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Question Number 198565 Answers: 0 Comments: 0

Let a,b,c ∈ R^+ such that a+b+c=1. Prove that: b+c≥16abc

$${Let}\:{a},{b},{c}\:\in\:{R}^{+} \:{such}\:{that}\:{a}+{b}+{c}=\mathrm{1}. \\ $$$$\:{Prove}\:{that}:\:\:\:\:{b}+{c}\geqslant\mathrm{16}{abc} \\ $$

Question Number 198563 Answers: 1 Comments: 0

find all numbers (with any number of digits) satisfying (abcd...xyz)×2=(zyx...dcba)

$${find}\:{all}\:{numbers}\:\left({with}\:{any}\:{number}\right. \\ $$$$\left.{of}\:{digits}\right)\:{satisfying} \\ $$$$\left(\underline{{abcd}...{xyz}}\right)×\mathrm{2}=\left(\underline{{zyx}...{dcba}}\right) \\ $$

Question Number 198562 Answers: 1 Comments: 0

f(tan x)+ 2f(cot x) = 4x f ′(x)= ?

$$\:\:\:\mathrm{f}\left(\mathrm{tan}\:\mathrm{x}\right)+\:\mathrm{2f}\left(\mathrm{cot}\:\mathrm{x}\right)\:=\:\mathrm{4x}\: \\ $$$$\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)=\:? \\ $$

Question Number 198559 Answers: 0 Comments: 0

Question Number 198558 Answers: 1 Comments: 1

Question Number 198555 Answers: 1 Comments: 2

Question Number 198624 Answers: 0 Comments: 1

Post have been cleanup for users and access blocked

$$\mathrm{Post}\:\mathrm{have}\:\mathrm{been}\:\mathrm{cleanup}\:\mathrm{for}\:\mathrm{users} \\ $$$$\mathrm{and}\:\mathrm{access}\:\mathrm{blocked} \\ $$

Question Number 198644 Answers: 2 Comments: 2

Question Number 198643 Answers: 0 Comments: 0

Given an isosceles triangle ABC which ∠A= 30°, AB = AC. A point D is midpoint of BC . A point P is chosen on then segment AD and a point Q is chosen on the side AB so that BP= PQ. Find the angle PQC

$$ \\ $$$$\mathrm{Given}\:\mathrm{an}\:\mathrm{isosceles}\:\mathrm{triangle}\:\mathrm{ABC} \\ $$$$\:\mathrm{which}\:\:\angle\mathrm{A}=\:\mathrm{30}°,\:\mathrm{AB}\:=\:\mathrm{AC}.\: \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{D}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{BC}\:.\: \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{P}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{then} \\ $$$$\mathrm{segment}\:\mathrm{AD}\:\mathrm{and}\:\mathrm{a}\:\mathrm{point}\:\mathrm{Q}\:\mathrm{is} \\ $$$$\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:\mathrm{AB}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{BP}=\:\mathrm{PQ}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{PQC} \\ $$

Question Number 198519 Answers: 1 Comments: 0

Find a,b,c and d such that { ((abc = 1 (mod 11))),((abd = 2 (mod 11) )),((acd = 3 (mod 11) )),((bcd = 4 (mod 11) )) :}

$$\:\:\mathrm{Find}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\begin{cases}{\mathrm{abc}\:=\:\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{11}\right)}\\{\mathrm{abd}\:=\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{11}\right)\:}\\{\mathrm{acd}\:=\:\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{11}\right)\:}\\{\mathrm{bcd}\:=\:\mathrm{4}\:\left(\mathrm{mod}\:\mathrm{11}\right)\:}\end{cases} \\ $$

Question Number 198517 Answers: 0 Comments: 0

Question Number 198516 Answers: 0 Comments: 2

To administrator Tinku Tara sir: please have a look at what the members Hridiana and HomeAlone are doing in the forum! They are rioting! Please ban them from the forum!

$${To}\:{administrator}\:{Tinku}\:{Tara}\:{sir}: \\ $$$${please}\:{have}\:{a}\:{look}\:{at}\:{what}\:{the}\: \\ $$$${members}\:\underline{{Hridiana}}\:{and}\:\underline{{HomeAlone}} \\ $$$${are}\:{doing}\:{in}\:{the}\:{forum}! \\ $$$${They}\:{are}\:{rioting}! \\ $$$${Please}\:{ban}\:{them}\:{from}\:{the}\:{forum}! \\ $$

Question Number 198497 Answers: 0 Comments: 0

∫_0 ^∞ ((e^(at) −e^(−at) )/(e^(πt) −e^(−πt) )) dt

$$\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{\mathrm{at}} −\mathrm{e}^{−\mathrm{at}} }{\mathrm{e}^{\pi\mathrm{t}} −\mathrm{e}^{−\pi\mathrm{t}} }\:\mathrm{dt} \\ $$

Question Number 198496 Answers: 1 Comments: 0

A nice series If , Ω = Σ_(n=2) ^∞ (( 1)/(n^( 2) +n −1)) =(( π tan( aπ ))/( b)) ⇒ find the value of (b/a) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{A}\:{nice}\:\:{series} \\ $$$$\:\:{If}\:,\:\:\Omega\:=\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\:\mathrm{1}}{{n}^{\:\mathrm{2}} \:+{n}\:−\mathrm{1}}\:=\frac{\:\pi\:{tan}\left(\:{a}\pi\:\right)}{\:{b}} \\ $$$$\:\:\:\:\:\Rightarrow\:{find}\:{the}\:{value}\:{of}\:\:\:\frac{{b}}{{a}}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 198489 Answers: 2 Comments: 0

Question Number 198483 Answers: 3 Comments: 0

resoudre dans ]−π;π] cosx+cos2x+cos3x=0

$$\left.{r}\left.{esoudre}\:{dans}\:\right]−\pi;\pi\right] \\ $$$${cosx}+{cos}\mathrm{2}{x}+{cos}\mathrm{3}{x}=\mathrm{0}\: \\ $$

Question Number 198482 Answers: 2 Comments: 0

x^2 + 1 =0 resoudre dans C

$${x}^{\mathrm{2}} \:+\:\mathrm{1}\:=\mathrm{0}\:{resoudre}\:{dans}\:\mathbb{C} \\ $$

Question Number 198479 Answers: 2 Comments: 2

Question Number 198477 Answers: 1 Comments: 2

find the Area (ABCD)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{Area}\:\left(\mathrm{ABCD}\right) \\ $$

Question Number 198474 Answers: 2 Comments: 0

16000 = (x^3 /((1−x)^2 )) x=?

$$\mathrm{16000}\:=\:\frac{\mathrm{x}^{\mathrm{3}} }{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} }\: \\ $$$$\:\mathrm{x}=? \\ $$

Question Number 198470 Answers: 0 Comments: 0

Question Number 198465 Answers: 0 Comments: 1

The furier series approximation to the forcing function is given by f(t)=5[1+(4/π)((/)((sin120πt)/1)+((sin360πt)/2)+((sin600πt)/3) +.........)] The transfer function for this problem T(s)=((X(s))/(f(s)))=(1/(ms^2 +cs+k)) =(1/(0.001s+1)) 1. plot the amplitude spectrum 2.Obtain the expression for steady displacement X(t)

$${The}\:{furier}\:{series}\:{approximation}\:{to}\: \\ $$$${the}\:{forcing}\:{function}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({t}\right)=\mathrm{5}\left[\mathrm{1}+\frac{\mathrm{4}}{\pi}\left(\frac{}{}\frac{{sin}\mathrm{120}\pi{t}}{\mathrm{1}}+\frac{{sin}\mathrm{360}\pi{t}}{\mathrm{2}}+\frac{{sin}\mathrm{600}\pi{t}}{\mathrm{3}}\right.\right. \\ $$$$\left.\:\left.\:\:\:\:\:+.........\right)\right] \\ $$$${The}\:{transfer}\:{function}\:{for}\:{this} \\ $$$${problem}\:\:{T}\left({s}\right)=\frac{{X}\left({s}\right)}{{f}\left({s}\right)}=\frac{\mathrm{1}}{{ms}^{\mathrm{2}} +{cs}+{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{0}.\mathrm{001}{s}+\mathrm{1}} \\ $$$$\mathrm{1}.\:{plot}\:{the}\:{amplitude}\:{spectrum}\: \\ $$$$\mathrm{2}.{Obtain}\:{the}\:{expression}\:{for}\:{steady}\: \\ $$$$\:\:\:\:\:\:\:\:{displacement}\:{X}\left({t}\right) \\ $$

Question Number 198460 Answers: 0 Comments: 0

In △ABC holds: Π (1 + (1/a) tan (A/2)) ≥ (1 + (1/(3R)))^3

$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Pi\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:\mathrm{tan}\:\frac{\mathrm{A}}{\mathrm{2}}\right)\:\geqslant\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{3R}}\right)^{\mathrm{3}} \\ $$

Question Number 198451 Answers: 0 Comments: 0

Solve the EDP x(y−z)(∂U/∂x)+y(z−x)(∂U/∂y)=z(x−y)

$${Solve}\:{the}\:{EDP} \\ $$$${x}\left({y}−{z}\right)\frac{\partial{U}}{\partial{x}}+{y}\left({z}−{x}\right)\frac{\partial{U}}{\partial{y}}={z}\left({x}−{y}\right) \\ $$

Question Number 198449 Answers: 0 Comments: 2

Question Number 198447 Answers: 2 Comments: 5

Given function f(4567,321567)= 567+321=888. f(32156,12062)= 156+120=276 find the value of f(((20^(22) )/(21)) ).

$$\:\:\mathrm{Given}\:\mathrm{function}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{4567},\mathrm{321567}\right)=\:\mathrm{567}+\mathrm{321}=\mathrm{888}. \\ $$$$\:\:\mathrm{f}\left(\mathrm{32156},\mathrm{12062}\right)=\:\mathrm{156}+\mathrm{120}=\mathrm{276} \\ $$$$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\mathrm{f}\left(\frac{\mathrm{20}^{\mathrm{22}} }{\mathrm{21}}\:\right). \\ $$

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