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Question Number 57618 Answers: 1 Comments: 0

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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

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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

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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