Question and Answers Forum

What mass of ice at −14 will be needed to cool 200 cm^3 of an orange drink (essentially water) from 25°C to 10°C (specific latent heat of fusion of ice = 3.36 × 10^5 jkg^(−1) specific heat capacity of ice = 2100 jkg^(−1) k^(−1) specific heat capacity of water = 4200 jkg^(−1) k^(−1) .

$W h a t m a s s o f i c e a t - 14 w i l l b e n e e d e d t o c o o l 200 {c m}^{3} o f$ $a n o r a n g e d r i n k (e s s e n t i a l l y w a t e r) f r o m 25 ° C t o 10 ° C$ $(s p e c i f i c l a t e n t h e a t o f f u s i o n o f i c e = 3.36 \times 10^{5} {j k g}^{- 1}$ $s p e c i f i c h e a t c a p a c i t y o f i c e = 2100 {j k g}^{- 1} k^{- 1}$ $s p e c i f i c h e a t c a p a c i t y o f w a t e r = 4200 {j k g}^{- 1} k^{- 1} .$

Question Number 6644 Answers: 0 Comments: 0

Prove (d/dt) e_ρ =φ e_φ , (d/dt) e_φ = −φ e_ρ where dots denote differentiation with respect to time t.

$P r o v e \frac{d}{d t} e_{ρ} = ϕ e_{ϕ}, \frac{d}{d t} e_{ϕ} = - ϕ e_{ρ} w h e r e d o t s d e n o t e$ $d i f f e r e n t i a t i o n w i t h r e s p e c t t o t i m e t .$

Question Number 6642 Answers: 0 Comments: 0

Represent the vector A=zi−2xj+yk in cylindrical coordinates. Thus determine A_ρ , A_φ , A_z .

$R e p r e s e n t t h e v e c t o r A = z i - 2 x j + y k i n c y l i n d r i c a l c o o r d i n a t e s .$ $T h u s d e t e r m i n e A_{ρ}, A_{ϕ}, A_{z} .$

Question Number 6641 Answers: 0 Comments: 0

Q(1) Express div A = ▽ . A in orthogonal coordinates. Q(2) Express ▽^2 φ in orthogonal curvilinear coordinates. Q(3) Express (a) ▽ × Aand (b) ▽^2 φ in spherical coordinates.

$Q (1) E x p r e s s d i v A = ▽ . A i n o r t h o g o n a l c o o r d i n a t e s .$ $Q (2) E x p r e s s ▽^{2} ϕ i n o r t h o g o n a l c u r v i l i n e a r c o o r d i n a t e s .$ $Q (3) E x p r e s s (a) ▽ \times A a n d (b) ▽^{2} ϕ i n s p h e r i c a l c o o r d i n a t e s .$

Question Number 6640 Answers: 0 Comments: 4

ABC is a triangle,whose one vertex is moving along a circular path. Discuss the nature of the path, along which the centroid of the triangle is moving.

$ABC i s a t r i a n g l e, w h o s e o n e v e r t e x$ $i s m o v i n g a l o n g a c i r c u l a r p a t h .$ $D i s c u s s t h e n a t u r e o f t h e p a t h, a l o n g$ $w h i c h t h e c e n t r o i d o f t h e t r i a n g l e$ $i s m o v i n g .$

Question Number 6638 Answers: 0 Comments: 0

The radius of curvature of a thin equiconvex lens is 40.0 cm the lens is made of glass of refractive index 1.660. find the position of the image of an object placed on the axis of the axis of the lens at a distance of 50.0 mm from the pole.

$T h e r a d i u s o f c u r v a t u r e o f a t h i n e q u i c o n v e x l e n s i s 40.0 c m$ $t h e l e n s i s m a d e o f g l a s s o f r e f r a c t i v e i n d e x 1.660 . f i n d t h e$ $p o s i t i o n o f t h e i m a g e o f a n o b j e c t p l a c e d o n t h e a x i s o f t h e$ $a x i s o f t h e l e n s a t a d i s t a n c e o f 50.0 m m f r o m t h e p o l e .$

Question Number 6635 Answers: 1 Comments: 2

Question Number 6630 Answers: 0 Comments: 0

A small source of sound emit energy uniformly in all direction for a particular frequency, the intensity of sound at a distane 2.0m from the source is 1.0 × 10^(−5) and corresponds to amplitude of oscillation on the air molecules of 7u . assuming sound is propagated with any loss of energy calculate: (1) Intensity of sound (2) the amplitude of oscillation of the air molecules at a distance of 5.0m from the source.

$A s m a l l s o u r c e o f s o u n d e m i t e n e r g y u n i f o r m l y i n a l l$ $d i r e c t i o n f o r a p a r t i c u l a r f r e q u e n c y, t h e i n t e n s i t y o f s o u n d$ $a t a d i s t a n e 2.0 m f r o m t h e s o u r c e i s 1.0 \times 10^{- 5} a n d$ $c o r r e s p o n d s t o a m p l i t u d e o f o s c i l l a t i o n o n t h e a i r m o l e c u l e s$ $o f 7 u . a s s u m i n g s o u n d i s p r o p a g a t e d w i t h a n y l o s s o f e n e r g y$ $c a l c u l a t e :$ $(1) I n t e n s i t y o f s o u n d$ $(2) t h e a m p l i t u d e o f o s c i l l a t i o n o f t h e a i r m o l e c u l e s$ $a t a d i s t a n c e o f 5.0 m f r o m t h e s o u r c e .$

Question Number 6612 Answers: 0 Comments: 0

S=(√(2+(√(4+(√(6+(√(...)))))))) S=???

$S = \sqrt{2 + \sqrt{4 + \sqrt{6 + \sqrt{. . .}}}}$ $S = ? ? ?$

Question Number 6610 Answers: 0 Comments: 5

If you have a real continuous function f(x), If you take a distance between f(x) and f(x+1), what is the average distance within a≤x≤b?

$If you have a real continuous function f (x),$ $If you take a distance between$ $f (x) and f (x + 1), what is the average$ $distance within a ⩽ x ⩽ b ?$

Question Number 6609 Answers: 0 Comments: 5

You have a 1x1 cm square. If you pick two random points inside the square, what is the average distance between those points?

$You have a 1 x 1 cm square . If you pick$ $two random points inside the square,$ $what is the average distance between$ $those points ?$

Question Number 6605 Answers: 0 Comments: 1

Let c be a constant. Using Var(X) = E [(X− E [X])^2 ], show that (a) Var(c X) = c^2 Var(X); (b) Var ( c+X) = Var(X).

$L e t c b e a c o n s t a n t . U s i n g V a r (X) = E [{(X - E [X])}^{2}], s h o w t h a t$ $(a) V a r (c X) = c^{2} V a r (X);$ $(b) V a r (c + X) = V a r (X) .$

Question Number 6604 Answers: 1 Comments: 3

If the density function of X equals f(x) = { ((c e^(−2x) , 0<x<∞)),((0 , x<0)) :} find c. What is P{X>2}?

$I f t h e d e n s i t y f u n c t i o n o f X e q u a l s$ $f (x) = {\begin{cases} c e^{- 2 x}, 0 < x < \infty \\ 0, x < 0 \end{cases}$ $f i n d c . W h a t i s P {X > 2} ?$

Question Number 6602 Answers: 0 Comments: 1

%ml

$% m l$

Question Number 6599 Answers: 1 Comments: 0

Prove that Σ_(j=1) ^N (X_j −1)^2 =Σ_(j=1) ^N X_j ^2 − 2 Σ_(j=1) ^N X_j + N.

$P r o v e t h a t \underset{j = 1}{\sum^{N}} {(X_{j} - 1)}^{2} = \underset{j = 1}{\sum^{N}} X_{j}^{2} - 2 \underset{j = 1}{\sum^{N}} X_{j} + N .$

Question Number 6593 Answers: 0 Comments: 2

Question Number 6590 Answers: 0 Comments: 1

Solve for a ((a^2 +1)/a)=(a/(1−a^2 ))

$Solve for a$ $\frac{a^{2} + 1}{a} = \frac{a}{1 - a^{2}}$

Question Number 6588 Answers: 0 Comments: 3

Expansion of Q6582 ∫_0 ^( ∞) e^(−ix^2 ) dx=???

$Expansion of Q 6582$ $\int_{0}^{\infty} e^{- {i x}^{2}} d x = ? ? ?$

Question Number 6583 Answers: 1 Comments: 0

An aqeous solution of tetraoxosulphate(IV) has a density of 1.80 g/cm^3 and 98% purity level. what volume of this solution must be diluted to give 250 cm^3 of 0.500 mol/dm^3 H_2 SO_4 solution ?

$A n a q e o u s s o l u t i o n o f t e t r a o x o s u l p h a t e (I V) h a s a d e n s i t y$ $o f 1.80 g / {c m}^{3} a n d 98 % p u r i t y l e v e l . w h a t v o l u m e o f t h i s$ $s o l u t i o n m u s t b e d i l u t e d t o g i v e 250 {c m}^{3} o f 0.500 m o l / {d m}^{3}$ $H_{2} {S O}_{4} s o l u t i o n ?$

Question Number 6582 Answers: 1 Comments: 0

∫e^(−ix^2 ) dx=??

$\int e^{- {i x}^{2}} d x = ? ?$

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