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Question Number 217238 Answers: 0 Comments: 0

Question Number 217235 Answers: 1 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: 2 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 217191 Answers: 1 Comments: 0

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

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

Question Number 217190 Answers: 2 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: 2 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: 2 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: 2 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.

Question Number 217101 Answers: 0 Comments: 0

is this right when (a+bi)^(c+di) =∣a+bi∣^(c+di) e^(i(c+di)arg(a+bi)) ? I had let arg(a+bi)= { ((tan^(−1) ((b/a))),(a≥0 and b≥0)),((π−tan^(−1) (−(b/a))),(a<0 and b≥0)),((−(π−tan^(−1) ((b/a)))),(a<0 and b<0)),((−tan^(−1) ((b/a))),(a≥0 and b<0)) :} before I solved it (a+bi)^(c+di) =∣a+bi∣^(c+di) e^(i(c+di)arg(a+bi)) =∣a+bi∣^c ∣a+bi∣^di e^(ic∙arg(a+bi)) e^(−d∙arg(a+bi)) =∣a+bi∣^c (c^di )^(ln∣a+bi∣) e^(ic∙arg(a+bi)) e^(−d∙arg(a+bi))

$$\mathrm{is}\:\mathrm{this}\:\mathrm{right}\:\mathrm{when}\:\left({a}+{bi}\right)^{{c}+{di}} =\mid{a}+{bi}\mid^{{c}+{di}} {e}^{{i}\left({c}+{di}\right)\mathrm{arg}\left({a}+{bi}\right)} ? \\ $$$$\mathrm{I}\:\mathrm{had}\:\mathrm{let}\:\mathrm{arg}\left({a}+{bi}\right)=\begin{cases}{\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{{a}}\right)}&{{a}\geqslant\mathrm{0}\:\mathrm{and}\:{b}\geqslant\mathrm{0}}\\{\pi−\mathrm{tan}^{−\mathrm{1}} \left(−\frac{{b}}{{a}}\right)}&{{a}<\mathrm{0}\:\mathrm{and}\:{b}\geqslant\mathrm{0}}\\{−\left(\pi−\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{{a}}\right)\right)}&{{a}<\mathrm{0}\:\mathrm{and}\:{b}<\mathrm{0}}\\{−\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{{a}}\right)}&{{a}\geqslant\mathrm{0}\:\mathrm{and}\:{b}<\mathrm{0}}\end{cases}\:\mathrm{before}\:\mathrm{I}\:\mathrm{solved}\:\mathrm{it} \\ $$$$\left({a}+{bi}\right)^{{c}+{di}} =\mid{a}+{bi}\mid^{{c}+{di}} {e}^{{i}\left({c}+{di}\right)\mathrm{arg}\left({a}+{bi}\right)} \\ $$$$=\mid{a}+{bi}\mid^{{c}} \mid{a}+{bi}\mid^{{di}} {e}^{{ic}\centerdot\mathrm{arg}\left({a}+{bi}\right)} {e}^{−{d}\centerdot\mathrm{arg}\left({a}+{bi}\right)} \\ $$$$=\mid{a}+{bi}\mid^{{c}} \left({c}^{{di}} \right)^{\mathrm{ln}\mid{a}+{bi}\mid} {e}^{{ic}\centerdot\mathrm{arg}\left({a}+{bi}\right)} {e}^{−{d}\centerdot\mathrm{arg}\left({a}+{bi}\right)} \\ $$

Question Number 217122 Answers: 1 Comments: 0

∫ ((√(cos 2x))/(cos x)) dx =?

$$\:\:\:\:\:\int\:\frac{\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 217121 Answers: 0 Comments: 0

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