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AllQuestion and Answers: Page 1894

Question Number 9699 Answers: 0 Comments: 3

Question Number 9698 Answers: 1 Comments: 0

a^2 +ab+b^2

$${a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} \\ $$

Question Number 9690 Answers: 1 Comments: 3

Question Number 9686 Answers: 1 Comments: 0

Question Number 9683 Answers: 0 Comments: 2

Question Number 9678 Answers: 0 Comments: 1

Question Number 9677 Answers: 1 Comments: 2

Question Number 9675 Answers: 0 Comments: 2

Question Number 9662 Answers: 1 Comments: 0

I have 2 buckets. Each bucket contains green and blue balls The first bucket contains 3 green balls and 7 blue balls. Second bucket contains 7 green balls and 8 blue balls. I want to take those balls with coin toss. If head, I will take 1 ball from each bucket. But if tail, I will take 2 balls from each bucket. What is the propability if all the balls that have been taken have the same color? (sorry for my grammar)

$$\mathrm{I}\:\mathrm{have}\:\mathrm{2}\:\mathrm{buckets}.\:\mathrm{Each}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{green}\:\mathrm{and}\:\mathrm{blue}\:\mathrm{balls} \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{green}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{7}\:\mathrm{blue}\:\mathrm{balls}. \\ $$$$\mathrm{Second}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{7}\:\mathrm{green}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{8}\:\mathrm{blue}\:\mathrm{balls}. \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{take}\:\mathrm{those}\:\mathrm{balls}\:\mathrm{with}\:\mathrm{coin}\:\mathrm{toss}. \\ $$$$\mathrm{If}\:\mathrm{head},\:\mathrm{I}\:\mathrm{will}\:\mathrm{take}\:\mathrm{1}\:\mathrm{ball}\:\mathrm{from}\:\mathrm{each}\:\mathrm{bucket}. \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{tail},\:\mathrm{I}\:\mathrm{will}\:\mathrm{take}\:\mathrm{2}\:\mathrm{balls}\:\mathrm{from}\:\mathrm{each}\:\mathrm{bucket}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{propability}\:\mathrm{if}\:\mathrm{all}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{that}\:\mathrm{have}\:\mathrm{been}\:\mathrm{taken} \\ $$$$\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}? \\ $$$$\left({sorry}\:{for}\:{my}\:{grammar}\right) \\ $$

Question Number 9661 Answers: 0 Comments: 3

a) 2^i = b) (a_1 + b_1 i)^(a_2 + b_2 i) = Powers of complex numbers ???

$$\left.{a}\right)\:\mathrm{2}^{{i}} \:=\: \\ $$$$ \\ $$$$\left.{b}\right)\:\left({a}_{\mathrm{1}} \:+\:{b}_{\mathrm{1}} {i}\right)^{{a}_{\mathrm{2}} \:+\:{b}_{\mathrm{2}} {i}} \:=\: \\ $$$${Powers}\:{of}\:{complex}\:{numbers}\:??? \\ $$

Question Number 9658 Answers: 1 Comments: 5

Experiment shows that the viscous force, F on a spherical body of radius, r moving with angular velocity, n is, F = Kr^a n^b ω^c . Where K is a dimentionless constant. using the method of dimentional analysis, determine the values of a, b and c

$$\mathrm{Experiment}\:\mathrm{shows}\:\mathrm{that}\:\mathrm{the}\:\mathrm{viscous}\:\mathrm{force},\:\mathrm{F} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{spherical}\:\mathrm{body}\:\mathrm{of}\:\mathrm{radius},\:\mathrm{r}\:\mathrm{moving}\:\mathrm{with} \\ $$$$\mathrm{angular}\:\mathrm{velocity},\:\mathrm{n}\:\mathrm{is},\:\mathrm{F}\:=\:\mathrm{Kr}^{\mathrm{a}} \mathrm{n}^{\mathrm{b}} \omega^{\mathrm{c}} . \\ $$$$\mathrm{Where}\:\mathrm{K}\:\mathrm{is}\:\mathrm{a}\:\mathrm{dimentionless}\:\mathrm{constant}. \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{dimentional}\:\mathrm{analysis}, \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c} \\ $$

Question Number 9654 Answers: 1 Comments: 0

lim_(x→4) ((ax+b−(√x))/(x−4))=(3/4), a+b=...?

$$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}−\sqrt{\mathrm{x}}}{\mathrm{x}−\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{4}},\:\:\mathrm{a}+\mathrm{b}=...? \\ $$

Question Number 9653 Answers: 0 Comments: 0

Question Number 9648 Answers: 1 Comments: 0

Question Number 9642 Answers: 0 Comments: 0

Question Number 9637 Answers: 2 Comments: 0

A body starts from rest and move with uniform acceleration of 6m/s^2 . what distance does it covered in the 3rd seconds.

$$\mathrm{A}\:\mathrm{body}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{and}\:\mathrm{move}\:\mathrm{with}\: \\ $$$$\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{6m}/\mathrm{s}^{\mathrm{2}} .\:\:\mathrm{what}\: \\ $$$$\mathrm{distance}\:\mathrm{does}\:\mathrm{it}\:\mathrm{covered}\:\mathrm{in}\:\mathrm{the}\:\mathrm{3rd}\:\mathrm{seconds}. \\ $$

Question Number 9636 Answers: 1 Comments: 4

The distance x m have used by a particle in time t sec is described by the equation x = 10 + 12t^2 Find the average speed of the particle between the interval t = 2 sec and t = 5 sec

$$\mathrm{The}\:\mathrm{distance}\:\mathrm{x}\:\mathrm{m}\:\mathrm{have}\:\mathrm{used}\:\mathrm{by}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{in} \\ $$$$\mathrm{time}\:\mathrm{t}\:\mathrm{sec}\:\mathrm{is}\:\mathrm{described}\:\mathrm{by}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}\:=\:\mathrm{10}\:+\:\mathrm{12t}^{\mathrm{2}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{average}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{interval}\:\mathrm{t}\:=\:\mathrm{2}\:\mathrm{sec}\:\mathrm{and}\:\mathrm{t}\:=\:\mathrm{5}\:\mathrm{sec} \\ $$

Question Number 9635 Answers: 2 Comments: 1

A body of mass 20g performs simple harmonic motion at a frequency of 5Hz, at a distance of 10cm from the mean position. its velocity is 200cm/s. calculate (i) Maximum displacement from the mean position (ii) Maximum velocity (iii) Maximum potential energy.

$$\mathrm{A}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{20g}\:\mathrm{performs}\:\mathrm{simple}\:\mathrm{harmonic} \\ $$$$\mathrm{motion}\:\mathrm{at}\:\mathrm{a}\:\mathrm{frequency}\:\mathrm{of}\:\mathrm{5Hz},\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance} \\ $$$$\mathrm{of}\:\mathrm{10cm}\:\mathrm{from}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{position}.\:\mathrm{its}\:\mathrm{velocity} \\ $$$$\mathrm{is}\:\mathrm{200cm}/\mathrm{s}.\:\:\mathrm{calculate} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Maximum}\:\mathrm{displacement}\:\mathrm{from}\:\mathrm{the}\:\mathrm{mean} \\ $$$$\mathrm{position} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Maximum}\:\mathrm{velocity} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{Maximum}\:\mathrm{potential}\:\mathrm{energy}. \\ $$

Question Number 9627 Answers: 1 Comments: 2

Question Number 9623 Answers: 1 Comments: 1

Evaluate : ∫_4 ^(5.2) ln(x) dx using trapezoidal rule. take h = 0.2

$$\mathrm{Evaluate}\::\:\int_{\mathrm{4}} ^{\mathrm{5}.\mathrm{2}} \:\mathrm{ln}\left(\mathrm{x}\right)\:\mathrm{dx}\:\: \\ $$$$\mathrm{using}\:\mathrm{trapezoidal}\:\mathrm{rule}.\:\mathrm{take}\:\mathrm{h}\:=\:\mathrm{0}.\mathrm{2} \\ $$

Question Number 9620 Answers: 2 Comments: 0

Two persons X and Y together can do a job in 36 days. If X′s ability to do the work is twice that of Y, then find the number of days in which Y can do the work individually.

$$\mathrm{Two}\:\mathrm{persons}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{together}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a} \\ $$$$\mathrm{job}\:\mathrm{in}\:\mathrm{36}\:\mathrm{days}.\:\mathrm{If}\:\mathrm{X}'\mathrm{s}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{do}\:\mathrm{the} \\ $$$$\mathrm{work}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{that}\:\mathrm{of}\:\mathrm{Y},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{days}\:\mathrm{in}\:\mathrm{which}\:\mathrm{Y}\:\mathrm{can} \\ $$$$\mathrm{do}\:\mathrm{the}\:\mathrm{work}\:\mathrm{individually}. \\ $$

Question Number 9617 Answers: 0 Comments: 2

Question Number 9604 Answers: 0 Comments: 0

is ▽×(▽×A)=▽(▽∙A)−▽^2 A F×(▽×A)=F(▽∙A)−▽^2 A the same?

$${is}\: \\ $$$$\bigtriangledown×\left(\bigtriangledown×{A}\right)=\bigtriangledown\left(\bigtriangledown\centerdot{A}\right)−\bigtriangledown^{\mathrm{2}} {A} \\ $$$${F}×\left(\bigtriangledown×{A}\right)={F}\left(\bigtriangledown\centerdot{A}\right)−\bigtriangledown^{\mathrm{2}} {A} \\ $$$${the}\:{same}? \\ $$

Question Number 9603 Answers: 2 Comments: 0

A regular hexagon has sides of lenght 8 cm. Find the perpendicular distance between two opposite faces.

$$\mathrm{A}\:\mathrm{regular}\:\mathrm{hexagon}\:\mathrm{has}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{8}\:\mathrm{cm}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{perpendicular}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{two} \\ $$$$\mathrm{opposite}\:\mathrm{faces}. \\ $$

Question Number 9600 Answers: 0 Comments: 1

Question Number 9594 Answers: 1 Comments: 0

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