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Question Number 36369 Answers: 0 Comments: 0

Question Number 36368 Answers: 0 Comments: 0

In an organic Compound Carbon = 85.7% Hydrogen = 14.3% and RMM= 56 find the molecular formular.

$In an organic Compound Carbon$ $= 85 . 7 % Hydrogen = 14 . 3 % and$ $RMM = 56 find the molecular$ $formular .$

Question Number 36367 Answers: 1 Comments: 0

Question Number 36359 Answers: 0 Comments: 0

decompose inside C(x) the fraction F(x)= (1/((x^2 +1)^n )) with n integr nstural.

$d e c o m p o s e i n s i d e C (x) t h e f r a c t i o n$ $F (x) = \frac{1}{{(x^{2} + 1)}^{n}} w i t h n i n t e g r n s t u r a l .$

Question Number 36352 Answers: 0 Comments: 1

let p(x) =x^n −e^(inα) with n integr and α fromR 1) find the roots of p(x) 2) factorize p(x) inside C[x] .

$l e t p (x) = x^{n} - e^{i n α} w i t h n i n t e g r a n d α f r o m R$ $1) f i n d t h e r o o t s o f p (x)$ $2) f a c t o r i z e p (x) i n s i d e C [x] .$

Question Number 36346 Answers: 0 Comments: 6

Question Number 36344 Answers: 0 Comments: 3

Question Number 36341 Answers: 1 Comments: 0

y=(((x−3)(x+5)^2 )/(x^2 (x+2))) Find local maxima and minima; hence draw the graph.Also find radius of circle touching all three sections of the curve that results.

$y = \frac{(x - 3) {(x + 5)}^{2}}{x^{2} (x + 2)}$ $F i n d l o c a l m a x i m a a n d m i n i m a;$ $h e n c e d r a w t h e g r a p h . A l s o f i n d$ $r a d i u s o f c i r c l e t o u c h i n g a l l t h r e e$ $s e c t i o n s o f t h e c u r v e t h a t r e s u l t s .$

Question Number 36338 Answers: 0 Comments: 0

prove (1+(1/1^2 ))(1+(1/2^2 ))(1+(1/3^2 ))...upto infinity =(1/Π)sinhΠ

$p r o v e (1 + \frac{1}{1^{2}}) (1 + \frac{1}{2^{2}}) (1 + \frac{1}{3^{2}}) . . . u p t o i n f i n i t y$ $= \frac{1}{Π} s i n h Π$

Question Number 36336 Answers: 0 Comments: 4

find f(x)= ∫_0 ^∞ arctan(xt^2 )dt with x>0

$f i n d f (x) = \int_{0}^{\infty} a r c t a n ({x t}^{2}) d t w i t h x > 0$

Question Number 36335 Answers: 0 Comments: 1

find f(t) = ∫_0 ^1 arctan(tx^2 )dx with t≥0 developp f at integr serie

$f i n d f (t) = \int_{0}^{1} a r c t a n ({t x}^{2}) d x w i t h t ⩾ 0$ $d e v e l o p p f a t i n t e g r s e r i e$

Question Number 36328 Answers: 0 Comments: 1

find the perimeter of a right angle triangle 4xcm high and 5xcm base

$find the perimeter of a right angle$ $triangle 4 x c m h i g h a n d 5 x c m b a s e$

Question Number 36316 Answers: 3 Comments: 0

Find domain and range of the function f(x)=((x^2 −6x+8)/(x−5)) . Also draw the graph.

$F i n d d o m a i n a n d r a n g e o f t h e$ $f u n c t i o n f (x) = \frac{x^{2} - 6 x + 8}{x - 5} .$ $A l s o d r a w t h e g r a p h .$

Question Number 36314 Answers: 1 Comments: 1

Question Number 36291 Answers: 1 Comments: 0

find the image of (−2,3) after the reflection on the a) x−axis b) y−axis

$find the image of (- 2, 3) after the$ $reflection on the$ $a) x - axis b) y - axis$

Question Number 36290 Answers: 2 Comments: 1

Find the angle between the lines l_1 :y − x −4 = 0 and l_2 :2x − y = 7 and hence the perpendicular distance from one point on l_1 to l_2 .

$Find the angle between the lines$ $l_{1} : y - x - 4 = 0 and l_{2} : 2 x - y = 7$ $and hence the perpendicular$ $distance from one point on l_{1}$ $to l_{2} .$

Question Number 36279 Answers: 1 Comments: 0

Consider a particle in a uniformly charge electric field, if the particle has a charge of 2C and is place 3m away from the charge plate. calculate the work needed to move the 2C particle to a distance of 1m from the plate.

$C o n s i d e r a p a r t i c l e i n a$ $u n i f o r m l y c h a r g e e l e c t r i c f i e l d,$ $i f t h e p a r t i c l e h a s a c h a r g e o f 2 C$ $a n d i s p l a c e 3 m a w a y f r o m t h e$ $c h a r g e p l a t e .$ $c a l c u l a t e t h e w o r k n e e d e d t o$ $m o v e t h e 2 C p a r t i c l e t o a$ $d i s t a n c e o f 1 m f r o m t h e$ $p l a t e .$

Question Number 36270 Answers: 1 Comments: 8

Question Number 36259 Answers: 4 Comments: 0

Question Number 36246 Answers: 1 Comments: 0

What is the absolute value of ( −10)?

$What is the absolute value of (- 10) ?$

Question Number 36239 Answers: 0 Comments: 1

the opposite side of a triangle is x + y,and the hypotenuse is 3x+y Given that that A is an acute angle find the value of Cos A

$the opposite side of a triangle is$ $x + y, and the hypotenuse is 3 x + y$ $Given that that A is an acute angle$ $find the value of Cos A$

Question Number 36237 Answers: 2 Comments: 0

Question Number 36227 Answers: 1 Comments: 0

1×10^(7 ) electrons pass through a conductor in 1.0μs.Find the current in Amperes flowing through the conductor. electronic charge=1.6×10^(−19) C

$1 \times 10^{7} e l e c t r o n s p a s s t h r o u g h a$ $c o n d u c t o r i n 1.0 μ s . F i n d t h e$ $c u r r e n t i n A m p e r e s f l o w i n g$ $t h r o u g h t h e c o n d u c t o r .$ $e l e c t r o n i c c h a r g e = 1.6 \times 10^{- 19} C$

Question Number 36221 Answers: 2 Comments: 1

a(b+(1/b))=−1 ....(i) b−(1/b)=a^2 ....(ii) Solve simultaneously for a, and b.

$a (b + \frac{1}{b}) = - 1 . . . . (i)$ $b - \frac{1}{b} = a^{2} . . . . (i i)$ $S o l v e s i m u l t a n e o u s l y f o r a, a n d b .$

Question Number 36219 Answers: 0 Comments: 2

in question 34992 this had to be solved: t^4 +8t^3 +2t^2 −8t+1=0 here another concept worked (I tried some) t_1 =a+b+c+d t_2 =a+b−c−d t_3 =a−b+c−d t_3 =a−b−c+d (t−t_1 )(t−t_2 )(t−t_3 )(t−t_4 )=0 leads to t^4 −4at^3 +2(3a^2 −b^2 −c^2 −d^2 )t^2 + +4(a(−a^2 +b^2 +c^2 +d^2 )−2bcd)t+ +a^4 +b^4 +c^4 +d^4 −2(a^2 (b^2 +c^2 +d^2 )+b^2 (c^2 +d^2 )+c^2 d^2 ) 1. −4a=8 2. 2(3a^2 −b^2 −c^2 −d^2 )=2 3. 4(a(−a^2 +b^2 +c^2 +d^2 )−2bcd)=−8 4. a^4 +b^4 +c^4 +d^4 −2(a^2 (b^2 +c^2 +d^2 )+b^2 (c^2 +d^2 )+c^2 d^2 )=1 1. a=−2 2. b^2 +c^2 +d^2 =11 3. b^2 +c^2 +d^2 +bcd=5 4. ... 3. −2. bcd=−6 now I tried by chance if there are easy real solutions b^2 =p, c^2 =q, d^2 =r, 0≤p≤q≤r p+q+r=11 this leads to p=2, q=3, p=6 ∣b∣=(√2), ∣c∣=(√3), ∣d∣=(√6) with one or three out of a, b, c negative because of bcd=−6 because of the nature of t_1 , t_2 , t_3 , t_4 these lead to the same solutions I took b=−(√2), c=−(√3), d=−(√6) t_1 =−2−(√2)−(√3)−(√6) t_2 =−2−(√2)+(√3)+(√6) t_3 =−2+(√2)−(√3)+(√6) t_4 =−2+(√2)+(√3)−(√6)

$in question 34992 this had to be solved :$ $t^{4} + 8 t^{3} + 2 t^{2} - 8 t + 1 = 0$ $here another concept worked (I tried some)$ $t_{1} = a + b + c + d$ $t_{2} = a + b - c - d$ $t_{3} = a - b + c - d$ $t_{3} = a - b - c + d$ $(t - t_{1}) (t - t_{2}) (t - t_{3}) (t - t_{4}) = 0$ $leads to$ $t^{4} - 4 {a t}^{3} + 2 (3 a^{2} - b^{2} - c^{2} - d^{2}) t^{2} +$ $+ 4 (a (- a^{2} + b^{2} + c^{2} + d^{2}) - 2 b c d) t +$ $+ a^{4} + b^{4} + c^{4} + d^{4} - 2 (a^{2} (b^{2} + c^{2} + d^{2}) + b^{2} (c^{2} + d^{2}) + c^{2} d^{2})$ $1 . - 4 a = 8$ $2 . 2 (3 a^{2} - b^{2} - c^{2} - d^{2}) = 2$ $3 . 4 (a (- a^{2} + b^{2} + c^{2} + d^{2}) - 2 b c d) = - 8$ $4 . a^{4} + b^{4} + c^{4} + d^{4} - 2 (a^{2} (b^{2} + c^{2} + d^{2}) + b^{2} (c^{2} + d^{2}) + c^{2} d^{2}) = 1$ $1 . a = - 2$ $2 . b^{2} + c^{2} + d^{2} = 11$ $3 . b^{2} + c^{2} + d^{2} + b c d = 5$ $4 . . . .$ $3 . - 2 . b c d = - 6$ $now I tried by chance if there are easy real solutions$ $b^{2} = p, c^{2} = q, d^{2} = r, 0 ⩽ p ⩽ q ⩽ r$ $p + q + r = 11$ $this leads to$ $p = 2, q = 3, p = 6$ $∣ b ∣= \sqrt{2}, ∣ c ∣= \sqrt{3}, ∣ d ∣= \sqrt{6} with one or three out$ $of a, b, c negative because of b c d = - 6$ $because of the nature of t_{1}, t_{2}, t_{3}, t_{4} these$ $lead to the same solutions$ $I took b = - \sqrt{2}, c = - \sqrt{3}, d = - \sqrt{6}$ $t_{1} = - 2 - \sqrt{2} - \sqrt{3} - \sqrt{6}$ $t_{2} = - 2 - \sqrt{2} + \sqrt{3} + \sqrt{6}$ $t_{3} = - 2 + \sqrt{2} - \sqrt{3} + \sqrt{6}$ $t_{4} = - 2 + \sqrt{2} + \sqrt{3} - \sqrt{6}$

Question Number 36218 Answers: 0 Comments: 1

proof that 2((√n) − 1) < 1 + (1/((√2) )) + (1/(√3))+...+ (1/(√n)) < 2(√n)

$proof that$ $2 (\sqrt{n} - 1) < 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + . . . +$ $\frac{1}{\sqrt{n}} < 2 \sqrt{n}$

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