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Question Number 93227 Answers: 0 Comments: 4

Question Number 93225 Answers: 0 Comments: 2

Question Number 93220 Answers: 0 Comments: 5

Please in an arithmetic mean a, A_1 , A_2 , A_3 , ... , A_n , b where A_1 , A_2 , A_3 , ... , A_n are nth arithmetic mean why is b = (n + 2)th term: like T_(n + 2) Please

Question Number 93209 Answers: 1 Comments: 6

Question Number 93208 Answers: 0 Comments: 8

Question Number 93204 Answers: 1 Comments: 1

Question Number 93203 Answers: 0 Comments: 1

what is the average area of a triangle formed by 3 random points in a 1×1 square?

$${what}\:{is}\:{the}\:{average}\:{area}\:{of}\:{a}\:{triangle} \\ $$$${formed}\:{by}\:\mathrm{3}\:{random}\:{points}\:{in}\:{a}\:\mathrm{1}×\mathrm{1} \\ $$$${square}? \\ $$

Question Number 93200 Answers: 1 Comments: 3

Question Number 93193 Answers: 1 Comments: 1

∫ ((ln(x+(√(x^2 −1))))/(√((x^2 −1)^3 ))) dx ?

$$\int\:\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)}{\sqrt{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} }}\:\mathrm{dx}\:?\: \\ $$

Question Number 93184 Answers: 0 Comments: 0

in solving the linear congruence ax ≡ b (mod n) ⇒ n∣(ax − b) ⇒ ax −b = kn ⇔ ax −kn = b ⇒ solving the linear diophantine equation ax −kn = b what are the general solution to the equation ax−kn = b

$$\mathrm{in}\:\mathrm{solving}\:\mathrm{the}\:\mathrm{linear}\:\mathrm{congruence} \\ $$$${ax}\:\equiv\:{b}\:\left(\mathrm{mod}\:{n}\right)\:\Rightarrow\:{n}\mid\left({ax}\:−\:{b}\right)\:\Rightarrow\:{ax}\:−{b}\:=\:{kn}\:\Leftrightarrow\:{ax}\:−{kn}\:=\:{b} \\ $$$$\Rightarrow\:\mathrm{solving}\:\mathrm{the}\:\mathrm{linear}\:\mathrm{diophantine}\:\mathrm{equation}\:{ax}\:−{kn}\:=\:{b} \\ $$$$\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:{ax}−{kn}\:=\:{b} \\ $$$$\: \\ $$$$ \\ $$

Question Number 93177 Answers: 0 Comments: 3

x^2 +(1/x^2 )=47 (√x)+(1/(√x))=...

$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{47} \\ $$$$\sqrt{{x}}+\frac{\mathrm{1}}{\sqrt{{x}}}=... \\ $$

Question Number 93175 Answers: 3 Comments: 1

∫ (dx/(√(sin^3 (x).cos^5 (x)))) ?

$$\int\:\frac{\mathrm{dx}}{\sqrt{\mathrm{sin}\:^{\mathrm{3}} \:\left(\mathrm{x}\right).\mathrm{cos}\:^{\mathrm{5}} \left(\mathrm{x}\right)}}\:?\: \\ $$

Question Number 93173 Answers: 1 Comments: 0

If a_(n + 3) = (a_(n − 1) /a_(n + 1) ) , and a_0 = 1, a_2 = 2 find a_n

$$\mathrm{If}\:\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{3}} \:\:=\:\:\frac{\mathrm{a}_{\mathrm{n}\:\:−\:\:\mathrm{1}} }{\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} }\:,\:\:\:\:\mathrm{and}\:\:\:\mathrm{a}_{\mathrm{0}} \:\:=\:\:\mathrm{1},\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{find}\:\:\:\mathrm{a}_{\mathrm{n}} \\ $$

Question Number 93170 Answers: 0 Comments: 2

x^2 +(1/x^2 )=27 (√x)+(1/(√x))=....

$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{27} \\ $$$$\sqrt{{x}}+\frac{\mathrm{1}}{\sqrt{{x}}}=.... \\ $$

Question Number 93166 Answers: 1 Comments: 0

Question Number 93146 Answers: 0 Comments: 2

lim_(x→0) ((∫_0 ^x (a+bcos t+c cos (2t))dt)/x^5 ) = 15

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\underset{\mathrm{0}} {\overset{\mathrm{x}} {\int}}\left(\mathrm{a}+\mathrm{bcos}\:\mathrm{t}+\mathrm{c}\:\mathrm{cos}\:\left(\mathrm{2t}\right)\right)\mathrm{dt}}{\mathrm{x}^{\mathrm{5}} }\:=\:\mathrm{15} \\ $$

Question Number 93144 Answers: 1 Comments: 0

∫ ((x^3 −1)/(x^3 +6x^2 +10x)) dx

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{3}} +\mathrm{6x}^{\mathrm{2}} +\mathrm{10x}}\:\mathrm{dx}\: \\ $$

Question Number 93138 Answers: 2 Comments: 0

{ ((18x^2 =3y(1+9x^2 ))),((18y^2 =3z(1+9y^2 ))),((18z^2 =3x(1+9z^2 ))) :}

$$\begin{cases}{\mathrm{18x}^{\mathrm{2}} =\mathrm{3y}\left(\mathrm{1}+\mathrm{9x}^{\mathrm{2}} \right)}\\{\mathrm{18y}^{\mathrm{2}} =\mathrm{3z}\left(\mathrm{1}+\mathrm{9y}^{\mathrm{2}} \right)}\\{\mathrm{18z}^{\mathrm{2}} =\mathrm{3x}\left(\mathrm{1}+\mathrm{9z}^{\mathrm{2}} \right)}\end{cases} \\ $$

Question Number 93129 Answers: 1 Comments: 2

derive x^2 −(α+β)x+αβ

$${derive}\:{x}^{\mathrm{2}} −\left(\alpha+\beta\right){x}+\alpha\beta \\ $$

Question Number 93125 Answers: 0 Comments: 3

Question Number 93118 Answers: 1 Comments: 0

sin(x)=a −1≤a≤1

$${sin}\left({x}\right)={a} \\ $$$$−\mathrm{1}\leqslant{a}\leqslant\mathrm{1} \\ $$

Question Number 93109 Answers: 0 Comments: 2

∫_0 ^(2π) cos^(2020) (x)dx

$$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\:{cos}^{\mathrm{2020}} \left({x}\right){dx} \\ $$

Question Number 93098 Answers: 0 Comments: 5

find the general solution to ∫ (1/(a sin x + b cos x)) dx and ∫ (1/(a cos x − bsin x)) dx where a , b are constants.

$$\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to} \\ $$$$\:\int\:\frac{\mathrm{1}}{{a}\:\mathrm{sin}\:{x}\:+\:{b}\:\mathrm{cos}\:{x}}\:{dx}\:\:\mathrm{and}\:\int\:\frac{\mathrm{1}}{{a}\:\mathrm{cos}\:{x}\:−\:{b}\mathrm{sin}\:{x}}\:{dx} \\ $$$$\mathrm{where}\:{a}\:,\:{b}\:\mathrm{are}\:\mathrm{constants}. \\ $$$$ \\ $$

Question Number 93091 Answers: 0 Comments: 1

Find the sum: Σ_(n=1) ^(2020) 2^2^n

$${Find}\:{the}\:{sum}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{2020}} {\sum}}\mathrm{2}^{\mathrm{2}^{{n}} } \\ $$

Question Number 93071 Answers: 1 Comments: 0

Question Number 95059 Answers: 0 Comments: 22

To Tinku Tara dear sir: i experienced following issues: 1. sometimes i got notification, but i didn′t see any update in the corresponding threads. what can be the reason? 2. when i activate the filter to show bookmarked posts, only some of the bookmarked posts will be displayed, others not. 3. it takes long time (some minutes, even hang up ) when the app updates after i have edited a post, added an image. (see picture below) 4. (old problem) when i leave the app just temporarily to go to an other app, the app starts again and i don′t come back to the place where i was before.

$${To}\:{Tinku}\:{Tara} \\ $$$${dear}\:{sir}:\:{i}\:{experienced}\:{following}\:{issues}: \\ $$$$\mathrm{1}.\:{sometimes}\:{i}\:{got}\:{notification},\:{but} \\ $$$${i}\:{didn}'{t}\:{see}\:{any}\:{update}\:{in}\:{the} \\ $$$${corresponding}\:{threads}.\:{what}\:{can}\:{be} \\ $$$${the}\:{reason}? \\ $$$$\mathrm{2}.\:{when}\:{i}\:{activate}\:{the}\:{filter}\:{to}\:{show} \\ $$$${bookmarked}\:{posts},\:{only}\:{some}\:{of}\:{the} \\ $$$${bookmarked}\:{posts}\:{will}\:{be}\:{displayed}, \\ $$$${others}\:{not}. \\ $$$$\mathrm{3}.\:{it}\:{takes}\:{long}\:{time}\:\left({some}\:{minutes},\right. \\ $$$$\left.{even}\:{hang}\:{up}\:\right)\:{when}\:{the}\:{app}\:{updates} \\ $$$${after}\:{i}\:{have}\:{edited}\:{a}\:{post},\:{added}\:{an} \\ $$$${image}.\:\left({see}\:{picture}\:{below}\right) \\ $$$$\mathrm{4}.\:\left({old}\:{problem}\right)\:{when}\:{i}\:{leave}\:{the}\:{app} \\ $$$${just}\:{temporarily}\:{to}\:{go}\:{to}\:{an}\:{other} \\ $$$${app},\:{the}\:{app}\:{starts}\:{again}\:{and}\:{i}\:{don}'{t} \\ $$$${come}\:{back}\:{to}\:{the}\:{place}\:{where}\:{i}\:{was} \\ $$$${before}. \\ $$

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