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Question Number 89977    Answers: 0   Comments: 2

Question Number 89973    Answers: 1   Comments: 1

x (dy/dx) −y = x^2 tan ((y/x))

$${x}\:\frac{{dy}}{{dx}}\:−{y}\:=\:{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{{y}}{{x}}\right)\: \\ $$

Question Number 89970    Answers: 0   Comments: 1

xy (dy/dx) = y^2 ((x^3 /(x^2 +1)))

$$\mathrm{xy}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\: \\ $$

Question Number 89955    Answers: 1   Comments: 2

9^(x+1) ∤28(3^x )+3=0

$$\mathrm{9}^{\mathrm{x}+\mathrm{1}} \nmid\mathrm{28}\left(\mathrm{3}^{\mathrm{x}} \right)+\mathrm{3}=\mathrm{0} \\ $$

Question Number 89953    Answers: 0   Comments: 1

solvethefollowingequation 5^(2x+y) =625and2^(4x∤2y) =(1/6)

$$\mathrm{solvethefollowingequation} \\ $$$$\mathrm{5}^{\mathrm{2x}+\mathrm{y}} =\mathrm{625and2}^{\mathrm{4x}\nmid\mathrm{2y}} =\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Question Number 89951    Answers: 0   Comments: 1

log _2 (sin (x+((5π)/(12)))) + log _2 (sin (x+(π/(12))))=−1

$$\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{sin}\:\left({x}+\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\right)\:+\:\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{12}}\right)\right)=−\mathrm{1} \\ $$

Question Number 89950    Answers: 0   Comments: 1

Question Number 89946    Answers: 1   Comments: 0

∫ _(−(π/2)) ^(π/2) (dx/(1+e^(sin x) ))

$$\int\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\:}}\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} } \\ $$

Question Number 89958    Answers: 0   Comments: 1

prove that (1+sin x/1+cos 3(1sin x/1+cosec x)=tanx

$${prove}\:{that}\:\left(\mathrm{1}+\mathrm{sin}\:{x}/\mathrm{1}+\mathrm{cos}\:\mathrm{3}\left(\mathrm{1sin}\:{x}/\mathrm{1}+\mathrm{cosec}\:{x}\right)={tanx}\right. \\ $$

Question Number 89956    Answers: 0   Comments: 1

simplifyκgivingκyourκanswerκinκindexκform (√((ac^2 )/(9a^2 c^4 )))

$$\mathrm{simplify}\kappa\mathrm{giving}\kappa\mathrm{your}\kappa\mathrm{answer}\kappa\mathrm{in}\kappa\mathrm{index}\kappa\mathrm{form} \\ $$$$\sqrt{\frac{\mathrm{ac}^{\mathrm{2}} }{\mathrm{9a}^{\mathrm{2}} \mathrm{c}^{\mathrm{4}} }} \\ $$

Question Number 89938    Answers: 0   Comments: 1

If x(x+1) = 1 find (x+1)^3 −(1/((x+1)^3 ))

$$\mathrm{If}\:\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{find}\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} −\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 89937    Answers: 0   Comments: 1

Prove that for all complex such as ∣z∣<1= Σ_(n=1) ^∞ (z^n /((z^n −1)^2 )) +Σ_(n=1) ^∞ ((nz^n )/(z^n −1)) = 0

$${Prove}\:{that}\:{for}\:{all}\:{complex}\:{such}\:{as}\:\mid{z}\mid<\mathrm{1}= \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{z}^{{n}} }{\left({z}^{{n}} −\mathrm{1}\right)^{\mathrm{2}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{nz}^{{n}} }{{z}^{{n}} −\mathrm{1}}\:=\:\mathrm{0}\: \\ $$

Question Number 89936    Answers: 1   Comments: 0

Prove that Σ_(p≥1,q≥1) (1/(pq(p+q−1))) =(π^2 /3)

$${Prove}\:{that}\:\underset{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}} {\sum}\:\:\frac{\mathrm{1}}{{pq}\left({p}+{q}−\mathrm{1}\right)}\:=\frac{\pi^{\mathrm{2}} }{\mathrm{3}}\: \\ $$

Question Number 89934    Answers: 0   Comments: 0

Let x∈]0;1[ Prove that Σ_(n=1) ^∞ (x^n /(1+x^n )) +Σ_(n=1) ^∞ (((−x)^n )/(1−x^n )) = 0

$$\left.{Let}\:{x}\in\right]\mathrm{0};\mathrm{1}\left[\:\:{Prove}\:{that}\right. \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{\mathrm{1}−{x}^{{n}} }\:=\:\mathrm{0} \\ $$

Question Number 89928    Answers: 1   Comments: 0

Question Number 89925    Answers: 0   Comments: 0

x^2 (yy′′−y^2 )+xyy′ = y(√(x^2 (y′)^2 +y^2 ))

$${x}^{\mathrm{2}} \left({yy}''−{y}^{\mathrm{2}} \right)+{xyy}'\:=\:{y}\sqrt{{x}^{\mathrm{2}} \left({y}'\right)^{\mathrm{2}} +{y}^{\mathrm{2}} }\: \\ $$

Question Number 89922    Answers: 0   Comments: 2

Question Number 89918    Answers: 0   Comments: 1

∫ ((x tan^(−1) (x))/((1+x^2 )^(3/2) )) dx

$$\int\:\frac{\mathrm{x}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\mathrm{dx}\: \\ $$

Question Number 89913    Answers: 1   Comments: 1

Question Number 89908    Answers: 0   Comments: 6

Solve the differential equstion: (d^2 y/dx^2 ) = ((y_0 − 2y_(−1) + y_(−2) )/h^2 )

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equstion}: \\ $$$$\:\:\:\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:\:=\:\:\:\frac{\mathrm{y}_{\mathrm{0}} \:\:−\:\:\mathrm{2y}_{−\mathrm{1}} \:\:+\:\:\mathrm{y}_{−\mathrm{2}} }{\mathrm{h}^{\mathrm{2}} } \\ $$

Question Number 89907    Answers: 1   Comments: 0

If the sum of 4 numbers is between 53 and 57 then the arithmetic mean of the numbers could be one of the following a)11.5 b)12 c)12.5 d)13 e)14

$${If}\:{the}\:{sum}\:{of}\:\mathrm{4}\:{numbers}\:{is}\:{between} \\ $$$$\mathrm{53}\:{and}\:\mathrm{57}\:{then}\:{the}\:{arithmetic}\:{mean}\:{of} \\ $$$${the}\:{numbers}\:{could}\:{be}\:{one}\:{of}\:{the} \\ $$$${following} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{1}\left..\mathrm{5}\:{b}\right)\mathrm{12}\:{c}\right)\mathrm{12}.\mathrm{5}\:{d}\right)\mathrm{13}\:{e}\right)\mathrm{14} \\ $$

Question Number 89906    Answers: 1   Comments: 0

Show that 2x^7 −4x^4 +4x^2 =6x^6 +3 Has no solution in N

$${Show}\:{that}\: \\ $$$$\mathrm{2}{x}^{\mathrm{7}} −\mathrm{4}{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} =\mathrm{6}{x}^{\mathrm{6}} +\mathrm{3} \\ $$$${Has}\:{no}\:{solution}\:{in}\:\mathbb{N} \\ $$

Question Number 89898    Answers: 0   Comments: 3

In a classroom when the students sit 2 per bench, 11 students are left with no sits. And when they sit 3 per bench 7 benches are left empty. Determine the number of students in this classroom.

$${In}\:{a}\:{classroom}\:{when}\:{the}\:{students}\:{sit} \\ $$$$\mathrm{2}\:{per}\:{bench},\:\mathrm{11}\:{students}\:{are}\:{left}\:{with} \\ $$$${no}\:{sits}.\:{And}\:{when}\:{they}\:{sit}\:\mathrm{3}\:{per}\:{bench} \\ $$$$\mathrm{7}\:{benches}\:{are}\:{left}\:{empty}.\:{Determine}\:{the}\:{number} \\ $$$${of}\:{students}\:{in}\:{this}\:{classroom}. \\ $$

Question Number 89896    Answers: 0   Comments: 4

Question Number 89891    Answers: 0   Comments: 1

calculate ∫_(1/e) ^1 ln(x)ln(1+x)dx

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

Question Number 89882    Answers: 2   Comments: 0

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