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Question Number 224608 Answers: 1 Comments: 1

Question Number 224606 Answers: 1 Comments: 0

α β = 9 (( (α+β))/( (α−β))) =?

$$\:\:\: \alpha\: \beta\:=\:\mathrm{9}\:\: \\ $$$$\:\:\:\:\frac{ \left(\alpha+\beta\right)}{ \left(\alpha−\beta\right)}\:=?\: \\ $$

Question Number 224600 Answers: 0 Comments: 5

i am back guys

$$\mathrm{i}\:\mathrm{am}\:\mathrm{back}\:\mathrm{guys} \\ $$

Question Number 224594 Answers: 0 Comments: 1

let I be the incenter of a non−isosceles ΔABC and let the incircle be tanget to the sides point D,E,F. the line AI intersects (ABC) at A and S. the line SD intersects (ABC) at S and T. let IT ∩ EF =M, (BIC) ∩ (DEF)=K,L. prove that KDLM is a kite.

$$ \\ $$$$\:\:\:\:\mathrm{let}\:{I}\:\mathrm{be}\:\mathrm{the}\:\mathrm{incenter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}−\mathrm{isosceles}\:\:\Delta{ABC}\:\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{and}\:\mathrm{let}\:\mathrm{the}\:\mathrm{incircle}\:\mathrm{be}\:\mathrm{tanget}\:\mathrm{to}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{point}\:{D},{E},{F}.\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{line}\:{AI}\:\mathrm{intersects}\: \left({ABC}\right)\:\mathrm{at}\:{A}\:\mathrm{and}\:{S}. \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{line}\:{SD}\:\mathrm{intersects}\: \left({ABC}\right)\:\mathrm{at}\:{S}\:\mathrm{and}\:{T}.\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{let}\:{IT}\:\cap\:{EF}\:={M},\: \left({BIC}\right)\:\cap\: \left({DEF}\right)={K},{L}. \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:{KDLM}\:\mathrm{is}\:\mathrm{a}\:\mathrm{kite}. \\ $$$$ \\ $$$$ \\ $$

Question Number 224592 Answers: 0 Comments: 3

Question Number 224591 Answers: 1 Comments: 0

p is a prime number prove that if p^2 +8 is prime ⇒ ⇒ p^3 +4 is also prime

$$\mathrm{p}\:{is}\:{a}\:{prime}\:{number} \\ $$$${prove}\:{that}\:{if}\:\mathrm{p}^{\mathrm{2}} +\mathrm{8}\:{is}\:{prime}\:\Rightarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:{p}^{\mathrm{3}} +\mathrm{4}\:{is}\:{also}\:{prime} \\ $$

Question Number 224587 Answers: 0 Comments: 0

Question Number 224586 Answers: 0 Comments: 0

Question Number 224585 Answers: 0 Comments: 0

Question Number 224570 Answers: 2 Comments: 0

Question Number 224568 Answers: 0 Comments: 1

(√x)=a { ((a∈Z=0)),((a∉Z=1)) :} ∫_0 ^( 3) (√x)dx=?

$$\sqrt{{x}}={a\begin{cases}{{a}\in\mathbb{Z}=\mathrm{0}}\\{{a}\notin\mathbb{Z}=\mathrm{1}}\end{cases}} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{3}} \:\sqrt{{x}}{dx}=? \\ $$

Question Number 224562 Answers: 0 Comments: 1

_1 =sin x , _2 =cos x _3 =tan x _n =1+cos x

$$\:\: _{\mathrm{1}} =\mathrm{sin}\:{x}\:,\: _{\mathrm{2}} =\mathrm{cos}\:{x}\: \\ $$$$ _{\mathrm{3}} =\mathrm{tan}\:{x}\: \\ $$$$ _{{n}} =\mathrm{1}+\mathrm{cos}\:{x}\: \\ $$

Question Number 224558 Answers: 0 Comments: 6

Question Number 224556 Answers: 1 Comments: 5

Question Number 224539 Answers: 3 Comments: 0

a^x =m, a^y =n ,a^2 =(m^y n^x )^z prove xyz=1

$${a}^{{x}} ={m},\:{a}^{{y}} ={n}\:,{a}^{\mathrm{2}} =\left({m}^{{y}} {n}^{{x}} \right)^{{z}} \\ $$$${prove}\:{xyz}=\mathrm{1} \\ $$

Question Number 224538 Answers: 2 Comments: 0

32^(4r^2 −8) =1 then find r=?

$$\mathrm{32}^{\mathrm{4r}^{\mathrm{2}} −\mathrm{8}} =\mathrm{1}\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{r}=? \\ $$

Question Number 224531 Answers: 2 Comments: 4

Question Number 224529 Answers: 2 Comments: 1

Question Number 224510 Answers: 2 Comments: 0

Question Number 224505 Answers: 0 Comments: 0

∫_0 ^1 e^(ax) J_0 (ȷ_(0m) x)dx Where J_0 is the Bessel function and ȷ_(0m) its m-th zero

$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{ax}} {J}_{\mathrm{0}} \left(\jmath_{\mathrm{0}{m}} {x}\right){dx} \\ $$$$\mathrm{Where}\:{J}_{\mathrm{0}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{and}\:\jmath_{\mathrm{0}{m}} \:\mathrm{its}\:{m}-\mathrm{th}\:\mathrm{zero} \\ $$

Question Number 224502 Answers: 1 Comments: 0

in a rhombus the perimeter is 2p and the sum of its diagonals is m. the area of rhombus is...

$${in}\:{a}\:{rhombus}\:{the}\:{perimeter} \\ $$$${is}\:\mathrm{2}{p}\:{and}\:{the}\:{sum}\:{of}\:{its}\:{diagonals} \\ $$$${is}\:{m}. \\ $$$${the}\:{area}\:{of}\:{rhombus}\:{is}... \\ $$

Question Number 224499 Answers: 0 Comments: 0

Question Number 224516 Answers: 1 Comments: 0

Question Number 224515 Answers: 1 Comments: 0

((sin 35)/(tan 56))

$$\frac{\mathrm{sin}\:\mathrm{35}}{\mathrm{tan}\:\mathrm{56}} \\ $$

Question Number 224489 Answers: 1 Comments: 3

Question Number 224475 Answers: 0 Comments: 0

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