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Question Number 157604 Answers: 1 Comments: 3

Question find the” minimum” value of: f (x):= ∣1+x∣+∣ 2+x∣ + ∣4 +2x∣

$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Q}{uestion}\: \\ $$$$\:{find}\:{the}''\:{minimum}''\:{value}\:{of}: \\ $$$$ \\ $$$${f}\:\left({x}\right):=\:\mid\mathrm{1}+{x}\mid+\mid\:\mathrm{2}+{x}\mid\:+\:\mid\mathrm{4}\:+\mathrm{2}{x}\mid \\ $$$$ \\ $$

Question Number 157598 Answers: 1 Comments: 0

Given a,b,c nonnegative numbers which satisfy a+b+c = 3. Prove that (1/(2ab^2 + 1)) + (1/(2bc^2 +1)) + (1/(2ac^2 + 1)) ≥ 1 .

$${Given}\:\:{a},{b},{c}\:\:{nonnegative}\:\:{numbers}\:\:{which}\:\:{satisfy}\:\:\:{a}+{b}+{c}\:=\:\mathrm{3}. \\ $$$${Prove}\:\:{that}\:\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{ab}^{\mathrm{2}} \:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{2}{bc}^{\mathrm{2}} +\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{2}{ac}^{\mathrm{2}} \:+\:\mathrm{1}}\:\geqslant\:\mathrm{1}\:. \\ $$

Question Number 157599 Answers: 1 Comments: 0

Find the number of x ∈ [1, 2016 ] , x ∈ N which making the expression 4x^6 + x^3 + 5 is divided by 11 .

$${Find}\:\:{the}\:\:{number}\:\:{of}\:\:{x}\:\in\:\left[\mathrm{1},\:\mathrm{2016}\:\right]\:\:,\:\:{x}\:\in\:\mathbb{N} \\ $$$${which}\:\:{making}\:\:{the}\:\:{expression}\:\:\mathrm{4}{x}^{\mathrm{6}} \:+\:\:{x}^{\mathrm{3}} \:+\:\mathrm{5}\:\:\:{is}\:\:{divided}\:\:\:{by}\:\:\mathrm{11}\:. \\ $$

Question Number 157593 Answers: 0 Comments: 0

let f:C→R z→min(y−[y],[y+1]−y) , y=Im(z) let w=e^(i((2π)/n)) , n∈N^∗ evaluate S_n =Σ_(0≤k<n) f(w^k )

$${let}\:{f}:{C}\rightarrow{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:{z}\rightarrow{min}\left({y}−\left[{y}\right],\left[{y}+\mathrm{1}\right]−{y}\right)\:,\:{y}={Im}\left({z}\right) \\ $$$${let}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} ,\:{n}\in{N}^{\ast} \\ $$$${evaluate}\:{S}_{{n}} =\underset{\mathrm{0}\leqslant{k}<{n}} {\sum}{f}\left({w}^{{k}} \right) \\ $$

Question Number 157592 Answers: 0 Comments: 0

let A={0^. ,1^. ,2^. } prove that every application from A to A is a 2nd degree polynom

$${let}\:{A}=\left\{\overset{.} {\mathrm{0}},\overset{.} {\mathrm{1}},\overset{.} {\mathrm{2}}\right\} \\ $$$${prove}\:{that}\:{every}\:{application}\:{from}\:{A}\: \\ $$$${to}\:{A}\:{is}\:{a}\:\mathrm{2}{nd}\:{degree}\:{polynom} \\ $$

Question Number 157591 Answers: 1 Comments: 0

lim_(x→π) ((x−π)^2 cos ((1/(x−π)))+x^4 +sin^3 x)=?

$$\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\left(\left({x}−\pi\right)^{\mathrm{2}} \mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}−\pi}\right)+{x}^{\mathrm{4}} +\mathrm{sin}\:^{\mathrm{3}} {x}\right)=? \\ $$

Question Number 157585 Answers: 1 Comments: 0

if 0<a≤b≤c<(π/2) then: (5/(tana)) + (3/(tanb)) + (1/(tanc)) ≥ ((27)/(tana + tanb + tanc))

$$\mathrm{if}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\leqslant\mathrm{c}<\frac{\pi}{\mathrm{2}}\:\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{5}}{\mathrm{tan}\boldsymbol{\mathrm{a}}}\:+\:\frac{\mathrm{3}}{\mathrm{tan}\boldsymbol{\mathrm{b}}}\:+\:\frac{\mathrm{1}}{\mathrm{tan}\boldsymbol{\mathrm{c}}}\:\geqslant\:\frac{\mathrm{27}}{\mathrm{tan}\boldsymbol{\mathrm{a}}\:+\:\mathrm{tan}\boldsymbol{\mathrm{b}}\:+\:\mathrm{tan}\boldsymbol{\mathrm{c}}} \\ $$

Question Number 157584 Answers: 3 Comments: 0

suppose the ratio of Jim to Rohn is 2:1 and the ratio of Rohn to Bill is 3:4, how do i find for the ratio of Jim to Bill.....???

$${suppose}\: \\ $$$${the}\:{ratio}\:{of}\:{Jim}\:{to}\:{Rohn}\:{is}\:\mathrm{2}:\mathrm{1} \\ $$$$\:{and}\:{the}\:{ratio}\:{of}\:{Rohn}\:{to}\:{Bill}\:{is} \\ $$$$\:\mathrm{3}:\mathrm{4},\:{how}\:{do}\:{i}\:{find}\:{for}\:{the}\:{ratio} \\ $$$${of}\:{Jim}\:{to}\:{Bill}.....??? \\ $$

Question Number 157576 Answers: 1 Comments: 2

Question Number 157575 Answers: 1 Comments: 3

(√((1/2)−(1/2)(√((1/2)+(1/2)cos 𝛂)))) (Π<𝛂<2Π)

$$ \\ $$$$\sqrt{\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\boldsymbol{\alpha}}} \\ $$$$\left(\Pi<\boldsymbol{\alpha}<\mathrm{2}\Pi\right) \\ $$

Question Number 157565 Answers: 0 Comments: 0

Question Number 157562 Answers: 2 Comments: 0

Question Number 157560 Answers: 0 Comments: 0

Question Number 157561 Answers: 0 Comments: 0

if a;b;c and a+b+c≥3 prove that: Σ (a^3 /(b + kbc)) ≥ (3/(1 + k)) ; k>0

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}\geqslant\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\mathrm{a}^{\mathrm{3}} }{\mathrm{b}\:+\:\mathrm{kbc}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{1}\:+\:\mathrm{k}}\:\:;\:\:\mathrm{k}>\mathrm{0}\: \\ $$

Question Number 157546 Answers: 1 Comments: 5

( _1 ^(2002) ) + ( _4 ^(2002) ) + ( _7 ^(2002) ) + …+ ( _(2002) ^(2002) ) = ? Thank you so much .

$$\left(\underset{\mathrm{1}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\left(\underset{\mathrm{4}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\left(\underset{\mathrm{7}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\ldots+\:\left(\underset{\mathrm{2002}} {\overset{\mathrm{2002}} {\:}}\right)\:\:=\:? \\ $$$${Thank}\:\:{you}\:\:{so}\:\:{much}\:. \\ $$

Question Number 157538 Answers: 1 Comments: 1

Question Number 157531 Answers: 2 Comments: 0

Question Number 157515 Answers: 0 Comments: 0

∫ ((x sin x)/(16x+9)) dx

$$\:\:\:\:\:\int\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{16}{x}+\mathrm{9}}\:{dx}\: \\ $$

Question Number 157508 Answers: 0 Comments: 1

Question Number 157494 Answers: 1 Comments: 0

Question Number 157487 Answers: 2 Comments: 0

Find the equation of the tangents drawn from the point (1,3) to the parabola y^2 =−16x.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{drawn} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{parabola} \\ $$$${y}^{\mathrm{2}} =−\mathrm{16}{x}. \\ $$

Question Number 157489 Answers: 2 Comments: 0

Solve for real numbers: tan(10x) = tan^5 (2x)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{tan}\left(\mathrm{10x}\right)\:=\:\mathrm{tan}^{\mathrm{5}} \left(\mathrm{2x}\right) \\ $$$$ \\ $$

Question Number 157478 Answers: 0 Comments: 12

Sir Tinku-Tara, I′ve been facing some difficulties eversince I changed my device 1• I can′t save my work as images to my new device. In case I have to upload my work to another plateform such as a whatsapp group, I′ll just have to send it directly from app. Whereas with my previous device I could save it as an image then send it from gallery while on another plateforme. 2• It′s impossible for me to send images after inserting page breaks. It has always been the case even with my previous device. The only difference being that, there, after launching the send process the images automatically get saved to my gallery. So I could send them from there.

$$\mathrm{Sir}\:\mathrm{Tinku}-\mathrm{Tara}, \\ $$$$\mathrm{I}'\mathrm{ve}\:\mathrm{been}\:\mathrm{facing}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{eversince}\:\mathrm{I}\:\mathrm{changed}\:\mathrm{my}\:\mathrm{device} \\ $$$$\mathrm{1}\bullet\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{save}\:\mathrm{my}\:\mathrm{work}\:\mathrm{as}\:\mathrm{images}\:\mathrm{to}\:\mathrm{my}\:\mathrm{new}\:\mathrm{device}. \\ $$$$\:\:\:\:\:\mathrm{In}\:\mathrm{case}\:\mathrm{I}\:\mathrm{have}\:\mathrm{to}\:\mathrm{upload}\:\mathrm{my}\:\mathrm{work}\:\mathrm{to}\:\mathrm{another}\:\mathrm{plateform}\:\mathrm{such}\:\mathrm{as}\:\mathrm{a}\: \\ $$$$\:\:\:\:\:\mathrm{whatsapp}\:\mathrm{group},\:\mathrm{I}'\mathrm{ll}\:\mathrm{just}\:\mathrm{have}\:\mathrm{to}\:\mathrm{send}\:\mathrm{it}\:\mathrm{directly}\:\mathrm{from}\:\mathrm{app}.\:\mathrm{Whereas} \\ $$$$\:\:\:\:\:\mathrm{with}\:\mathrm{my}\:\mathrm{previous}\:\mathrm{device}\:\mathrm{I}\:\mathrm{could}\:\mathrm{save}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{image}\:\mathrm{then}\:\mathrm{send}\:\mathrm{it}\:\mathrm{from} \\ $$$$\:\:\:\:\:\mathrm{gallery}\:\mathrm{while}\:\mathrm{on}\:\mathrm{another}\:\mathrm{plateforme}. \\ $$$$\mathrm{2}\bullet\:\mathrm{It}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{for}\:\mathrm{me}\:\mathrm{to}\:\mathrm{send}\:\mathrm{images}\:\mathrm{after}\:\mathrm{inserting}\:\mathrm{page}\:\mathrm{breaks}.\:\mathrm{It}\:\mathrm{has} \\ $$$$\:\:\:\:\:\:\mathrm{always}\:\mathrm{been}\:\mathrm{the}\:\mathrm{case}\:\mathrm{even}\:\mathrm{with}\:\mathrm{my}\:\mathrm{previous}\:\mathrm{device}.\:\mathrm{The}\:\mathrm{only}\:\mathrm{difference} \\ $$$$\:\:\:\:\:\mathrm{being}\:\mathrm{that},\:\mathrm{there},\:\mathrm{after}\:\mathrm{launching}\:\mathrm{the}\:\mathrm{send}\:\mathrm{process}\:\mathrm{the}\:\mathrm{images}\: \\ $$$$\:\:\:\:\:\:\mathrm{automatically}\:\mathrm{get}\:\mathrm{saved}\:\mathrm{to}\:\mathrm{my}\:\mathrm{gallery}.\:\mathrm{So}\:\mathrm{I}\:\mathrm{could}\:\mathrm{send}\:\mathrm{them}\:\mathrm{from}\:\mathrm{there}. \\ $$

Question Number 157469 Answers: 1 Comments: 0

calculate : Ω:= ∫_(0 ) ^( 1) (( ln(1+x).ln(1−x))/(1+x)) dx =?

$$ \\ $$$$\:\:\:\:{calculate}\:: \\ $$$$\:\Omega:=\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}+{x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}}\:{dx}\:=? \\ $$$$\:\:\:\: \\ $$

Question Number 157457 Answers: 3 Comments: 0

xy^′ + y = y^2 ln x

$$\mathrm{xy}^{'} \:+\:\mathrm{y}\:=\:\mathrm{y}^{\mathrm{2}} \:\mathrm{ln}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 157456 Answers: 4 Comments: 0

∫ 5^(3−2x) dx =?

$$\:\int\:\mathrm{5}^{\mathrm{3}−\mathrm{2}{x}} \:{dx}\:=? \\ $$

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