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Question Number 175457    Answers: 3   Comments: 0

23+2323+232323+....(n terms)=?

$$ \\ $$$$\mathrm{23}+\mathrm{2323}+\mathrm{232323}+....\left({n}\:{terms}\right)=? \\ $$$$ \\ $$

Question Number 175430    Answers: 0   Comments: 2

Question Number 175426    Answers: 0   Comments: 0

Question Number 181496    Answers: 1   Comments: 0

Question Number 181494    Answers: 0   Comments: 0

Question Number 175458    Answers: 2   Comments: 0

2^m βˆ’2^n = 2016 find m and n

$$\mathrm{2}^{{m}} βˆ’\mathrm{2}^{{n}} =\:\mathrm{2016} \\ $$$${find}\:{m}\:{and}\:{n} \\ $$

Question Number 175420    Answers: 2   Comments: 0

solve for x 2^x .3^x^2 = 6

$${solve}\:{for}\:{x} \\ $$$$\mathrm{2}^{{x}} .\mathrm{3}^{{x}^{\mathrm{2}} } =\:\mathrm{6} \\ $$

Question Number 175411    Answers: 2   Comments: 3

7+67+667+6667+.....(n terms)=?

$$ \\ $$$$\mathrm{7}+\mathrm{67}+\mathrm{667}+\mathrm{6667}+.....\left({n}\:{terms}\right)=? \\ $$$$ \\ $$

Question Number 175410    Answers: 1   Comments: 0

A=∫9xcos 2x dx

$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{A}=\int\mathrm{9}{x}\mathrm{cos}\:\mathrm{2}{x}\:\:{dx} \\ $$$$ \\ $$

Question Number 175409    Answers: 0   Comments: 3

exercise Consider a polygon with an odd number 𝗻 of vertices. We connect any 3 vertices of this polygon to form a triangle. What is the probability that this triangle contains the center of the circle circumscribing the polygon?

$$\mathrm{exercise} \\ $$Consider a polygon with an odd number 𝗻 of vertices. We connect any 3 vertices of this polygon to form a triangle. What is the probability that this triangle contains the center of the circle circumscribing the polygon?

Question Number 175407    Answers: 2   Comments: 0

Trouver la somme de S_n Si S_n =1+11+111+...+1111...111

$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\underline{\mathrm{Trouver}\:\mathrm{la}\:\mathrm{somme}\:\mathrm{de}\:\mathrm{S}_{{n}} }\:\: \\ $$$$\:\:\:\mathrm{Si}\:\:\:\:\:\:{S}_{{n}} =\mathrm{1}+\mathrm{11}+\mathrm{111}+...+\mathrm{1111}...\mathrm{111}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 175406    Answers: 1   Comments: 0

(d^2 y/dx^2 ) βˆ’tan (x)(dy/dx) = 0

$$\frac{{d}^{\mathrm{2}} \boldsymbol{{y}}}{\boldsymbol{{dx}}^{\mathrm{2}} }\:βˆ’\mathrm{tan}\:\left(\boldsymbol{{x}}\right)\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}\:=\:\mathrm{0} \\ $$

Question Number 175402    Answers: 0   Comments: 1

solve for x x_(n+1) =rx_n (1βˆ’x_n )

$${solve}\:{for}\:{x} \\ $$$${x}_{{n}+\mathrm{1}} ={rx}_{{n}} \left(\mathrm{1}βˆ’{x}_{{n}} \right) \\ $$

Question Number 175399    Answers: 0   Comments: 3

if (x+1)^4 (√4)=x+1 find x

$${if}\:\left({x}+\mathrm{1}\right)^{\mathrm{4}} \sqrt{\mathrm{4}}={x}+\mathrm{1}\:\:{find}\:{x} \\ $$

Question Number 175396    Answers: 2   Comments: 0

Question Number 175395    Answers: 0   Comments: 0

f(4) = (1/4) and f(8) = (1/2) ∫_4 ^8 (( [fβ€²(x)]^2 )/([f(x)]^4 ))dx = 1 then f(6)= ?

$$\:\:\:\:\:{f}\left(\mathrm{4}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:{and}\:\:\:\:{f}\left(\mathrm{8}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\int_{\mathrm{4}} ^{\mathrm{8}} \:\frac{\:\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{\left[{f}\left({x}\right)\right]^{\mathrm{4}} }{dx}\:\:=\:\:\mathrm{1}\:\:\:\:{then}\:\:\:{f}\left(\mathrm{6}\right)=\:? \\ $$

Question Number 175394    Answers: 0   Comments: 0

Question Number 175393    Answers: 0   Comments: 0

if (x+1)_(√4) ^4 =x+1 find x

$${if}\:\left({x}+\mathrm{1}\right)_{\sqrt{\mathrm{4}}} ^{\mathrm{4}} ={x}+\mathrm{1}\:\:{find}\:{x} \\ $$

Question Number 175387    Answers: 2   Comments: 1

J=∫_0 ^(Ο€/2) ((sin x)/(1+sin x+cos x)) dx

$$\:{J}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:{dx} \\ $$

Question Number 175386    Answers: 0   Comments: 0

∫_5 ^7 (([ (1/4)x+3 ])/( (√(9x^2 βˆ’12x+4)))) dx=? [ ..] =floor function

$$\:\:\:\underset{\mathrm{5}} {\overset{\mathrm{7}} {\int}}\:\frac{\left[\:\frac{\mathrm{1}}{\mathrm{4}}{x}+\mathrm{3}\:\right]}{\:\sqrt{\mathrm{9}{x}^{\mathrm{2}} βˆ’\mathrm{12}{x}+\mathrm{4}}}\:{dx}=? \\ $$$$\:\left[\:..\right]\:={floor}\:{function} \\ $$

Question Number 175375    Answers: 1   Comments: 0

Question Number 175369    Answers: 1   Comments: 0

solve for x log_(∣sinx∣ ) (x^2 βˆ’8x+23) > (3/(log_2 ∣sinx∣ ))

$$\:\:\mathrm{solve}\:\mathrm{for}\:{x} \\ $$$$\:\:\:\mathrm{log}_{\mid\mathrm{sin}{x}\mid\:} \left({x}^{\mathrm{2}} βˆ’\mathrm{8}{x}+\mathrm{23}\right)\:>\:\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{2}} \mid\mathrm{sin}{x}\mid\:} \\ $$

Question Number 175362    Answers: 1   Comments: 2

lim_(xβ†’(Ο€/4)) ((sin xβˆ’cos x)/(tan ((Ο€/8)βˆ’(x/2)))) =?

$$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}βˆ’\mathrm{cos}\:{x}}{\mathrm{tan}\:\left(\frac{\pi}{\mathrm{8}}βˆ’\frac{{x}}{\mathrm{2}}\right)}\:=? \\ $$

Question Number 175353    Answers: 1   Comments: 0

ax^2 +bx+c = 0 x = ((βˆ’bΒ±(√(b^2 βˆ’4ac)))/(2a)) Example: Find the values of x in the equation x^2 +5x+4 = 0 In order to solve for that, letβ€²s first take a look on what are the values of a, b and c 1x^2 + 5x + 4 = 0 a = 1 ; b = 5 ; c = 4 Now, using the quadratic formula x = ((βˆ’5Β±(√(5^2 βˆ’4(1)(4))))/(2(1))) = ((βˆ’5Β±(√(25βˆ’16)))/2) = ((βˆ’5Β±3)/2)

$$\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:\frac{βˆ’\mathrm{b}\pm\sqrt{\mathrm{b}^{\mathrm{2}} βˆ’\mathrm{4ac}}}{\mathrm{2a}} \\ $$$$\: \\ $$$$\:\mathrm{Example}: \\ $$$$\: \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\mathrm{x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{4}\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\:\mathrm{In}\:\mathrm{order}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{for}\:\mathrm{that},\:\mathrm{let}'\mathrm{s}\:\mathrm{first}\:\mathrm{take} \\ $$$$\:\mathrm{a}\:\mathrm{look}\:\mathrm{on}\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}\: \\ $$$$\: \\ $$$$\:\mathrm{1x}^{\mathrm{2}} \:+\:\mathrm{5x}\:+\:\mathrm{4}\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\:\mathrm{a}\:=\:\mathrm{1}\:;\:\mathrm{b}\:=\:\mathrm{5}\:;\:\mathrm{c}\:=\:\mathrm{4} \\ $$$$\: \\ $$$$\:\mathrm{Now},\:\mathrm{using}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{formula} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:\frac{βˆ’\mathrm{5}\pm\sqrt{\mathrm{5}^{\mathrm{2}} βˆ’\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{4}\right)}}{\mathrm{2}\left(\mathrm{1}\right)}\: \\ $$$$\:\:\:\:=\:\frac{βˆ’\mathrm{5}\pm\sqrt{\mathrm{25}βˆ’\mathrm{16}}}{\mathrm{2}} \\ $$$$\:\:\:\:=\:\frac{βˆ’\mathrm{5}\pm\mathrm{3}}{\mathrm{2}} \\ $$

Question Number 175351    Answers: 1   Comments: 0

∫_0 ^(Ο€/2) ((sin^3 x)/(sin x+cos x)) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{3}} {x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$

Question Number 175374    Answers: 0   Comments: 0

lim_(nβ†’βˆž) (Ξ£_(j=1) ^n Ξ£_(i = 1) ^n ((i+j)/(i^2 +j^2 ))βˆ’((Ο€/2)+ ln 2)n + ln n) = ?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\frac{{i}+{j}}{{i}^{\mathrm{2}} +{j}^{\mathrm{2}} }βˆ’\left(\frac{\pi}{\mathrm{2}}+\:\mathrm{ln}\:\mathrm{2}\right){n}\:+\:\mathrm{ln}\:{n}\right)\:=\:? \\ $$

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