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Question Number 37168 Answers: 0 Comments: 0

A stone is thrown into a circular pond of radius 1m.Suppose the stone falls uniformly at random on the area of the pond.What will be the expected distance od the stone from the centre of the pond. a)1/3 b)1/2 c)2/3 d)1/(√2)

$${A}\:{stone}\:{is}\:{thrown}\:{into}\:{a}\:{circular} \\ $$$${pond}\:{of}\:{radius}\:\mathrm{1}{m}.{Suppose}\:{the} \\ $$$${stone}\:{falls}\:{uniformly}\:{at}\:{random} \\ $$$${on}\:{the}\:{area}\:{of}\:{the}\:{pond}.{What} \\ $$$${will}\:{be}\:{the}\:{expected}\:{distance}\:{od} \\ $$$${the}\:{stone}\:{from}\:{the}\:{centre}\:{of}\:{the} \\ $$$${pond}. \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left./\mathrm{3}\:{b}\right)\mathrm{1}/\mathrm{2}\:{c}\right)\mathrm{2}/\mathrm{3}\:{d}\right)\mathrm{1}/\sqrt{\mathrm{2}} \\ $$

Question Number 37166 Answers: 0 Comments: 2

if 3x^2 +2αxy+2y^2 +2ax−4y+1 can be resolved into two linear factors, prove that ′α′ is a root of the equation x^2 +4ax+2a^2 +6=0

$${if}\:\:\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}\alpha{xy}+\mathrm{2}{y}^{\mathrm{2}} +\mathrm{2}{ax}−\mathrm{4}{y}+\mathrm{1} \\ $$$${can}\:{be}\:{resolved}\:\:{into}\:\:{two}\:\:{linear} \\ $$$${factors},\:\:{prove}\:\:{that}\:\:'\alpha'\:\:{is}\:{a}\:{root}\: \\ $$$${of}\:{the}\:{equation}\:{x}^{\mathrm{2}} +\mathrm{4}{ax}+\mathrm{2}{a}^{\mathrm{2}} +\mathrm{6}=\mathrm{0} \\ $$

Question Number 37155 Answers: 0 Comments: 4

3cos x−4sin x=tan^2 x locate x.

$$\mathrm{3cos}\:{x}−\mathrm{4sin}\:{x}=\mathrm{tan}\:^{\mathrm{2}} {x} \\ $$$${locate}\:{x}. \\ $$

Question Number 37146 Answers: 0 Comments: 0

Question Number 37143 Answers: 0 Comments: 0

Why are following statements wrong? a) There exists a function with domain R satisfying f(x)<0 ∀x , f′(x)>0∀x and f′′(x)>0∀x. b) If f′′(c)=0 then (c,f(c)) is an inflection point.

$$\mathrm{Why}\:\mathrm{are}\:\mathrm{following}\:\mathrm{statements}\:\mathrm{wrong}? \\ $$$$\left.\mathrm{a}\right)\:\mathrm{There}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{function}\:\mathrm{with}\:\mathrm{domain}\: \\ $$$$\mathrm{R}\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{x}\right)<\mathrm{0}\:\forall\mathrm{x}\:,\:\mathrm{f}'\left(\mathrm{x}\right)>\mathrm{0}\forall\mathrm{x}\:\mathrm{and} \\ $$$$\mathrm{f}''\left(\mathrm{x}\right)>\mathrm{0}\forall\mathrm{x}. \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{If}\:\mathrm{f}''\left(\mathrm{c}\right)=\mathrm{0}\:\mathrm{then}\:\left(\mathrm{c},\mathrm{f}\left(\mathrm{c}\right)\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{inflection} \\ $$$$\mathrm{point}. \\ $$

Question Number 37133 Answers: 0 Comments: 0

Question Number 37132 Answers: 0 Comments: 0

Question Number 37131 Answers: 0 Comments: 2

Question Number 37136 Answers: 0 Comments: 1

Question Number 37139 Answers: 2 Comments: 0

if α , β are the roots of the quadratic equation ax^2 +bx+c =0 then find the quadratic equation whose roots are α^(2 ) , β^2

$${if}\:\alpha\:,\:\beta\:\:{are}\:{the}\:{roots}\:{of}\:{the}\:{quadratic} \\ $$$${equation}\:{ax}^{\mathrm{2}} +{bx}+{c}\:=\mathrm{0}\:{then}\:\:{find} \\ $$$${the}\:{quadratic}\:{equation}\:{whose}\:{roots} \\ $$$${are}\:\:\alpha^{\mathrm{2}\:\:\:} ,\:\beta^{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$

Question Number 37137 Answers: 2 Comments: 4

Find minimum distance between y^2 =8x and x^2 +(y+6)^2 =1.

$$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{y}^{\mathrm{2}} =\mathrm{8}{x}\:{and}\:{x}^{\mathrm{2}} +\left({y}+\mathrm{6}\right)^{\mathrm{2}} =\mathrm{1}. \\ $$

Question Number 37129 Answers: 0 Comments: 0

Question Number 37128 Answers: 0 Comments: 0

Question Number 37511 Answers: 0 Comments: 3

To the developer of Tinku Tara: dear sir: for some unknown reasons I don′t get any notification from the app when a post, in which I am involved, has been updated. Where is the problem and how can I solve it? Thank you!

$${To}\:{the}\:{developer}\:{of}\:{Tinku}\:{Tara}: \\ $$$${dear}\:{sir}:\:{for}\:{some}\:{unknown}\:{reasons} \\ $$$${I}\:{don}'{t}\:{get}\:{any}\:{notification}\:{from}\:{the} \\ $$$${app}\:{when}\:{a}\:{post},\:{in}\:{which}\:{I}\:{am}\:{involved}, \\ $$$${has}\:{been}\:{updated}.\:{Where}\:{is}\:{the} \\ $$$${problem}\:{and}\:{how}\:{can}\:{I}\:{solve}\:{it}? \\ $$$${Thank}\:{you}! \\ $$

Question Number 37123 Answers: 0 Comments: 1

draw ΔAB^ C and its image ΔA′B^′ C^′ after a reflection in line y=x if A(0,3),B(3,0),C(3,2).what is the line of symmetry of the two figures?

$${draw}\:\Delta{A}\overset{} {{B}C}\:{and}\:{its}\:{image}\:\:\Delta{A}'{B}^{'} {C}^{'} \: \\ $$$${after}\:{a}\:{reflection}\:{in}\:{line}\:{y}={x} \\ $$$${if}\:{A}\left(\mathrm{0},\mathrm{3}\right),{B}\left(\mathrm{3},\mathrm{0}\right),{C}\left(\mathrm{3},\mathrm{2}\right).{what}\:{is}\:{the} \\ $$$${line}\:{of}\:{symmetry}\:\:{of}\:{the}\:{two}\:{figures}? \\ $$

Question Number 37122 Answers: 0 Comments: 0

draw ΔAB^ C and its image ΔA′B^′ C^′ after a reflection in line y=x if A(0,3),B(3,0),C(3,2).what is the line of symmetry of the two figures?

Question Number 37110 Answers: 1 Comments: 2

prove that (cos𝛝−sin𝛝)^2 +(cosec𝛝+sin𝛝)^2 =2

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{cos}\vartheta}−\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{cosec}\vartheta}+\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} =\mathrm{2} \\ $$

Question Number 37108 Answers: 1 Comments: 0

If 4x+8cos x+tan x−2sec x−4log {cosx(1+sin x)}≥6 ∀ x ε [0,ψ) then largest value of ψ is ?

$$\mathrm{If}\:\mathrm{4}{x}+\mathrm{8cos}\:{x}+\mathrm{tan}\:{x}−\mathrm{2sec}\:{x}−\mathrm{4log}\:\left\{\mathrm{cos}{x}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\right\}\geqslant\mathrm{6} \\ $$$$\forall\:{x}\:\epsilon\:\left[\mathrm{0},\psi\right)\:\mathrm{then}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\psi\:\mathrm{is}\:? \\ $$