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Question Number 217245 Answers: 1 Comments: 0

find the following differential equation by eliminating the arbritrary constant (1)y=Ae^x +Bcosx (2) xy=Ae^x +Be^(−x) +x^2

$${find}\:{the}\:{following}\:{differential}\:{equation}\: \\ $$$${by}\:{eliminating}\:{the}\:{arbritrary}\:{constant} \\ $$$$\left(\mathrm{1}\right){y}={Ae}^{{x}} +{Bcosx} \\ $$$$\left(\mathrm{2}\right)\:{xy}={Ae}^{{x}} +{Be}^{−{x}} +{x}^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 217238 Answers: 2 Comments: 0

Question Number 217235 Answers: 3 Comments: 0

∫_( 0) ^( 1) ((x ln^2 (x))/(1 + x^2 )) dx

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

Question Number 217228 Answers: 3 Comments: 0

Question Number 217225 Answers: 1 Comments: 0

Find: ∫ − (dx/( (√(24x − 16x^2 − 8)))) = ?

$$\mathrm{Find}:\:\:\:\:\:\int\:−\:\frac{{d}\mathrm{x}}{\:\sqrt{\mathrm{24x}\:−\:\mathrm{16x}^{\mathrm{2}} \:−\:\mathrm{8}}}\:=\:? \\ $$

Question Number 217219 Answers: 1 Comments: 0

calculate determinant ((( L ( ∫_1 ^( ∞) (( e^( −tx) )/x)dx ) =_(transfom) ^(laplace) ? ; t>0 )))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{calculate} \\ $$$$\begin{array}{|c|}{\:\:\mathscr{L}\:\:\left(\:\int_{\mathrm{1}} ^{\:\infty} \frac{\:\mathrm{e}^{\:−{tx}} }{{x}}{dx}\:\right)\:\underset{\mathrm{transfom}} {\overset{\mathrm{laplace}} {=}}?\:\:;\:\:{t}>\mathrm{0}\:}\\\hline\end{array} \\ $$$$ \\ $$$$\:\:\: \\ $$

Question Number 217211 Answers: 1 Comments: 0

a nice one: prove ∫_0 ^1 (√(−((ln t)/t))) dt=(√(2π))

$$\mathrm{a}\:\mathrm{nice}\:\mathrm{one}: \\ $$$$\mathrm{prove}\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{−\frac{\mathrm{ln}\:{t}}{{t}}}\:{dt}=\sqrt{\mathrm{2}\pi} \\ $$

Question Number 217205 Answers: 1 Comments: 0

Question Number 217203 Answers: 2 Comments: 0

A farmer has 100 meters of fencing and wants to enclose an rectagular field along a river. Thei rver forms one side of the rectangle so fencing is needed onlyo for the other three sides. What dimesions should the farmer chooseto maximize the enclosed area?

$$\mathrm{A}\:\mathrm{farmer}\:\mathrm{has}\:\mathrm{100}\:\mathrm{meters}\:\mathrm{of}\: \\ $$$$\mathrm{fencing}\:\mathrm{and}\:\mathrm{wants}\:\mathrm{to}\:\mathrm{enclose}\:\mathrm{an} \\ $$$$\mathrm{rectagular}\:\mathrm{field}\:\mathrm{along}\:\mathrm{a}\:\mathrm{river}.\:\mathrm{Thei} \\ $$$$\mathrm{rver}\:\mathrm{forms}\:\mathrm{one}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{rectangle}\:\mathrm{so}\:\mathrm{fencing}\:\mathrm{is}\:\mathrm{needed}\:\mathrm{onlyo} \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{other}\:\mathrm{three}\:\mathrm{sides}.\:\mathrm{What}\: \\ $$$$\mathrm{dimesions}\:\mathrm{should}\:\mathrm{the}\:\mathrm{farmer}\: \\ $$$$\mathrm{chooseto}\:\mathrm{maximize}\:\mathrm{the}\:\mathrm{enclosed} \\ $$$$\mathrm{area}? \\ $$

Question Number 217199 Answers: 2 Comments: 1

Question Number 217198 Answers: 1 Comments: 0

Question Number 217197 Answers: 1 Comments: 0

Find: ((−32))^(1/5) + (((−3)^8 ))^(1/8) = ?

$$\mathrm{Find}: \\ $$$$\sqrt[{\mathrm{5}}]{−\mathrm{32}}\:\:+\:\:\sqrt[{\mathrm{8}}]{\left(−\mathrm{3}\right)^{\mathrm{8}} }\:\:=\:\:? \\ $$

Question Number 217244 Answers: 1 Comments: 0

Find all two-digit numbers such that when the number is divided by the sum of its digits the quotient is 4 and the remainder is 3.

$$\:\mathrm{Find}\:\mathrm{all}\:\mathrm{two}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its}\:\mathrm{digits}\:\mathrm{the}\:\mathrm{quotient}\: \\ $$$$\mathrm{is}\:\mathrm{4}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{3}. \\ $$

Question Number 217262 Answers: 2 Comments: 0

Solve: ((x^2 +3x)/(x^3 −4x))−(2/(x^2 +2x))=(1/(x−2))

$${Solve}: \\ $$$$\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{4}{x}}−\frac{\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{2}{x}}=\frac{\mathrm{1}}{{x}−\mathrm{2}} \\ $$

Question Number 217191 Answers: 1 Comments: 0

(a/b)+(b/a)=1

$$\:\frac{{a}}{{b}}+\frac{{b}}{{a}}=\mathrm{1} \\ $$

Question Number 217190 Answers: 1 Comments: 0

Given a_(n+1) = a_n + a_(n+2) where a_3 = 4 and a_5 = 6 find a_n .

$$\mathrm{Given}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} \:+\:\mathrm{a}_{\mathrm{n}+\mathrm{2}} \: \\ $$$$\:\:\mathrm{where}\:\mathrm{a}_{\mathrm{3}} =\:\mathrm{4}\:\mathrm{and}\:\mathrm{a}_{\mathrm{5}} =\:\mathrm{6} \\ $$$$\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \:. \\ $$

Question Number 217186 Answers: 3 Comments: 0

((x−4051)/(2024))+((x−4050)/(2025))+((x−4049)/(2026))=3

$$\frac{{x}−\mathrm{4051}}{\mathrm{2024}}+\frac{{x}−\mathrm{4050}}{\mathrm{2025}}+\frac{{x}−\mathrm{4049}}{\mathrm{2026}}=\mathrm{3} \\ $$

Question Number 217178 Answers: 2 Comments: 0

Find: 100-99+98-97+96-95+...+2-1 = ?

$$\mathrm{Find}: \\ $$$$\mathrm{100}-\mathrm{99}+\mathrm{98}-\mathrm{97}+\mathrm{96}-\mathrm{95}+...+\mathrm{2}-\mathrm{1}\:=\:? \\ $$

Question Number 217164 Answers: 1 Comments: 0

Question Number 217163 Answers: 2 Comments: 0

If a+b=b+c=4 find: a^2 −b^2 −8c = ?

$$\mathrm{If}\:\:\:\mathrm{a}+\mathrm{b}=\mathrm{b}+\mathrm{c}=\mathrm{4} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{8c}\:=\:? \\ $$

Question Number 217159 Answers: 3 Comments: 0

Solve for x: ((x+3)/(x−2))+((2x−5)/(x+4))=((4x+1)/(x^2 +2x−8))

$${Solve}\:{for}\:{x}: \\ $$$$\frac{{x}+\mathrm{3}}{{x}−\mathrm{2}}+\frac{\mathrm{2}{x}−\mathrm{5}}{{x}+\mathrm{4}}=\frac{\mathrm{4}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{8}} \\ $$

Question Number 217158 Answers: 1 Comments: 0

circle= (x−3)^2 +(y−4)^2 =1 parabola= ax(x−10)=y what is the values of a where the parabola is tangent to the circle

$$\mathrm{circle}= \\ $$$$\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({y}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{parabola}= \\ $$$${ax}\left({x}−\mathrm{10}\right)={y} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a}\:\mathrm{where} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\mathrm{is}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{circle} \\ $$$$ \\ $$

Question Number 217149 Answers: 1 Comments: 0

Question Number 217148 Answers: 2 Comments: 0

I have seen a relationship in the curve path of a thrown object at β while the total passed distance D_v and highest point had passedD_u then β = arctan(((4D_u )/D_v )) but cant find the proof. I would like to say would anyone like to proove it?then please.

$${I}\:{have}\:{seen}\:{a}\:{relationship}\:{in}\:{the}\:{curve} \\ $$$${path}\:{of}\:{a}\:{thrown}\:{object}\:{at}\:\beta\: \\ $$$${while}\:{the}\:{total}\:{passed}\:{distance}\:{D}_{{v}} \:{and} \\ $$$${highest}\:{point}\:{had}\:{passedD}_{{u}} \\ $$$${then}\:\beta\:=\:{arctan}\left(\frac{\mathrm{4}{D}_{{u}} }{{D}_{{v}} }\right) \\ $$$${but}\:{cant}\:{find}\:{the}\:{proof}. \\ $$$${I}\:{would}\:{like}\:{to}\:{say}\:{would}\:{anyone}\:{like} \\ $$$${to}\:{proove}\:{it}?{then}\:{please}. \\ $$

Question Number 217146 Answers: 1 Comments: 1

determiner le cote du care ABCD inscrit dans l elipse {(−3,+3):(−8,+8)}

$$\mathrm{determiner}\:\mathrm{le}\:\mathrm{cote}\:\mathrm{du}\:\mathrm{care}\:\boldsymbol{\mathrm{ABCD}} \\ $$$$\mathrm{inscrit}\:\mathrm{dans}\:\mathrm{l}\:\mathrm{elipse}\:\left\{\left(−\mathrm{3},+\mathrm{3}\right):\left(−\mathrm{8},+\mathrm{8}\right)\right\} \\ $$

Question Number 217140 Answers: 1 Comments: 0

if a, b, c are three digits, abc and bca are two numbers. where abc +cba = 444, b =2. find the value of a+b+c.

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