}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 115674 Answers: 1 Comments: 0

Solve for x x ≡ 1 mod 3 x ≡ 4 mod 5 x ≡ 6 mod 7

$${Solve}\:\:{for}\:\:{x} \\ $$$$\:\:\:\:\:\:{x}\:\:\equiv\:\:\mathrm{1}\:\:{mod}\:\:\mathrm{3} \\ $$$$\:\:\:\:\:\:{x}\:\:\equiv\:\:\mathrm{4}\:\:{mod}\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:{x}\:\:\equiv\:\:\mathrm{6}\:\:{mod}\:\:\mathrm{7} \\ $$

Question Number 115664 Answers: 2 Comments: 0

If lim_(x→p) ((p^x −x^p )/(x^x −p^p )) = 1 then p = ?

$${If}\:\underset{{x}\rightarrow{p}} {\mathrm{lim}}\:\frac{{p}^{{x}} −{x}^{{p}} }{{x}^{{x}} −{p}^{{p}} }\:=\:\mathrm{1}\:{then}\:{p}\:=\:? \\ $$

Question Number 115661 Answers: 2 Comments: 0

(1) ∫ sin ((√x)) dx (2) ∫ cos ((√x) ) dx (3) ∫ tan ((√x) ) dx

$$\left(\mathrm{1}\right)\:\int\:\mathrm{sin}\:\left(\sqrt{{x}}\right)\:{dx} \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{cos}\:\left(\sqrt{{x}}\:\right)\:{dx}\: \\ $$$$\left(\mathrm{3}\right)\:\int\:\mathrm{tan}\:\left(\sqrt{{x}}\:\right)\:{dx}\: \\ $$

Question Number 115683 Answers: 1 Comments: 0

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