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Question Number 57491 Answers: 1 Comments: 0

If R is a region enclosed by y = f(x), y = g(x), x = a, x = b, is it possible to have f(x) and g(x) such that the center of gravity (x^ , y^ ) is not inside R ?

$$\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{by}\:{y}\:=\:{f}\left({x}\right),\:{y}\:=\:{g}\left({x}\right),\:{x}\:=\:{a},\:{x}\:=\:{b}, \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{have}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{gravity}\:\left(\bar {{x}},\:\bar {{y}}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{inside}\:{R}\:? \\ $$

Question Number 57405 Answers: 1 Comments: 0

calculate lim_(x→0) ((1−cosx.cos(2x)....cos(nx))/x^2 ) with n integr natural not 0.

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{1}−{cosx}.{cos}\left(\mathrm{2}{x}\right)....{cos}\left({nx}\right)}{{x}^{\mathrm{2}} } \\ $$$${with}\:{n}\:{integr}\:{natural}\:{not}\:\mathrm{0}. \\ $$

Question Number 57348 Answers: 1 Comments: 2

Question Number 57309 Answers: 0 Comments: 0

Question Number 57284 Answers: 1 Comments: 1

y is varies directly as the square of x and inversely as z. if x is inceased by 10% and z is decreased by 20%, find the percentage change in y.

$${y}\:{is}\:{varies}\:{directly}\:{as}\:{the}\:{square}\:{of}\:{x}\:{and} \\ $$$${inversely}\:{as}\:{z}. \\ $$$${if}\:{x}\:{is}\:{inceased}\:{by}\:\mathrm{10\%}\:{and}\:{z}\:\:{is}\: \\ $$$${decreased}\:{by}\:\mathrm{20\%},\:{find}\:{the}\:{percentage} \\ $$$${change}\:{in}\:{y}. \\ $$

Question Number 57184 Answers: 2 Comments: 1

Question Number 57075 Answers: 1 Comments: 5

Question Number 57074 Answers: 1 Comments: 0

Solve the system. ^x C_(y + 1) = 20, ^(x − 1) C_y = 10

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}. \\ $$$$\:\:\:\:\:\:\overset{\mathrm{x}} {\:}\mathrm{C}_{\mathrm{y}\:+\:\mathrm{1}} \:\:=\:\:\mathrm{20},\:\:\:\:\:\:\:\:\:\:\:\overset{\mathrm{x}\:−\:\mathrm{1}} {\:}\mathrm{C}_{\mathrm{y}} \:\:=\:\:\mathrm{10} \\ $$

Question Number 57062 Answers: 2 Comments: 2

find the sum of all three digital natural numbers that are divisible by 7

$${find}\:{the}\:{sum}\:{of}\:{all} \\ $$$${three}\:{digital}\:{natural} \\ $$$${numbers}\:{that}\:{are}\: \\ $$$${divisible}\:{by}\:\mathrm{7} \\ $$

Question Number 56971 Answers: 1 Comments: 1

Question Number 56949 Answers: 0 Comments: 1

Question Number 56932 Answers: 1 Comments: 0

let f_n (t) =∫_0 ^∞ (dx/((x^2 +t^2 )^n )) with n from N and n≥1 1. find a explicit form of f_n (t) 2. what is the value of g_n (t)=∫_0 ^∞ ((t dx)/((x^2 +t^2 )^(n+1) )) ? 3. calculate ∫_0 ^∞ (dx/((x^2 +3)^4 )) and ∫_0 ^∞ (dx/((x^2 +16)^3 ))

$${let}\:{f}_{{n}} \left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{{n}} } \\ $$$${with}\:{n}\:{from}\:{N}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\mathrm{1}.\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({t}\right) \\ $$$$\mathrm{2}.\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$${g}_{{n}} \left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{t}\:{dx}}{\left({x}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)^{{n}+\mathrm{1}} }\:? \\ $$$$\mathrm{3}.\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{4}} } \\ $$$${and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{16}\right)^{\mathrm{3}} } \\ $$

Question Number 56900 Answers: 1 Comments: 0

Question Number 56890 Answers: 0 Comments: 0

d^2 y/dx^2 =x^2 y=0

$${d}^{\mathrm{2}} {y}/{dx}^{\mathrm{2}} ={x}^{\mathrm{2}} {y}=\mathrm{0} \\ $$

Question Number 56854 Answers: 0 Comments: 1

There was a post sime time back about not being able to backup or restore. Can anyone send the requirdd information if you faced the same problem?

$$\mathrm{There}\:\mathrm{was}\:\mathrm{a}\:\mathrm{post}\:\mathrm{sime}\:\mathrm{time}\:\mathrm{back} \\ $$$$\mathrm{about}\:\mathrm{not}\:\mathrm{being}\:\mathrm{able}\:\mathrm{to}\:\mathrm{backup} \\ $$$$\mathrm{or}\:\mathrm{restore}.\:\mathrm{Can}\:\mathrm{anyone}\:\mathrm{send}\:\mathrm{the}\:\mathrm{requirdd} \\ $$$$\mathrm{information}\:\mathrm{if}\:\mathrm{you}\:\mathrm{faced}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{problem}? \\ $$

Question Number 56851 Answers: 0 Comments: 0

let: [u_n =(√u_(n−1) )+(√u_(n−2) ),u_0 =1,u_1 =1] ⇒ Σ_0 ^∞ ((1/u_n ))=?

$${let}:\:\left[\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}} =\sqrt{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}−\mathrm{1}} }+\sqrt{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}−\mathrm{2}} },\boldsymbol{\mathrm{u}}_{\mathrm{0}} =\mathrm{1},\boldsymbol{\mathrm{u}}_{\mathrm{1}} =\mathrm{1}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\underset{\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}} }\right)=? \\ $$

Question Number 56847 Answers: 0 Comments: 2

d2y/dx2=x2y=0

$${d}\mathrm{2}{y}/{dx}\mathrm{2}={x}\mathrm{2}{y}=\mathrm{0} \\ $$

Question Number 56823 Answers: 1 Comments: 1

Question Number 56775 Answers: 0 Comments: 1

if x,y∍ℜ,show that ∣x+y∣=∣x∣+∣y∣ iff xy≥0

$${if}\:{x},{y}\backepsilon\Re,{show}\:{that}\:\mid{x}+{y}\mid=\mid{x}\mid+\mid{y}\mid\:{iff}\:{xy}\geqslant\mathrm{0} \\ $$

Question Number 56664 Answers: 0 Comments: 2

Question Number 56663 Answers: 0 Comments: 0

i think everybody are in deep thought...

$${i}\:{think}\:{everybody}\:{are}\:{in}\:{deep}\:{thought}... \\ $$

Question Number 56661 Answers: 0 Comments: 0

Question Number 56660 Answers: 0 Comments: 5

Question Number 56659 Answers: 0 Comments: 1

Question Number 56569 Answers: 0 Comments: 0

Question Number 56565 Answers: 0 Comments: 2

It is my kind request to those who post questions ...pls go through the details of answer...and give feed back...pls activate yourselves to pay your attention in the details of answer...do not become self satisfied by getting your desired results.. unfurl your mind and act in such away that we get a tip of iceberg of your satisfation.Tanmay

$${It}\:{is}\:{my}\:{kind}\:{request}\:{to}\:{those}\:{who}\:{post}\:{questions} \\ $$$$...{pls}\:{go}\:{through}\:{the}\:{details}\:{of}\:{answer}...{and}\:{give} \\ $$$${feed}\:{back}...{pls}\:{activate}\:{yourselves}\:{to}\:{pay}\:{your} \\ $$$${attention}\:{in}\:{the}\:{details}\:{of}\:{answer}...{do}\:{not}\:{become} \\ $$$${self}\:{satisfied}\:{by}\:{getting}\:{your}\:{desired}\:{results}.. \\ $$$${unfurl}\:{your}\:{mind}\:{and}\:{act}\:{in}\:{such}\:{away}\:{that} \\ $$$${we}\:{get}\:{a}\:{tip}\:{of}\:{iceberg}\:{of}\:{your}\:{satisfation}.{Tanmay} \\ $$

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