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Question Number 153568 Answers: 1 Comments: 0

solve in x∈C sin x=(3/2)

$${solve}\:{in}\:{x}\in\mathbb{C} \\ $$$$\:\mathrm{sin}\:{x}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$ \\ $$

Question Number 153565 Answers: 1 Comments: 4

define d(n) to be the sum of the digits of n. i.e d(1000) = 1 , d(999) = 27 find d(d(d(d(d(5^(10^(100) ) )))))

$$\: \\ $$$$\:\mathrm{define}\:{d}\left({n}\right)\:\mathrm{to}\:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\: \\ $$$$\:\mathrm{of}\:{n}.\:\:\: \\ $$$$\:\mathrm{i}.\mathrm{e}\:\:{d}\left(\mathrm{1000}\right)\:=\:\mathrm{1}\:,\:\:\:\:{d}\left(\mathrm{999}\right)\:=\:\mathrm{27} \\ $$$$\: \\ $$$$\:\mathrm{find}\:\:{d}\left({d}\left({d}\left({d}\left({d}\left(\mathrm{5}^{\mathrm{10}^{\mathrm{100}} } \right)\right)\right)\right)\right) \\ $$$$\: \\ $$

Question Number 153563 Answers: 1 Comments: 0

∫ (1/(1+(√(2x)) )) dx =?

$$\int\:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}{x}}\:}\:{dx}\:=? \\ $$

Question Number 153555 Answers: 1 Comments: 0

Ω := ∫_0 ^( (π/2)) cos(2x).ln(sin(x))dx=^? −(π/4) solution (1 ) Ω := ∫_0 ^( (π/2)) ( 2cos^( 2) (x)−1)ln(sin(x))dx := 2∫_0 ^( (π/2)) cos^( 2) (x).ln(sin(x))dx−∫_0 ^( (π/2)) ln(sin(x))dx we know that : ∫_0 ^(π/2) ln(sin(x))dx=_(earlier) ^(derived) ((−π)/2) ln(2) ∫_0 ^( (π/2)) cos^( 2) (x).ln(sin(x))dx=_(posts) ^(previous) −(π/4)ln(2)−(π/8) ∴ Ω := −(π/2) ln(2) −(π/4) +(π/2) ln(2) ◂ Ω =− (π/4) ▶ m.n

$$ \\ $$$$\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {cos}\left(\mathrm{2}{x}\right).{ln}\left({sin}\left({x}\right)\right){dx}\overset{?} {=}\:−\frac{\pi}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:{solution}\:\left(\mathrm{1}\:\right) \\ $$$$\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\:\mathrm{2}{cos}^{\:\mathrm{2}} \left({x}\right)−\mathrm{1}\right){ln}\left({sin}\left({x}\right)\right){dx} \\ $$$$\:\:\:\:\:\::=\:\mathrm{2}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {cos}^{\:\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx}−\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {ln}\left({sin}\left({x}\right)\right){dx} \\ $$$$\:\:\:\:\:{we}\:{know}\:{that}\::\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sin}\left({x}\right)\right){dx}\underset{{earlier}} {\overset{{derived}} {=}}\:\frac{−\pi}{\mathrm{2}}\:{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {cos}^{\:\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx}\underset{{posts}} {\overset{{previous}} {=}}\:−\frac{\pi}{\mathrm{4}}{ln}\left(\mathrm{2}\right)−\frac{\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\therefore\:\:\:\Omega\::=\:−\frac{\pi}{\mathrm{2}}\:{ln}\left(\mathrm{2}\right)\:−\frac{\pi}{\mathrm{4}}\:+\frac{\pi}{\mathrm{2}}\:{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacktriangleleft\:\:\:\:\Omega\:=−\:\frac{\pi}{\mathrm{4}}\:\:\blacktriangleright\:\:\:\:\:\:{m}.{n} \\ $$

Question Number 153553 Answers: 1 Comments: 0

sin(9) + sin(21)+sin(39)=^? (ϕ/( (√2))) ϕ:= golden ratio m.n

$$ \\ $$$$\:{sin}\left(\mathrm{9}\right)\:+\:{sin}\left(\mathrm{21}\right)+{sin}\left(\mathrm{39}\right)\overset{?} {=}\frac{\varphi}{\:\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\varphi:=\:{golden}\:{ratio} \\ $$$$\:{m}.{n} \\ $$

Question Number 153542 Answers: 1 Comments: 0

y′′′+y′=sec x

$$\:{y}'''+{y}'=\mathrm{sec}\:{x}\: \\ $$

Question Number 153537 Answers: 1 Comments: 0

Question Number 153535 Answers: 1 Comments: 0

find ∫((√(x^2 −9))/x^3 ) dx=?

$${find}\:\int\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{{x}^{\mathrm{3}} }\:{dx}=? \\ $$

Question Number 153532 Answers: 0 Comments: 0

sin(sin(sin(x^(2πx) −1))) = cos(cos(cos(x^(2ex) +1))) x = ?

$$\: \\ $$$$\:\mathrm{sin}\left(\mathrm{sin}\left(\mathrm{sin}\left({x}^{\mathrm{2}\pi{x}} −\mathrm{1}\right)\right)\right)\:=\:\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}^{\mathrm{2}{ex}} +\mathrm{1}\right)\right)\right)\: \\ $$$$\:{x}\:=\:? \\ $$$$\: \\ $$

Question Number 153518 Answers: 2 Comments: 0

Show whether Σ_(n = 1) ^∞ ((x^2 /(3 + n^2 x^2 ))) is uniformly convegence for real value of x.

$$\mathrm{Show}\:\mathrm{whether}\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{3}\:\:\:\:+\:\:\:\mathrm{n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\right)\:\:\:\:\:\mathrm{is}\:\mathrm{uniformly}\:\mathrm{convegence}\:\mathrm{for}\:\mathrm{real} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 153517 Answers: 0 Comments: 2

L=lim_(x→1) (((√(2019x−2018))−1)/( (x^(2019) )^(1/(2018)) −1)) then 2×L =?

$$\:\:{L}=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt{\mathrm{2019}{x}−\mathrm{2018}}−\mathrm{1}}{\:\sqrt[{\mathrm{2018}}]{{x}^{\mathrm{2019}} }−\mathrm{1}} \\ $$$$\:{then}\:\mathrm{2}×{L}\:=? \\ $$

Question Number 153513 Answers: 2 Comments: 0

((x/5) + (y/3))((5/x) + (3/y)) = 139, ∀x,y ∈ R_(>0) find maximum and minimum of ((x + y)/( (√(xy))))

$$\left(\frac{{x}}{\mathrm{5}}\:+\:\frac{{y}}{\mathrm{3}}\right)\left(\frac{\mathrm{5}}{{x}}\:+\:\frac{\mathrm{3}}{{y}}\right)\:=\:\mathrm{139},\:\forall{x},{y}\:\in\:\mathbb{R}_{>\mathrm{0}} \\ $$$$\mathrm{find}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum}\:\mathrm{of}\:\:\frac{{x}\:+\:{y}}{\:\sqrt{{xy}}} \\ $$

Question Number 153512 Answers: 1 Comments: 0

a,b,c ∈ Z ∣a−b∣^3 + ∣b−c∣^3 = 1 Find the value of ∣a−b∣ + ∣b−c∣ + ∣c−a∣

$${a},{b},{c}\:\:\in\:\:\mathbb{Z} \\ $$$$\mid{a}−{b}\mid^{\mathrm{3}} \:+\:\mid{b}−{c}\mid^{\mathrm{3}} \:=\:\mathrm{1} \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\mid{a}−{b}\mid\:+\:\mid{b}−{c}\mid\:+\:\mid{c}−{a}\mid \\ $$

Question Number 153508 Answers: 1 Comments: 0

Question Number 153500 Answers: 0 Comments: 0

Evaluate the line integral space if f(r)=Zi+Xj+Yk and C is a helix given by C: r(t)=(cost,sint,−3t) 0≤t≤2π

$${Evaluate}\:{the}\:{line}\:{integral}\:{space} \\ $$$${if}\:{f}\left({r}\right)={Zi}+{Xj}+{Yk}\:{and}\:{C}\:{is}\:{a}\:{helix} \\ $$$${given}\:{by}\:{C}:\:{r}\left({t}\right)=\left({cost},{sint},−\mathrm{3}{t}\right)\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2}\pi \\ $$

Question Number 153488 Answers: 0 Comments: 2

my notifications dont work. am i the only one with this problem? how can i contact tinku tara and do they still update the app?

$$\:\mathrm{my}\:\mathrm{notifications}\:\mathrm{dont}\:\mathrm{work}. \\ $$$$\:\mathrm{am}\:\mathrm{i}\:\mathrm{the}\:\mathrm{only}\:\mathrm{one}\:\mathrm{with}\:\mathrm{this}\:\mathrm{problem}?\: \\ $$$$\:\mathrm{how}\:\mathrm{can}\:\mathrm{i}\:\mathrm{contact}\:\mathrm{tinku}\:\mathrm{tara}\:\mathrm{and}\: \\ $$$$\:\mathrm{do}\:\mathrm{they}\:\mathrm{still}\:\mathrm{update}\:\mathrm{the}\:\mathrm{app}?\: \\ $$

Question Number 153486 Answers: 1 Comments: 0

Question Number 153483 Answers: 2 Comments: 6

Question Number 153479 Answers: 1 Comments: 0

Find area of region that satisfy ∣x−2∣ + ∣y+3∣ < 3

$${Find}\:\:{area}\:\:{of}\:\:{region}\:\:{that}\:\:{satisfy}\:\: \\ $$$$\:\:\:\mid{x}−\mathrm{2}\mid\:+\:\mid{y}+\mathrm{3}\mid\:<\:\mathrm{3} \\ $$

Question Number 153478 Answers: 0 Comments: 0

2016−2x = ∣x−a∣+∣x−b∣+∣x−c∣ has only one solution . a<b<c a,b,c ∈ Z Find the lowest value of c.

$$\mathrm{2016}−\mathrm{2}{x}\:=\:\mid{x}−{a}\mid+\mid{x}−{b}\mid+\mid{x}−{c}\mid\:\:\:{has}\:\:{only}\:\:{one}\:\:{solution}\:. \\ $$$${a}<{b}<{c}\:\: \\ $$$${a},{b},{c}\:\in\:\mathbb{Z} \\ $$$${Find}\:\:{the}\:\:{lowest}\:\:{value}\:\:{of}\:\:{c}. \\ $$

Question Number 153505 Answers: 1 Comments: 1

Question Number 153472 Answers: 0 Comments: 0

Question Number 176888 Answers: 1 Comments: 3

Question Number 153458 Answers: 0 Comments: 1

Given a set consisting of 22 integer A={±a_1 ,±a_2 ,...,±a_(11) }. Show that exist subset of S with properties (1) for every i=1,2,3,...,11 have least one between a_i or −a_i element of S (2)the sum all possible numbers in S divisible by 2015

$${Given}\:{a}\:{set}\:{consisting}\:{of}\:\mathrm{22}\:{integer} \\ $$$$\:{A}=\left\{\pm{a}_{\mathrm{1}} ,\pm{a}_{\mathrm{2}} ,...,\pm{a}_{\mathrm{11}} \right\}.\:{Show}\:{that} \\ $$$${exist}\:{subset}\:{of}\:{S}\:{with}\:{properties} \\ $$$$\left(\mathrm{1}\right)\:{for}\:{every}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{11}\: \\ $$$$\:{have}\:{least}\:{one}\:{between}\:{a}_{{i}} \:{or}\:−{a}_{{i}} \\ $$$$\:{element}\:{of}\:{S} \\ $$$$\left(\mathrm{2}\right){the}\:{sum}\:{all}\:{possible}\:{numbers} \\ $$$${in}\:{S}\:{divisible}\:{by}\:\mathrm{2015} \\ $$

Question Number 153457 Answers: 2 Comments: 0

Question Number 153450 Answers: 1 Comments: 0

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

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

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