Question and Answers Forum

AllQuestion and Answers: Page 736

Question Number 139502 Answers: 1 Comments: 0

(√(x^2 +8x)) ≤ 24−(x+2)(x+6)

$\sqrt{x^{2} + 8 x} ⩽ 24 - (x + 2) (x + 6)$

Question Number 139501 Answers: 1 Comments: 0

Question Number 139489 Answers: 0 Comments: 0

^• I am uncomcofortable and so is my writer. ^• My writer sometimes regrets after writing me and wants to delete me. WHO AM I ? ^■ I am an answer of some question of this forum WITHOUT ANY FEEDBACK OF THE QUESTIONER !

$^{∙} I a m u n c o m c o f o r t a b l e a n d s o$ $i s m y w r i t e r .$ $^{∙} M y w r i t e r s o m e t i m e s r e g r e t s$ $a f t e r w r i t i n g m e a n d w a n t s$ $t o d e l e t e m e .$ $\underset{―}{WHO AM I ?}$ $^{◼} I a m a n a n s w e r o f s o m e$ $q u e s t i o n o f t h i s f o r u m$ $W I T H O U T A N Y F E E D B A C K$ $O F T H E Q U E S T I O N E R!$

Question Number 139484 Answers: 1 Comments: 0

If α,β and γ are the interior angles of a triangle, find the value of determinant (((tan α),1,1),(1,(tan β),1),(1,1,(tan γ)))

$If α, β and γ are the interior angles of a$ $triangle, find the value of$ $| \begin{matrix} \tan α & 1 & 1 \\ 1 & \tan β & 1 \\ 1 & 1 & \tan γ \end{matrix} |$

Question Number 139483 Answers: 1 Comments: 0

Γ(z^− )=Γ(z)^(−) why?

$Γ (\bar{z}) = \overset{―}{Γ (z)} w h y ?$

Question Number 139481 Answers: 0 Comments: 0

1+(π^6 /(27.6!))+(π^(12) /(27^2 .12!))+(π^(18) /(27^3 .18!))+...=((e^(π/( (√a))) +e^(−(π/( (√a)))) )/(2a)) Find a

$1 + \frac{π^{6}}{27.6!} + \frac{π^{12}}{27^{2} . 12!} + \frac{π^{18}}{27^{3} . 18!} + . . . = \frac{e^{\frac{π}{\sqrt{a}}} + e^{- \frac{π}{\sqrt{a}}}}{2 a}$ $F i n d a$

Question Number 139479 Answers: 1 Comments: 0

....advanced ....★★★.....calculus..... :=Σ_(n=1) ^∞ (((sin(n))/n))^3 =?

$. . . . a d v a n c e d . . . . ★ ★ ★ . . . . . c a l c u l u s . . . . .$ $:= \underset{n = 1}{\sum^{\infty}} {(\frac{s i n (n)}{n})}^{3} = ?$

Question Number 139478 Answers: 0 Comments: 0

......... nice ... ... ... calculus........ Φ:=∫_0 ^( 1) ((ln(((1+x)/2)))/(x^2 −1))dx=(π^2 /(24)) NOTE :: li_2 (z)+li_2 (1−z)=(π^2 /6)−ln(z)ln(1−z) Hence :: li_2 ((1/2))=(π^2 /(12))−(1/2)ln^2 (2) Φ:=^(⟨ ((1+x)/2)=y ⟩) 2∫_(1/2) ^( 1) ((ln(y))/(4y^2 −4y))dy :=(1/2)∫_(1/2) ^( 1) ((ln(y))/(y(y−1)))dy=(1/2) ∫_(1/2) ^( 1) {((ln(y))/(y−1))−((ln(y))/y)}dy :=−(1/2) [(1/2) ln^2 (y)]_((1 )/2) ^1 +(1/2){li_2 (1)−li_2 ((1/2))} :=(1/4)ln^2 (2)+(π^2 /(12))+(1/2)(−(π^2 /(12))−(1/2)ln^2 (2)) Φ:=(π^2 /(24))

$. . . . . . . . . n i c e . . . . . . . . . c a l c u l u s . . . . . . . .$ $Φ := \int_{0}^{1} \frac{l n (\frac{1 + x}{2})}{x^{2} - 1} d x = \frac{π^{2}}{24}$ $N O T E :: {l i}_{2} (z) + {l i}_{2} (1 - z) = \frac{π^{2}}{6} - l n (z) l n (1 - z)$ $H e n c e :: {l i}_{2} (\frac{1}{2}) = \frac{π^{2}}{12} - \frac{1}{2} {l n}^{2} (2)$ $Φ : \overset{⟨ \frac{1 + x}{2} = y ⟩}{=} 2 \int_{\frac{1}{2}}^{1} \frac{l n (y)}{4 y^{2} - 4 y} d y$ $:= \frac{1}{2} \int_{\frac{1}{2}}^{1} \frac{l n (y)}{y (y - 1)} d y = \frac{1}{2} \int_{\frac{1}{2}}^{1} {\frac{l n (y)}{y - 1} - \frac{l n (y)}{y}} d y$ $:= - \frac{1}{2} {[\frac{1}{2} {l n}^{2} (y)]}_{\frac{1}{2}}^{1} + \frac{1}{2} {{l i}_{2} (1) - {l i}_{2} (\frac{1}{2})}$ $:= \frac{1}{4} {l n}^{2} (2) + \frac{π^{2}}{12} + \frac{1}{2} (- \frac{π^{2}}{12} - \frac{1}{2} {l n}^{2} (2))$ $Φ := \frac{π^{2}}{24}$

Question Number 139476 Answers: 1 Comments: 0

Question Number 139474 Answers: 1 Comments: 0

let: Ω_n =∫_( 0) ^( 2π) cos(x)∙cos(2x)∙...∙cos(nx) dx for which integers n, 1≤n≤10, is Ω_n ≠0?

$l e t : Ω_{n} = \underset{0}{\int^{2 π}} c o s (x) \cdot c o s (2 x) \cdot . . . \cdot c o s (n x) d x$ $f o r w h i c h i n t e g e r s n, 1 ⩽ n ⩽ 10, i s Ω_{n} \neq 0 ?$

Question Number 139468 Answers: 1 Comments: 0

prove: (√(3+(√2)−(√(9+4(√2))))) = (√(2−(√2)))

$p r o v e : \sqrt{3 + \sqrt{2} - \sqrt{9 + 4 \sqrt{2}}} = \sqrt{2 - \sqrt{2}}$

Question Number 139457 Answers: 1 Comments: 0

_ prove that :: Σ_(n=0) ^∞ (1/((3n)!)) =(e/3)+(2/(3(√e))) cos(((√3)/2))

$_{}$ $p r o v e t h a t ::$ $\underset{n = 0}{\sum^{\infty}} \frac{1}{(3 n)!} = \frac{e}{3} + \frac{2}{3 \sqrt{e}} c o s (\frac{\sqrt{3}}{2})$

Question Number 139456 Answers: 1 Comments: 0

E=log_a (√(c/b^(log_(ab) c) ))+log_b (√(c/a^(log_(ab) c) ))

$E = \log_{a} \sqrt{\frac{c}{b^{\log_{ab} c}}} + \log_{b} \sqrt{\frac{c}{a^{\log_{ab} c}}}$

Question Number 139455 Answers: 1 Comments: 0

# calculus# evaluate: 𝛗:=Σ_(k=1) ^∞ (((−1)^(k−1) Γ ((k/2)))/(k Γ(((k+1)/2)))) =?

$You can't use 'macro parameter character #' in math mode$ $e v a l u a t e :$ $ϕ := \underset{k = 1}{\sum^{\infty}} \frac{{(- 1)}^{k - 1} Γ (\frac{k}{2})}{k Γ (\frac{k + 1}{2})} = ?$

Question Number 139454 Answers: 1 Comments: 0

Question Number 139490 Answers: 2 Comments: 0

If w≠1 is a cube root of unity, x=a+b, y=aw+bw^2 and z=aw^2 +bw, then x^3 +y^3 +z^3 =?

$If w \neq 1 is a cube root of unity, x = a + b, y = a w + {b w}^{2}$ $and z = {a w}^{2} + b w, then x^{3} + y^{3} + z^{3} = ?$

Question Number 139445 Answers: 1 Comments: 0

Question Number 139432 Answers: 2 Comments: 0

Question Number 139429 Answers: 0 Comments: 0

∫ sin^4 (12x) ((cos 6x))^(1/(5 )) dx =?

$\int \sin^{4} (12 x) \sqrt[5]{\cos 6 x} dx = ?$

Question Number 139427 Answers: 2 Comments: 0

∫_( (√2)) ^(3(√2)) (√(x^2 −2))dx+∫_0 ^4 (√(x^2 +2))dx =?

$\underset{\sqrt{2}}{\int^{3 \sqrt{2}}} \sqrt{x^{2} - 2} d x + \underset{0}{\int^{4}} \sqrt{x^{2} + 2} d x = ?$

Question Number 139426 Answers: 1 Comments: 0

Question Number 139424 Answers: 0 Comments: 0

Question Number 139422 Answers: 0 Comments: 1

C_n ^( 2) =(1/8)P_(n ) ^( 8) find n

$C_{n}^{2} = \frac{1}{8} P_{n}^{8}$ $f i n d n$

Question Number 139419 Answers: 0 Comments: 5

ABCD is a rectangle such that AD=2AB and its center is O. H is the top of a pyramid which has ABCD as base. All lateral faces are isosceles triangles. planes (HAB) and (HCD) are ⊥. i have joined a graphic. 1. show that (OH)⊥(ABC). 2. show that OH=((√3)/2)AB

$A B C D i s a r e c t a n g l e s u c h t h a t$ $A D = 2 A B a n d i t s c e n t e r i s O .$ $H i s t h e t o p o f a p y r a m i d w h i c h$ $h a s A B C D a s b a s e . A l l l a t e r a l$ $f a c e s a r e i s o s c e l e s t r i a n g l e s . p l a n e s$ $(H A B) a n d (H C D) a r e ⊥ .$ $i h a v e j o i n e d a g r a p h i c .$ $1 . s h o w t h a t (O H) ⊥ (A B C) .$ $2 . s h o w t h a t O H = \frac{\sqrt{3}}{2} A B$

Question Number 139414 Answers: 1 Comments: 1

∫_( 0) ^( π/2) ((cos^2 x)/(cos(x−π/4))) dx

$\underset{0}{\int^{π / 2}} \frac{{c o s}^{2} x}{c o s (x - π / 4)} d x$

Question Number 139409 Answers: 1 Comments: 0

hi ! prove this : cos (π/(10)) + cos ((4π)/(10)) + cos ((6π)/(10)) + cos ((9π)/(10)) = 0. (by the easiest possible way...!)

$hi!$ $prove this :$ $c o s \frac{π}{10} + c o s \frac{4 π}{10} + c o s \frac{6 π}{10} + c o s \frac{9 π}{10} = 0 .$ $(by the easiest possible way . . .!)$

Pg 731 Pg 732 Pg 733 Pg 734 Pg 735 Pg 736 Pg 737 Pg 738 Pg 739 Pg 740

Contact: info@tinkutara.com