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AllQuestion and Answers: Page 1636

Question Number 39280 Answers: 3 Comments: 1

∫_0 ^(π/2) cos^(10) x.sin 12x dx = ? Given reduction formula : ∫ cos^m x sin nx dx I_(m,n) = −((cos^m x . cosnx)/(m+n)) + (m/(m+n)) I_(m−1,n−1)

$\int_{0}^{\frac{π}{2}} \cos^{10} x . \sin 12 x d x = ?$ $Given$ $reduction formula :$ $\int \cos^{m} x s i n n x d x$ $I_{m, n} = - \frac{\cos^{m} x . c o s n x}{m + n} + \frac{m}{m + n} I_{m - 1, n - 1}$

Question Number 40946 Answers: 1 Comments: 0

Each of two long straight wires 4cm apart carry equal electric currents and experience a force of 2×10^(−4) N/m. What is the magnitude of the electric current in each?

$E a c h o f t w o l o n g s t r a i g h t w i r e s 4 c m$ $a p a r t c a r r y e q u a l e l e c t r i c c u r r e n t s$ $a n d e x p e r i e n c e a f o r c e o f 2 \times 10^{- 4} N / m .$ $W h a t i s t h e m a g n i t u d e o f t h e$ $e l e c t r i c c u r r e n t i n e a c h ?$

Question Number 40142 Answers: 1 Comments: 1

calculate ∫_(−(π/6)) ^(π/6) ((1+tan(x))/(1+sin(2x)))dx

$c a l c u l a t e \int_{- \frac{π}{6}}^{\frac{π}{6}} \frac{1 + t a n (x)}{1 + s i n (2 x)} d x$

Question Number 39272 Answers: 0 Comments: 1

∫_0 ^( 2π) (((acos α−bcos θ)dθ)/([a^2 +b^2 −2abcos (θ−α)]^(3/2) )) = ?

$\int_{0}^{2 π} \frac{(a \cos α - b \cos θ) d θ}{{[a^{2} + b^{2} - 2 a b \cos (θ - α)]}^{3 / 2}} = ?$

Question Number 39267 Answers: 1 Comments: 1

Question Number 39257 Answers: 0 Comments: 0

Question Number 39256 Answers: 0 Comments: 0

Question Number 39255 Answers: 0 Comments: 0

Question Number 39253 Answers: 0 Comments: 2

Question Number 39258 Answers: 0 Comments: 0

Question Number 39237 Answers: 0 Comments: 1

Calculate the triple point for an electrical resistance thermometer, assuming the ratio of resistance at the triple point to that at initial point is 2.0.

$C a l c u l a t e t h e t r i p l e p o i n t f o r a n$ $e l e c t r i c a l r e s i s t a n c e t h e r m o m e t e r,$ $a s s u m i n g t h e r a t i o o f r e s i s t a n c e$ $a t t h e t r i p l e p o i n t t o t h a t a t i n i t i a l$ $p o i n t i s 2.0 .$

Question Number 39236 Answers: 0 Comments: 3

If a petrol tank costs $2000.00 to fill it up at 10°C ,how much extra dollar must I pay to fill up the tank at 50°C,if the petrol costs $50.00 per litre and its cubic expansivity is 9.5×10^(−4) K^(−1) ?

$I f a p e t r o l t a n k c o s t s $ 2000.00 t o$ $f i l l i t u p a t 10 ° C, h o w m u c h e x t r a$ $d o l l a r m u s t I p a y t o f i l l u p t h e t a n k$ $a t 50 ° C, i f t h e p e t r o l c o s t s $ 50.00$ $p e r l i t r e a n d i t s c u b i c e x p a n s i v i t y$ $i s 9.5 \times 10^{- 4} K^{- 1} ?$

Question Number 39235 Answers: 0 Comments: 1

The length of a mercury column in a mercury in glass thermometer is 4cm at triple point.What is the length of the column when the scale indicates temperature of 560K.

$T h e l e n g t h o f a m e r c u r y c o l u m n$ $i n a m e r c u r y i n g l a s s t h e r m o m e t e r$ $i s 4 c m a t t r i p l e p o i n t . W h a t i s t h e$ $l e n g t h o f t h e c o l u m n w h e n t h e$ $s c a l e i n d i c a t e s t e m p e r a t u r e o f 560 K .$

Question Number 39231 Answers: 1 Comments: 0

(sin^(−1) x)^2 + (sin^(−1) y)^2 + 2(sin^(−1) x) (sin^(−1) y)= π^2 ,then x^2 +y^2 is equal to?

${({s i n}^{- 1} x)}^{2} + {({s i n}^{- 1} y)}^{2} + 2 ({s i n}^{- 1} x)$ $({s i n}^{- 1} y) = π^{2}, t h e n x^{2} + y^{2} i s e q u a l t o ?$

Question Number 39230 Answers: 2 Comments: 0

∫(dα/(sin 2α +sin 3α +sin 5α))=?

$\int \frac{d α}{\sin 2 α + \sin 3 α + \sin 5 α} = ?$

Question Number 39222 Answers: 1 Comments: 5

Question Number 39218 Answers: 1 Comments: 0

Question Number 39214 Answers: 0 Comments: 1

let f(x)= (e^(−3x) /(x^2 +4)) developp f at integr serie.

$l e t f (x) = \frac{e^{- 3 x}}{x^{2} + 4}$ $d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 39204 Answers: 0 Comments: 0

study tbe variation of f(x) =(2x+1)ln(1+e^(−x) ) and give its graph 2) calculate ∫_0 ^4 f(x)dx .

$s t u d y t b e v a r i a t i o n o f f (x) = (2 x + 1) l n (1 + e^{- x})$ $a n d g i v e i t s g r a p h$ $2) c a l c u l a t e \int_{0}^{4} f (x) d x .$

Question Number 39203 Answers: 0 Comments: 0

study and give the graph of f(x) = (e^(−x^2 ) /(x^2 +3 e^x ))

$s t u d y a n d g i v e t h e g r a p h o f$ $f (x) = \frac{e^{- x^{2}}}{x^{2} + 3 e^{x}}$

Question Number 39177 Answers: 2 Comments: 2

Question Number 39175 Answers: 1 Comments: 0

Question Number 39174 Answers: 1 Comments: 0

Question Number 39173 Answers: 0 Comments: 0

Given that A and B are two independent Events where P(A) = (4/5) and P(A ∪ B) = ((13)/5) . find a) P(A∩B) b) P(A∣B). hence draw tree Diagram for each posible out come

$G i v e n t h a t A a n d B a r e t w o$ $i n d e p e n d e n t E v e n t s$ $w h e r e P (A) = \frac{4}{5} a n d$ $P (A \cup B) = \frac{13}{5} .$ $f i n d a) P (A \cap B)$ $b) P (A ∣ B) .$ $h e n c e d r a w t r e e D i a g r a m$ $f o r e a c h p o s i b l e o u t c o m e$

Question Number 39172 Answers: 1 Comments: 1

find the angle between 3i − 4j and i − j

$f i n d t h e a n g l e b e t w e e n$ $3 i - 4 j a n d i - j$

Question Number 39171 Answers: 1 Comments: 0

Given that y = 3x^4 and x increases at the rate of 34% . find the percentage increase in y. [hint: using Bionomial method]

$G i v e n t h a t$ $y = 3 x^{4} a n d x i n c r e a s e s$ $a t t h e r a t e o f 34 % .$ $f i n d t h e p e r c e n t a g e i n c r e a s e$ $i n y .$ $[h i n t : u s i n g B i o n o m i a l$ $m e t h o d]$

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