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Question Number 79670 Answers: 0 Comments: 0

find the covulation coefficient from the regression equation x=15.03−0.98y and y=14.72−0.93x

$${find}\:{the}\:{covulation}\:{coefficient}\:{from}\: \\ $$$${the}\:{regression}\:{equation}\:{x}=\mathrm{15}.\mathrm{03}−\mathrm{0}.\mathrm{98}{y} \\ $$$${and}\:{y}=\mathrm{14}.\mathrm{72}−\mathrm{0}.\mathrm{93}{x} \\ $$

Question Number 79652 Answers: 0 Comments: 0

what is the value of Σ_(n=1) ^∞ [(4n^2 −1)ln(1−(1/(4n^2 )))+1]

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left[\left(\mathrm{4n}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4n}^{\mathrm{2}} }\right)+\mathrm{1}\right]\: \\ $$

Question Number 79649 Answers: 1 Comments: 6

given a,ar,ar^2 ,ar^3 ,... is a GPwith n→∞ ,r < 1 if : a,x_1 ,x_2 ,ar,x_3 , x_4 ,x_5 ,x_6 ,ar^2 , x_7 ,x_8 ,x_9 ,x_(10) ,x_(11) ,x_(12) , ar^3 ,... . where : a,x_1 ,x_2 ,ar ⇒AP ar,x_3 ,x_4 ,x_5 ,x_6 ,ar^2 ⇒AP ar^2 ,x_7 ,x_8 ,x_9 ,x_(10) ,x_(11) ,x_(12) ,ar^3 ⇒AP ...etc if lim_(n→∞) (x_1 +x_2 +x_3 +...)= ((21)/(16))×(a/(1−r)) what is r ?

$$\mathrm{given}\:\mathrm{a},\mathrm{ar},\mathrm{ar}^{\mathrm{2}} ,\mathrm{ar}^{\mathrm{3}} ,...\:\mathrm{is}\:\mathrm{a}\:\mathrm{GPwith}\: \\ $$$$\mathrm{n}\rightarrow\infty\:,\mathrm{r}\:<\:\mathrm{1} \\ $$$$\mathrm{if}\::\:\mathrm{a},\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{ar},\mathrm{x}_{\mathrm{3}} ,\:\mathrm{x}_{\mathrm{4}} ,\mathrm{x}_{\mathrm{5}} ,\mathrm{x}_{\mathrm{6}} ,\mathrm{ar}^{\mathrm{2}} , \\ $$$$\mathrm{x}_{\mathrm{7}} ,\mathrm{x}_{\mathrm{8}} ,\mathrm{x}_{\mathrm{9}} ,\mathrm{x}_{\mathrm{10}} ,\mathrm{x}_{\mathrm{11}} ,\mathrm{x}_{\mathrm{12}} ,\:\mathrm{ar}^{\mathrm{3}} ,...\:. \\ $$$$\mathrm{where}\::\:\mathrm{a},\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{ar}\:\Rightarrow\mathrm{AP} \\ $$$$\mathrm{ar},\mathrm{x}_{\mathrm{3}} ,\mathrm{x}_{\mathrm{4}} ,\mathrm{x}_{\mathrm{5}} ,\mathrm{x}_{\mathrm{6}} ,\mathrm{ar}^{\mathrm{2}} \Rightarrow\mathrm{AP} \\ $$$$\mathrm{ar}^{\mathrm{2}} ,\mathrm{x}_{\mathrm{7}} ,\mathrm{x}_{\mathrm{8}} ,\mathrm{x}_{\mathrm{9}} ,\mathrm{x}_{\mathrm{10}} ,\mathrm{x}_{\mathrm{11}} ,\mathrm{x}_{\mathrm{12}} ,\mathrm{ar}^{\mathrm{3}} \Rightarrow\mathrm{AP} \\ $$$$...\mathrm{etc} \\ $$$$\mathrm{if}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{x}_{\mathrm{1}} +\mathrm{x}_{\mathrm{2}} +\mathrm{x}_{\mathrm{3}} +...\right)=\:\frac{\mathrm{21}}{\mathrm{16}}×\frac{\mathrm{a}}{\mathrm{1}−\mathrm{r}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{r}\:? \\ $$

Question Number 79647 Answers: 1 Comments: 2

discussion back with mr W. consider this equation (x^2 −2x−3)(3^x −27)=0 does the equation have two roots or three roots?

$$\mathrm{discussion}\:\mathrm{back}\:\mathrm{with}\:\mathrm{mr}\:\mathrm{W}. \\ $$$$\mathrm{consider}\:\mathrm{this}\:\mathrm{equation}\: \\ $$$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}\right)\left(\mathrm{3}^{\mathrm{x}} −\mathrm{27}\right)=\mathrm{0} \\ $$$$\mathrm{does}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{have}\:\mathrm{two}\:\mathrm{roots} \\ $$$$\mathrm{or}\:\mathrm{three}\:\mathrm{roots}? \\ $$

Question Number 79646 Answers: 0 Comments: 1

calculate A_n =∫_0 ^1 cos(narcosx)dx with n integr natural

$${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left({narcosx}\right){dx} \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 79645 Answers: 0 Comments: 0

find ∫_0 ^1 ln(1+x^4 )dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx} \\ $$

Question Number 79644 Answers: 1 Comments: 1

f(x) = ((4(4x^2 +3))/(4x^2 +4x+5)) prove that f(x) ≥ 2 .

$${f}\left({x}\right)\:=\:\frac{\mathrm{4}\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}\right)}{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:{f}\left({x}\right)\:\geqslant\:\mathrm{2}\:. \\ $$

Question Number 79635 Answers: 0 Comments: 9

Sum: (1/1) + (1/(1 + 2)) + (1/(1 + 2 + 3)) + ... + (1/(1 + 2 + 3 + ... + 8016))

$$\mathrm{Sum}:\:\:\frac{\mathrm{1}}{\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:...\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:...\:+\:\mathrm{8016}} \\ $$

Question Number 79634 Answers: 1 Comments: 3

Question Number 79627 Answers: 0 Comments: 2

1) expicite f(x)=∫_0 ^1 ((ln(1+xt^2 ))/(1+t^2 ))dt with x≥0 2)calculate ∫_0 ^1 ((ln(1+t^2 ))/(1+t^2 ))dt and ∫_0 ^1 ((ln(1+2t^2 ))/(1+t^2 ))dt

$$\left.\mathrm{1}\right)\:{expicite}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{with}\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 79626 Answers: 1 Comments: 0

find tbe general solution of the D.E y^(′′) −5y^′ +4y=e^t cos(t)

$${find}\:{tbe}\:{general}\:{solution}\:{of}\:{the}\:{D}.{E} \\ $$$${y}^{''} −\mathrm{5}{y}^{'} +\mathrm{4}{y}={e}^{{t}} {cos}\left({t}\right) \\ $$

Question Number 79625 Answers: 1 Comments: 0

if n>1 prove that 2ln(n)−ln(n+1)−ln(n−1)=(1/n^2 )+(1/(2n^4 ))+(1/(3n^6 ))+...=

$${if}\:{n}>\mathrm{1}\:{prove}\:{that} \\ $$$$\mathrm{2}{ln}\left({n}\right)−{ln}\left({n}+\mathrm{1}\right)−{ln}\left({n}−\mathrm{1}\right)=\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{3}{n}^{\mathrm{6}} }+...= \\ $$

Question Number 79615 Answers: 0 Comments: 3

prove that with using hypergeometric function ∫_0 ^π sin(x^2 )=(π^3 /3) 1F_2 [(3/4);(3/2);(7/4);((−π^4 )/4)]

$${prove}\:{that}\:{with}\:{using}\:{hypergeometric}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\pi} {sin}\left({x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{3}} }{\mathrm{3}}\:\mathrm{1}{F}_{\mathrm{2}} \left[\frac{\mathrm{3}}{\mathrm{4}};\frac{\mathrm{3}}{\mathrm{2}};\frac{\mathrm{7}}{\mathrm{4}};\frac{−\pi^{\mathrm{4}} }{\mathrm{4}}\right]\: \\ $$

Question Number 79609 Answers: 1 Comments: 1

Question Number 79607 Answers: 0 Comments: 1

Solve this ∫_ (((x−yz))/((x^2 +y^2 −2xyz)^(3/2) ))dz

$${Solve}\:{this} \\ $$$$\int_{} \frac{\left({x}−{yz}\right)}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xyz}\right)^{\mathrm{3}/\mathrm{2}} }{dz} \\ $$$$ \\ $$$$ \\ $$

Question Number 79588 Answers: 1 Comments: 3

f(x) = (1/(1+2(√(2x))+2x))+(x/4) prove that f(x) ≥ (3/8) .

$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}{x}}+\mathrm{2}{x}}+\frac{{x}}{\mathrm{4}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:{f}\left({x}\right)\:\geqslant\:\frac{\mathrm{3}}{\mathrm{8}}\:. \\ $$

Question Number 79580 Answers: 0 Comments: 5

does this matter reasonable ∫ sin^x (x) dx ?

$$\mathrm{does}\:\mathrm{this}\:\mathrm{matter}\:\mathrm{reasonable} \\ $$$$\int\:\mathrm{sin}\:^{\mathrm{x}} \left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$

Question Number 79572 Answers: 1 Comments: 1

Question Number 79571 Answers: 1 Comments: 5

Solve for x: ((x + ((x + ((x + ...))^(1/3) ))^(1/3) ))^(1/3) = ((x ((x ((x ....))^(1/3) ))^(1/3) ))^(1/3)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}: \\ $$$$\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:+\:\:...}}}\:\:\:\:\:\:\:=\:\:\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:....}}} \\ $$

Question Number 79613 Answers: 1 Comments: 0

3xy(2x−y)−3bx+3c=0 3xy(x−2y)−3by−3c=0 find non-zero, real values of x,y if b,c∈R.

$$\mathrm{3}{xy}\left(\mathrm{2}{x}−{y}\right)−\mathrm{3}{bx}+\mathrm{3}{c}=\mathrm{0} \\ $$$$\mathrm{3}{xy}\left({x}−\mathrm{2}{y}\right)−\mathrm{3}{by}−\mathrm{3}{c}=\mathrm{0} \\ $$$${find}\:{non}-{zero},\:{real}\:{values} \\ $$$${of}\:{x},{y}\:\:{if}\:{b},{c}\in\mathbb{R}. \\ $$

Question Number 79612 Answers: 1 Comments: 0

∫ (dx/((√(x ))((x)^(1/(4 )) +1)^(10) )) = ?

$$\int\:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}\:}\left(\sqrt[{\mathrm{4}\:}]{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{10}} }\:=\:? \\ $$

Question Number 79565 Answers: 0 Comments: 2

lim_(x→∞) (x−(√(x^2 −x+1)) )×(((ln(e^x +x))/x))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}\:\right)×\left(\frac{\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}} +\mathrm{x}\right)}{\mathrm{x}}\right) \\ $$

Question Number 79560 Answers: 0 Comments: 1

(√(1+x)) ≤ ((5−x))^(1/(4 ))

$$\sqrt{\mathrm{1}+\mathrm{x}}\:\leqslant\:\sqrt[{\mathrm{4}\:}]{\mathrm{5}−\mathrm{x}} \\ $$

Question Number 79538 Answers: 1 Comments: 13

Question Number 79536 Answers: 0 Comments: 4

Question Number 79532 Answers: 1 Comments: 2

Given function f : R ⇒ R x^2 f(x) + f(1 − x) = 2x − x^4 f(2019) = ?

$${Given}\:\:{function}\:\:{f}\::\:\mathbb{R}\:\:\Rightarrow\:\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:{f}\left({x}\right)\:+\:{f}\left(\mathrm{1}\:−\:{x}\right)\:\:=\:\:\mathrm{2}{x}\:−\:{x}^{\mathrm{4}} \\ $$$${f}\left(\mathrm{2019}\right)\:\:=\:\:? \\ $$

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