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Question Number 168278 Answers: 1 Comments: 2

((log_3 (12))/(log_(36) (3)))−((log_3 (4))/(log_(108) (3))) = x x =

$$\:\:\:\:\:\frac{{log}_{\mathrm{3}} \left(\mathrm{12}\right)}{{log}_{\mathrm{36}} \left(\mathrm{3}\right)}−\frac{{log}_{\mathrm{3}} \left(\mathrm{4}\right)}{{log}_{\mathrm{108}} \left(\mathrm{3}\right)}\:=\:{x} \\ $$$$\:\:\:\:\:{x}\:=\: \\ $$

Question Number 168277 Answers: 0 Comments: 1

Prove that ((sin(((3π)/5)))/(sin(((4π)/5)))) = ((1+(√5))/2)

$$\:\mathrm{Prove}\:\mathrm{that}\:\frac{\mathrm{sin}\left(\frac{\mathrm{3}\pi}{\mathrm{5}}\right)}{\mathrm{sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)}\:=\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\: \\ $$

Question Number 168276 Answers: 3 Comments: 2

y = (√(x+(√(x+(√x))))) y′ =

$$\:\:\:\:{y}\:=\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}} \\ $$$$\:\:\:\:{y}'\:=\: \\ $$$$\:\:\:\:\: \\ $$

Question Number 168274 Answers: 1 Comments: 0

Question Number 168267 Answers: 1 Comments: 0

Solve this integral : ∫(((√(x+1))−1)/( (√(x+1))+1))

$$\:\:\:\:\:\:{Solve}\:\:{this}\:{integral}\:: \\ $$$$\:\:\:\:\:\:\:\int\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{x}+\mathrm{1}}+\mathrm{1}} \\ $$$$ \\ $$

Question Number 168264 Answers: 1 Comments: 0

Question Number 168259 Answers: 1 Comments: 0

If the odds in favour of an event be (1/3).Find the probability of an occurrence of the event.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{odds}\:\mathrm{in}\:\mathrm{favour}\:\mathrm{of}\:\mathrm{an}\:\mathrm{event} \\ $$$$\mathrm{be}\:\frac{\mathrm{1}}{\mathrm{3}}.\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{an}\:\mathrm{occurrence}\:\mathrm{of}\:\mathrm{the}\:\mathrm{event}. \\ $$

Question Number 168256 Answers: 1 Comments: 0

lim_(x→∞) ((n!)/n^n )=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{n}!}{{n}^{{n}} }=? \\ $$

Question Number 168248 Answers: 0 Comments: 1

Question Number 168247 Answers: 2 Comments: 0

Solve for x ((8^x +27^x )/(12^x +18^x ))=(7/6) Mastermind

$${Solve}\:{for}\:{x} \\ $$$$\frac{\mathrm{8}^{{x}} +\mathrm{27}^{{x}} }{\mathrm{12}^{{x}} +\mathrm{18}^{{x}} }=\frac{\mathrm{7}}{\mathrm{6}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168244 Answers: 3 Comments: 0

Question Number 168233 Answers: 1 Comments: 0

{ ((u_0 = 3 : u_1 = 4)),((u_(n+1) = u_n + 6u_(n−1) )) :} Express u_n in terms of n

$$\begin{cases}{{u}_{\mathrm{0}} \:=\:\mathrm{3}\::\:{u}_{\mathrm{1}} \:=\:\mathrm{4}}\\{{u}_{{n}+\mathrm{1}} \:=\:{u}_{{n}} \:+\:\mathrm{6}{u}_{{n}−\mathrm{1}} }\end{cases} \\ $$$${Express}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n} \\ $$

Question Number 168231 Answers: 0 Comments: 4

∫ x (√(1−x^6 )) dx = ?

$$\int\:\:{x}\:\sqrt{\mathrm{1}−{x}^{\mathrm{6}} }\:\:{dx}\:\:=\:\:? \\ $$

Question Number 168229 Answers: 1 Comments: 0

Question Number 168225 Answers: 2 Comments: 0

hi ! x ∈ ](π/4) ; (π/3)[ f (x) = (1/(cos x)) primitive of f(x).

$$\mathrm{hi}\:! \\ $$$$\left.{x}\:\in\:\right]\frac{\pi}{\mathrm{4}}\:;\:\frac{\pi}{\mathrm{3}}\left[\right. \\ $$$${f}\:\left({x}\right)\:=\:\frac{\mathrm{1}}{{cos}\:{x}} \\ $$$$\mathrm{primitive}\:\mathrm{of}\:{f}\left({x}\right). \\ $$

Question Number 168210 Answers: 1 Comments: 0

Question Number 168209 Answers: 0 Comments: 0

Question Number 168208 Answers: 2 Comments: 1

If (x+yi)^4 =a+bi, show that a^2 +b^2 =(x^2 +y^2 )^4

$$\:{If}\:\left({x}+{y}\boldsymbol{{i}}\right)^{\mathrm{4}} ={a}+{b}\boldsymbol{{i}}, \\ $$$$\:{show}\:{that}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{4}} \\ $$

Question Number 168206 Answers: 1 Comments: 0

Question Number 168203 Answers: 1 Comments: 0

Question Number 168198 Answers: 0 Comments: 0

Question Number 168190 Answers: 0 Comments: 5

Question Number 168189 Answers: 1 Comments: 11

Question Number 168188 Answers: 4 Comments: 1

∫ ((1−sin 2x)/((1+sin 2x)^2 )) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$

Question Number 168187 Answers: 2 Comments: 0

Prove that : sinh^(−1) tanθ = log tan((θ/2)+(π/4)) Mastermind

$${Prove}\:{that}\::\: \\ $$$${sinh}^{−\mathrm{1}} {tan}\theta\:=\:{log}\:{tan}\left(\frac{\theta}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168185 Answers: 0 Comments: 0

Separate cos^(−1) e^(iθ) into real and imaginary parts. Mastermind

$${Separate}\:{cos}^{−\mathrm{1}} {e}^{{i}\theta} \:{into}\: \\ $$$${real}\:{and}\:{imaginary}\:{parts}. \\ $$$$ \\ $$$${Mastermind} \\ $$

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