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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=??

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

Question Number 6564 Answers: 1 Comments: 5

Let φ={ l_1 , l_2 , l_3 } be a set of three, nonparallel lines that all meet at one point R in the plane. Investigate conditions on φ such that R is the centroid of some triangle.

$L e t ϕ = {l_{1}, l_{2}, l_{3}} b e a s e t o f t h r e e, n o n p a r a l l e l$ $l i n e s t h a t a l l m e e t a t o n e p o i n t R i n$ $t h e p l a n e . I n v e s t i g a t e c o n d i t i o n s o n ϕ$ $s u c h t h a t R i s t h e c e n t r o i d o f s o m e t r i a n g l e .$

Question Number 6558 Answers: 1 Comments: 1

If secx − tanx = (1/4) find secx + tanx

$I f s e c x - t a n x = \frac{1}{4}$ $f i n d s e c x + t a n x$

Question Number 6553 Answers: 0 Comments: 10

Question Number 6549 Answers: 0 Comments: 0

A table with three legs sits smoothly on every kind of surface, whereas a table with four legs may not sit on rough surface. Why?

$A t a b l e w i t h t h r e e l e g s s i t s s m o o t h l y$ $o n e v e r y k i n d o f s u r f a c e, w h e r e a s a$ $t a b l e w i t h f o u r l e g s m a y n o t s i t o n$ $r o u g h s u r f a c e . W h y ?$

Question Number 6535 Answers: 0 Comments: 4

Σ_(x=1) ^∞ (1/x) = 1+(1/2)+(1/3)+(1/4)+(1/5)+... Is the following true? ∴Σ(1/x)=Σ((1/(2x))+(1/(2x−1))) =Σ(((2x−1+2x)/(2x(2x−1)))) =Σ(((2x−2+1+2x)/(2x(2x−1)))) =Σ(((4x−2)/(2x(2x−1)))+(1/(2x(2x−1)))) =Σ(((2(2x−1))/(2x(2x−1)))+(1/(2x(2x−1)))) =Σ((1/x)+(1/(2x(2x−1)))) ∴ Σ_(x=1) ^∞ (1/x) =Σ_(x=1) ^∞ (1/x) +Σ_(x=1) ^∞ (1/(2x(2x−1)))

$\underset{x = 1}{\sum^{\infty}} \frac{1}{x} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + . . .$ $Is the following true ?$ $∴ Σ \frac{1}{x} = Σ (\frac{1}{2 x} + \frac{1}{2 x - 1})$ $= Σ (\frac{2 x - 1 + 2 x}{2 x (2 x - 1)})$ $= Σ (\frac{2 x - 2 + 1 + 2 x}{2 x (2 x - 1)})$ $= Σ (\frac{4 x - 2}{2 x (2 x - 1)} + \frac{1}{2 x (2 x - 1)})$ $= Σ (\frac{2 (2 x - 1)}{2 x (2 x - 1)} + \frac{1}{2 x (2 x - 1)})$ $= Σ (\frac{1}{x} + \frac{1}{2 x (2 x - 1)})$ $∴ \underset{x = 1}{\sum^{\infty}} \frac{1}{x} = \underset{x = 1}{\sum^{\infty}} \frac{1}{x} + \underset{x = 1}{\sum^{\infty}} \frac{1}{2 x (2 x - 1)}$

Question Number 6524 Answers: 0 Comments: 0

The yearly requirement for a particular product is 16000 units and its unit price is $100.00, if the holding cost is 10% of the unit price while its ordering cost is $50.00 calculate the amount of order per annum.

$T h e y e a r l y r e q u i r e m e n t f o r a p a r t i c u l a r p r o d u c t i s 16000 u n i t s$ $a n d i t s u n i t p r i c e i s $ 100.00, i f t h e h o l d i n g c o s t i s 10 % o f t h e$ $u n i t p r i c e w h i l e i t s o r d e r i n g c o s t i s $ 50.00$ $c a l c u l a t e t h e a m o u n t o f o r d e r p e r a n n u m .$