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Question Number 5838 Answers: 0 Comments: 3

∫(1/(1+cot x))dx

Question Number 5835 Answers: 0 Comments: 2

Evaluate the integral. ∫[(x−(x^3 /2)+(x^5 /(2.4))−(x^7 /(2.4.6))+...)(1−(x^2 /2^2 )+(x^4 /(2^2 .4^2 ))−(x^6 /(2^2 .4^2 .6^2 ))+....)]dx for 0<x<∞ Please help

$E v a l u a t e t h e i n t e g r a l .$ $\int [(x - \frac{x^{3}}{2} + \frac{x^{5}}{2.4} - \frac{x^{7}}{2.4.6} + . . .) (1 - \frac{x^{2}}{2^{2}} + \frac{x^{4}}{2^{2} . 4^{2}} - \frac{x^{6}}{2^{2} . 4^{2} . 6^{2}} + . . . .)] d x$ $f o r 0 < x < \infty$ $P l e a s e h e l p$

Question Number 5834 Answers: 0 Comments: 2

Find all positive integers n for which there exist non−negative integer . a_(1 ) a_2 a_3 ....... a_n . Such that (1/2^a_1 ) + (1/2^a_2 ) + (1/2^a_3 ) + .... + (1/2^a_n ) = (1/3^a_1 ) + (2/3^a_2 ) + .... + (n/3^a_n ) = 1 Please help.

$F i n d a l l p o s i t i v e i n t e g e r s n f o r w h i c h t h e r e e x i s t$ $n o n - n e g a t i v e i n t e g e r . a_{1} a_{2} a_{3} . . . . . . . a_{n} . S u c h t h a t$ $\frac{1}{2^{a_{1}}} + \frac{1}{2^{a_{2}}} + \frac{1}{2^{a_{3}}} + . . . . + \frac{1}{2^{a_{n}}} = \frac{1}{3^{a_{1}}} + \frac{2}{3^{a_{2}}} + . . . . + \frac{n}{3^{a_{n}}} = 1$ $P l e a s e h e l p .$

Question Number 5825 Answers: 1 Comments: 1

Question Number 6081 Answers: 0 Comments: 1

∫e^(−st) (t^n /(n!))dt=?

$\int e^{- s t} \frac{t^{n}}{n!} d t = ?$

Question Number 5822 Answers: 0 Comments: 0

Prove that among all triangles, which have same circum-radius, the equilateral triangle has maximum area.

$P r o v e t h a t a m o n g a l l t r i a n g l e s,$ $w h i c h h a v e s a m e c i r c u m - r a d i u s,$ $t h e e q u i l a t e r a l t r i a n g l e h a s$ $m a x i m u m a r e a .$

Question Number 5821 Answers: 1 Comments: 0

L=lim_(x→0) x^x

$L = \lim_{x \to 0} x^{x}$

Question Number 5809 Answers: 1 Comments: 1

Question Number 5807 Answers: 0 Comments: 0

Town A is 36 kilometers from town B. Two persons start to travel at the same time, one from A to B and other from B to A. After meeting in a way the first person covers the remaining distance in 2 hours and the second in 8 hours. Determine their speed. (From a book)

$T o w n A i s 36 k i l o m e t e r s f r o m$ $t o w n B . T w o p e r s o n s s t a r t t o t r a v e l$ $a t t h e s a m e t i m e, o n e f r o m A t o B$ $a n d o t h e r f r o m B t o A . A f t e r m e e t i n g$ $i n a w a y t h e f i r s t p e r s o n c o v e r s t h e$ $r e m a i n i n g d i s t a n c e i n 2 h o u r s a n d$ $t h e s e c o n d i n 8 h o u r s . D e t e r m i n e t h e i r$ $s p e e d . (From a book)$

Question Number 5802 Answers: 0 Comments: 0

Solve simultaneously 2x + y − z = 8 ........... (i) x^2 − y^2 +2z^2 = 14 .......... (ii) 3x^3 + 4y^3 + z^3 = 195 ......... (iii) please help me.

$S o l v e s i m u l t a n e o u s l y$ $2 x + y - z = 8 . . . . . . . . . . . (i)$ $x^{2} - y^{2} + 2 z^{2} = 14 . . . . . . . . . . (i i)$ $3 x^{3} + 4 y^{3} + z^{3} = 195 . . . . . . . . . (i i i)$ $p l e a s e h e l p m e .$

Question Number 5800 Answers: 1 Comments: 1

∫((cos2x)/(sin^2 x∙cos^2 x))dx

$\int \frac{c o s 2 x}{{s i n}^{2} x \cdot {c o s}^{2} x} d x$

Question Number 5816 Answers: 0 Comments: 2

Prove that among all cyclic n-gons, which have same radius, regular n-gon has maximum area.

$P r o v e t h a t a m o n g a l l c y c l i c n - g o n s,$ $w h i c h h a v e s a m e r a d i u s, r e g u l a r n - g o n$ $h a s m a x i m u m a r e a .$

Question Number 5814 Answers: 0 Comments: 1

Please help me with that simultaneous equation

$P l e a s e h e l p m e w i t h t h a t s i m u l t a n e o u s e q u a t i o n$

Question Number 5796 Answers: 0 Comments: 6

How many ways can you express 30,030 as the product of 4 positive numbers? (excluding 1)

$How many ways can you express$ $30, 030 as the product of 4 positive numbers ?$ $(excluding 1)$

Question Number 5792 Answers: 0 Comments: 0

Solve simultaneously 2x + y − z = 8 ...... equation(i) x^2 − y^2 + 2z^2 = 14 .... equation(ii) 3x^3 + 4x^3 + z^3 = 195 ..... equation(iii) please help thanks.

$S o l v e s i m u l t a n e o u s l y$ $2 x + y - z = 8 . . . . . . e q u a t i o n (i)$ $x^{2} - y^{2} + 2 z^{2} = 14 . . . . e q u a t i o n (i i)$ $3 x^{3} + 4 x^{3} + z^{3} = 195 . . . . . e q u a t i o n (i i i)$ $p l e a s e h e l p t h a n k s .$

Question Number 5785 Answers: 0 Comments: 0

Solve simultaneously 2x + y − z = 8 ........... (i) x^2 − y^2 + 2z^2 = 14 .......... (ii) 3x^3 + 4y^3 + z^3 = 195 ........... (iii) Please help. though equation. Thanks for your help.

$S o l v e s i m u l t a n e o u s l y$ $2 x + y - z = 8 . . . . . . . . . . . (i)$ $x^{2} - y^{2} + 2 z^{2} = 14 . . . . . . . . . . (i i)$ $3 x^{3} + 4 y^{3} + z^{3} = 195 . . . . . . . . . . . (i i i)$ $P l e a s e h e l p . t h o u g h e q u a t i o n .$ $T h a n k s f o r y o u r h e l p .$

Question Number 5784 Answers: 1 Comments: 0

Determine: 1+((a+r)/(ar))+((a+2r)/(ar^2 ))+...+((a+(n−1)r)/(ar^(n−1) ))

$D e t e r m i n e :$ $1 + \frac{a + r}{a r} + \frac{a + 2 r}{{a r}^{2}} + . . . + \frac{a + (n - 1) r}{{a r}^{n - 1}}$

Question Number 5783 Answers: 0 Comments: 0

Determine: a^a +(ar)^(a+r) +(ar^2 )^(a+2r) +...+(ar^(n−1) )^(a+(n−1)r)

$D e t e r m i n e :$ $a^{a} + {(a r)}^{a + r} + {({a r}^{2})}^{a + 2 r} + . . . + {({a r}^{n - 1})}^{a + (n - 1) r}$

Question Number 5782 Answers: 2 Comments: 0

Why x+x=2x ? Explain by properties/laws.

$Why x + x = 2 x ?$ $Explain by properties / laws .$

Question Number 5780 Answers: 0 Comments: 0

at developers can we please have capital greek symbols? It would make things so much better when writing functions <3

$a t d e v e l o p e r s$ $c a n w e p l e a s e h a v e c a p i t a l g r e e k s y m b o l s ?$ $It would make things so much better$ $when writing functions < 3$

Question Number 5777 Answers: 0 Comments: 2

∃x∈Z^+ :x=p_1 p_2 ...p_n ∧∀p≠x, p∈Z^+ x=(factors of p_1 )(fact. p_2 )...(fact. p_n ) How could you formally write the number of ways you can write x in terms of the product of n integers?

$\exists x \in Z^{+} : x = p_{1} p_{2} . . . p_{n} \land \forall p \neq x, p \in Z^{+}$ $x = (f a c t o r s o f p_{1}) (f a c t . p_{2}) . . . (f a c t . p_{n})$ $How could you formally write the$ $number of ways you can write x in terms$ $of the product of n integers ?$

Question Number 5824 Answers: 0 Comments: 5

The exponent of 12 in 100! is

$The exponent of 12 in 100! is$

Question Number 5772 Answers: 0 Comments: 1

$q +$

Question Number 5771 Answers: 0 Comments: 1

Find to the nearest hundredth the positive cube-root of 29 .

$Find to the nearest hundredth the positive$ $cube - root of 29 .$

Question Number 5765 Answers: 0 Comments: 1

(√((x−1)/(3x+2))) + 2 ((√((3x+2)/(x−1))) ) = 3 Find the value of x

$\sqrt{\frac{x - 1}{3 x + 2}} + 2 (\sqrt{\frac{3 x + 2}{x - 1}}) = 3$ $F i n d t h e v a l u e o f x$

Question Number 5764 Answers: 0 Comments: 1

2^x = 4x Solution 2^x = 4x This can be re write as (1+1)^x = 4x Using combination to epand from the identity. (1+x)^n = 1+nx+((n(n−1))/(2!))x^2 +((n(n−1)(n−2))/(3!))x^3 +....+nCrx^(r ) Therefore. (1+1)^x = 4x 1+x+((x(x−1))/(2!))(1^2 )+((x(x−1)(x−2))/(3!))(1^3 )+......+1 = 4x ignore the continuity (what rule is ..... ignore the +...+) is it linear approximation 1+x+((x^2 −x)/(2×1))+(((x^2 −x)(x−2))/(3×2×1))+1 = 4x 1+x+((x^2 −x)/2)+((x^3 −2x^2 −x^2 +2x)/6)+1 = 4x 1+x+((x^2 −x)/2)+((x^3 −3x^2 +2x)/6)+1 = 4x Multiply through by 6 6+6x+3(x^2 −x)+x^3 −3x^2 +2x+6 = 24x 12+6x+3x^2 −3x+x^3 −3x^2 +2x+6 = 24x 12+5x+x^3 = 24x 12+5x+x^3 −24x = 0 x^3 −19x+12 = 0 Factorize x^3 −4x^2 +4x^2 −16x−3x+12 = 0 (x^3 −4x^2 )+(4x^2 −16x)−(3x+12) = 0 x^2 (x−4)+4x(x−4)−3(x−4) = 0 Factor out (x−4) (x−4)(x^2 +4x−3) = 0 x−4 = 0 or x^( 2) +4x−3 = 0 x = 4 or x = 0.6458 or x = −4.6458 The only real solution is x = 4 Therefore x = 4 DONE! Please confirm the solution. is it correct or please corect it or show me alternative. This is my trial. Thanks.

$2^{x} = 4 x$ $S o l u t i o n$ $2^{x} = 4 x$ $T h i s c a n b e r e w r i t e a s$ ${(1 + 1)}^{x} = 4 x$ $U s i n g c o m b i n a t i o n t o e p a n d$ $f r o m t h e i d e n t i t y .$ ${(1 + x)}^{n} = 1 + n x + \frac{n (n - 1)}{2!} x^{2} + \frac{n (n - 1) (n - 2)}{3!} x^{3} + . . . . + {n C r x}^{r}$ $T h e r e f o r e .$ ${(1 + 1)}^{x} = 4 x$ $1 + x + \frac{x (x - 1)}{2!} (1^{2}) + \frac{x (x - 1) (x - 2)}{3!} (1^{3}) + . . . . . . + 1 = 4 x$ $i g n o r e t h e c o n t i n u i t y (w h a t r u l e i s . . . . . i g n o r e t h e + . . . +) i s i t$ $l i n e a r a p p r o x i m a t i o n$ $1 + x + \frac{x^{2} - x}{2 \times 1} + \frac{(x^{2} - x) (x - 2)}{3 \times 2 \times 1} + 1 = 4 x$ $1 + x + \frac{x^{2} - x}{2} + \frac{x^{3} - 2 x^{2} - x^{2} + 2 x}{6} + 1 = 4 x$ $1 + x + \frac{x^{2} - x}{2} + \frac{x^{3} - 3 x^{2} + 2 x}{6} + 1 = 4 x$ $M u l t i p l y t h r o u g h b y 6$ $6 + 6 x + 3 (x^{2} - x) + x^{3} - 3 x^{2} + 2 x + 6 = 24 x$ $12 + 6 x + 3 x^{2} - 3 x + x^{3} - 3 x^{2} + 2 x + 6 = 24 x$ $12 + 5 x + x^{3} = 24 x$ $12 + 5 x + x^{3} - 24 x = 0$ $x^{3} - 19 x + 12 = 0$ $F a c t o r i z e$ $x^{3} - 4 x^{2} + 4 x^{2} - 16 x - 3 x + 12 = 0$ $(x^{3} - 4 x^{2}) + (4 x^{2} - 16 x) - (3 x + 12) = 0$ $x^{2} (x - 4) + 4 x (x - 4) - 3 (x - 4) = 0$ $F a c t o r o u t (x - 4)$ $(x - 4) (x^{2} + 4 x - 3) = 0$ $x - 4 = 0 o r x^{2} + 4 x - 3 = 0$ $x = 4 o r x = 0.6458 o r x = - 4.6458$ $T h e o n l y r e a l s o l u t i o n i s x = 4$ $T h e r e f o r e$ $x = 4$ $D O N E!$ $P l e a s e c o n f i r m t h e s o l u t i o n . i s i t c o r r e c t o r p l e a s e c o r e c t i t o r$ $s h o w m e a l t e r n a t i v e .$ $T h i s i s m y t r i a l .$ $T h a n k s .$

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