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Question Number 77221 Answers: 2 Comments: 0

∫ (((√(2+x)) dx)/(√x^5 )) = ?

$$\int\:\frac{\sqrt{\mathrm{2}+{x}}\:{dx}}{\sqrt{{x}^{\mathrm{5}} }}\:=\:? \\ $$

Question Number 77219 Answers: 1 Comments: 0

if log_9 (a)=log_4 (a+b)=log_6 (b) what is (a/b) ?

$${if}\:\mathrm{log}_{\mathrm{9}} \left({a}\right)=\mathrm{log}_{\mathrm{4}} \left({a}+{b}\right)=\mathrm{log}_{\mathrm{6}} \left({b}\right)\: \\ $$$${what}\:{is}\:\frac{{a}}{{b}}\:? \\ $$

Question Number 77218 Answers: 1 Comments: 0

what is solution in R ((sin (x)−∣x+2∣)/(x^2 −4x−5))≥0 ?

$${what}\:{is}\:{solution}\:{in}\:\mathbb{R}\: \\ $$$$\frac{\mathrm{sin}\:\left({x}\right)−\mid{x}+\mathrm{2}\mid}{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}}\geqslant\mathrm{0}\:?\: \\ $$

Question Number 77216 Answers: 0 Comments: 0

Question Number 77213 Answers: 0 Comments: 3

Question Number 77208 Answers: 0 Comments: 1

some thoughts on this forum... we cannot solve the unanswered questions much greater mathematicians haven′t been able to solve yet thus it makes absolutely no sense to post them here also it makes no sense to post problems from books or from the www if you don′t have the foggiest idea of their meaning or how to solve them. it might be fun for us to solve some of them but mostly it′s like casting pearls...

$$\mathrm{some}\:\mathrm{thoughts}\:\mathrm{on}\:\mathrm{this}\:\mathrm{forum}... \\ $$$$\mathrm{we}\:\mathrm{cannot}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{unanswered}\:\mathrm{questions} \\ $$$$\mathrm{much}\:\mathrm{greater}\:\mathrm{mathematicians}\:\mathrm{haven}'\mathrm{t}\:\mathrm{been} \\ $$$$\mathrm{able}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{yet} \\ $$$$\mathrm{thus}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{absolutely}\:\mathrm{no}\:\mathrm{sense}\:\mathrm{to}\:\mathrm{post} \\ $$$$\mathrm{them}\:\mathrm{here} \\ $$$$\mathrm{also}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{no}\:\mathrm{sense}\:\mathrm{to}\:\mathrm{post}\:\mathrm{problems}\:\mathrm{from} \\ $$$$\mathrm{books}\:\mathrm{or}\:\mathrm{from}\:\mathrm{the}\:\mathrm{www}\:\mathrm{if}\:\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{the} \\ $$$$\mathrm{foggiest}\:\mathrm{idea}\:\mathrm{of}\:\mathrm{their}\:\mathrm{meaning}\:\mathrm{or}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\mathrm{them}.\:\mathrm{it}\:\mathrm{might}\:\mathrm{be}\:\mathrm{fun}\:\mathrm{for}\:\mathrm{us}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{some}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{but}\:\mathrm{mostly}\:\mathrm{it}'\mathrm{s}\:\mathrm{like}\:\mathrm{casting}\:\mathrm{pearls}... \\ $$

Question Number 77204 Answers: 0 Comments: 2

is there a general solution for the equation x[x[x[x...]]]_(n times x) =m with x>0, m>0.

$${is}\:{there}\:{a}\:{general}\:{solution}\:{for} \\ $$$${the}\:{equation} \\ $$$$\underset{{n}\:{times}\:{x}} {\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}...\right]\right]\right]}=\boldsymbol{{m}} \\ $$$${with}\:{x}>\mathrm{0},\:{m}>\mathrm{0}. \\ $$

Question Number 77199 Answers: 0 Comments: 4

Question Number 77234 Answers: 1 Comments: 0

Question Number 77186 Answers: 1 Comments: 0

given { ((3^y −1= (6/2^x ))),(((3)^(y/x) = 2 )) :} find (1/x)+(1/y).

$$\mathrm{given}\: \\ $$$$\begin{cases}{\mathrm{3}^{\mathrm{y}} −\mathrm{1}=\:\frac{\mathrm{6}}{\mathrm{2}^{\mathrm{x}} }}\\{\left(\mathrm{3}\right)^{\frac{\mathrm{y}}{\mathrm{x}}} \:=\:\mathrm{2}\:}\end{cases}\:\:\mathrm{find}\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}. \\ $$

Question Number 77183 Answers: 1 Comments: 0

what is x satisfy inequality 3^x^2 × 5^(x−1) ≥ 3

$$\mathrm{what}\:\mathrm{is}\:\mathrm{x}\: \\ $$$$\mathrm{satisfy}\:\mathrm{inequality}\: \\ $$$$\mathrm{3}^{\mathrm{x}^{\mathrm{2}} } ×\:\mathrm{5}^{\mathrm{x}−\mathrm{1}} \:\geqslant\:\mathrm{3} \\ $$

Question Number 77182 Answers: 1 Comments: 1

evaluate lim_(x→0) ((∫_a ^x (((cos t)/t))dt)/x) .

$$ \\ $$$$ \\ $$$$\mathrm{evaluate}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\underset{\mathrm{a}} {\overset{\mathrm{x}} {\int}}\left(\frac{\mathrm{cos}\:\mathrm{t}}{\mathrm{t}}\right)\mathrm{dt}}{\mathrm{x}}\:. \\ $$

Question Number 77180 Answers: 1 Comments: 0

given a quadratic equation 3x^2 −x+(t^2 −4t+3)=0 has roots sin α and cos α. find the value (√(t^2 −4t+5)) .

$$ \\ $$$$ \\ $$$$\mathrm{given}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}+\left(\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{3}\right)=\mathrm{0}\:\mathrm{has} \\ $$$$\mathrm{roots}\:\mathrm{sin}\:\alpha\:\mathrm{and}\:\mathrm{cos}\:\alpha.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\sqrt{\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{5}}\:. \\ $$

Question Number 77178 Answers: 1 Comments: 0

given cos^(−1) (x)+cos^(−1) (y)+cos^(−1) (z)=π and x+y+z=(3/2) prove that x = y = z .

$$ \\ $$$${given}\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)+\mathrm{cos}^{−\mathrm{1}} \left({y}\right)+\mathrm{cos}^{−\mathrm{1}} \left({z}\right)=\pi \\ $$$${and}\:{x}+{y}+{z}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${prove}\:{that}\:{x}\:=\:{y}\:=\:{z}\:. \\ $$

Question Number 77164 Answers: 1 Comments: 2

Question Number 77160 Answers: 1 Comments: 1

Question Number 77158 Answers: 0 Comments: 4

∫_(−2) ^( 2) (x^3 cos(x/2) + (1/2))(√(4 − x^2 )) dx

$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{3}} \:\mathrm{cos}\frac{\mathrm{x}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 77154 Answers: 0 Comments: 6

Question Number 77149 Answers: 0 Comments: 2

Any reference to a book or video that coould help me solve Differential equations? please help

$$\mathrm{Any}\:\mathrm{reference}\:\mathrm{to}\:\mathrm{a}\:\mathrm{book}\:\mathrm{or}\:\mathrm{video} \\ $$$$\mathrm{that}\:\mathrm{coould}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{Differential}\:\mathrm{equations}?\: \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 77147 Answers: 0 Comments: 1

Σ_(r=1) ^∞ (1/r^k ) is divergent for: A. k ≤ 1 B. k > 2 C. k ≤ 2 D. 0 ≤ k < 2

$$\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{r}^{{k}} }\:{is}\:{divergent}\:{for}: \\ $$$${A}.\:{k}\:\leqslant\:\mathrm{1} \\ $$$${B}.\:{k}\:>\:\mathrm{2} \\ $$$${C}.\:{k}\:\leqslant\:\mathrm{2} \\ $$$${D}.\:\mathrm{0}\:\leqslant\:{k}\:<\:\mathrm{2} \\ $$

Question Number 77144 Answers: 1 Comments: 2

Question Number 77143 Answers: 1 Comments: 2

Question Number 77132 Answers: 0 Comments: 1

Question Number 77129 Answers: 1 Comments: 0

solve in R ∣tan2x∣−(√3)≥0

$$\mathrm{solve}\:\mathrm{in}\:\mathrm{R} \\ $$$$\mid\mathrm{tan2}{x}\mid−\sqrt{\mathrm{3}}\geqslant\mathrm{0} \\ $$

Question Number 77128 Answers: 2 Comments: 0

Find the value of constant “a” such that axe^(−x ) is a solution of Differential equation (d^2 y/dx^2 )+3(dy/dx)+2y=2e^(−x) solve D.E for which y=1 and (dy/dx)=3 when x=0

$${Find}\:{the}\:{value}\:{of}\:{constant} \\ $$$$``{a}''\:{such}\:{that}\:{axe}^{−{x}\:} {is} \\ $$$${a}\:{solution}\:{of}\:{Differential} \\ $$$${equation} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{3}\frac{{dy}}{{dx}}+\mathrm{2}{y}=\mathrm{2}{e}^{−{x}} \\ $$$${solve}\:{D}.{E}\:{for}\:\:{which} \\ $$$${y}=\mathrm{1}\:{and}\:\frac{{dy}}{{dx}}=\mathrm{3}\:{when} \\ $$$${x}=\mathrm{0} \\ $$

Question Number 77127 Answers: 2 Comments: 0

Prove that line lx+my+n=0 is tangent to the ellipse (x^2 /a^2 )+(y^2 /b^(2 ) )=1 if a^2 l^2 +b^2 m^2 =n^2

$${Prove}\:{that}\:{line}\:{lx}+{my}+{n}=\mathrm{0} \\ $$$${is}\:{tangent}\:{to}\:{the}\:{ellipse} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}\:} }=\mathrm{1}\:{if}\:{a}^{\mathrm{2}} {l}^{\mathrm{2}} +{b}^{\mathrm{2}} {m}^{\mathrm{2}} ={n}^{\mathrm{2}} \\ $$

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