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Question Number 170906    Answers: 2   Comments: 0

Question Number 170904    Answers: 0   Comments: 0

show that the padel equation of the curve x = acos𝛉 βˆ’acos 2𝛉 , y = 2asin 𝛉 βˆ’asin 2𝛉 is 9(r^2 βˆ’a^2 ) = 8p^2

$$\:\:\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{padel}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{{the}} \\ $$$$\:\:\:\boldsymbol{\mathrm{curve}}\:\:\:\boldsymbol{\mathrm{x}}\:=\: \boldsymbol{{a}\mathrm{cos}\theta}\:βˆ’\boldsymbol{\mathrm{acos}}\:\mathrm{2}\boldsymbol{\theta}\:\:, \\ $$$$\:\boldsymbol{\mathrm{y}}\:=\:\mathrm{2}\boldsymbol{\mathrm{a}}\mathrm{sin}\:\boldsymbol{\theta}\:βˆ’\boldsymbol{\mathrm{a}}\mathrm{sin}\:\mathrm{2}\boldsymbol{\theta}\:\:\mathrm{is}\:\mathrm{9}\left(\mathrm{r}^{\mathrm{2}} βˆ’\mathrm{a}^{\mathrm{2}} \right)\:=\:\mathrm{8}{p}^{\mathrm{2}} \\ $$

Question Number 170902    Answers: 0   Comments: 2

prove that sec((2Ο€)/7)+sec((4Ο€)/7)+sec((8Ο€)/7)=βˆ’4

$${prove}\:{that} \\ $$$${sec}\frac{\mathrm{2}\pi}{\mathrm{7}}+{sec}\frac{\mathrm{4}\pi}{\mathrm{7}}+{sec}\frac{\mathrm{8}\pi}{\mathrm{7}}=βˆ’\mathrm{4} \\ $$$$ \\ $$

Question Number 170900    Answers: 0   Comments: 0

Question Number 170893    Answers: 0   Comments: 0

Question Number 170894    Answers: 0   Comments: 0

Question Number 170891    Answers: 0   Comments: 1

Question Number 170888    Answers: 0   Comments: 0

Question Number 170890    Answers: 2   Comments: 0

Find the equation of a circle which touches the line xβˆ’3y+13 = 0 and passes through the points (6, 3) and (4, βˆ’1).

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{which} \\ $$$$\mathrm{touches}\:\mathrm{the}\:\mathrm{line}\:{x}βˆ’\mathrm{3}{y}+\mathrm{13}\:=\:\mathrm{0}\: \\ $$$$\mathrm{and}\:\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points}\:\left(\mathrm{6},\:\mathrm{3}\right) \\ $$$$\mathrm{and}\:\left(\mathrm{4},\:βˆ’\mathrm{1}\right). \\ $$

Question Number 170889    Answers: 1   Comments: 1

Question Number 170878    Answers: 1   Comments: 0

Question Number 170868    Answers: 1   Comments: 0

Solve: ∣x βˆ’ 1∣ + ∣x βˆ’ 2∣ β‰₯ 4

$$\mathrm{Solve}:\:\:\:\mid\mathrm{x}\:\:\:βˆ’\:\:\:\mathrm{1}\mid\:\:\:\:+\:\:\:\mid\mathrm{x}\:\:\:\:βˆ’\:\:\:\mathrm{2}\mid\:\:\:\:\geqslant\:\:\:\:\mathrm{4} \\ $$

Question Number 170856    Answers: 1   Comments: 2

in AB^Ξ” C : cos (A)+cos(B)+cos(C)=(7/4) (R/r) =?

$$ \\ $$$$\:\:{in}\:{A}\overset{\Delta} {{B}C}\::\:\:{cos}\:\left({A}\right)+{cos}\left({B}\right)+{cos}\left({C}\right)=\frac{\mathrm{7}}{\mathrm{4}} \\ $$$$\:\:\:\frac{{R}}{{r}}\:=? \\ $$

Question Number 170855    Answers: 1   Comments: 0

⌊xβŒ‹= log_2 (4^( x) βˆ’2^( x) βˆ’1)β‡’ ⌊ 4^( x) βŒ‹=?

$$ \\ $$$$\:\:\:\lfloor{x}\rfloor=\:{log}_{\mathrm{2}} \left(\mathrm{4}^{\:{x}} βˆ’\mathrm{2}^{\:{x}} βˆ’\mathrm{1}\right)\Rightarrow\:\lfloor\:\mathrm{4}^{\:{x}} \rfloor=? \\ $$$$ \\ $$

Question Number 181349    Answers: 0   Comments: 0

Question Number 170872    Answers: 1   Comments: 0

Question Number 170871    Answers: 1   Comments: 0

Why is it equal? (1/2)∫_0 ^Ο€ sin^(2p) udu=∫_0 ^(Ο€/2) sin^(2p) udu

$${Why}\:{is}\:{it}\:{equal}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{0}} {\overset{\pi} {\int}}{sin}^{\mathrm{2}{p}} {udu}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{sin}^{\mathrm{2}{p}} {udu} \\ $$

Question Number 170849    Answers: 1   Comments: 0

2x+(√x)=(1/2) 8x+(1/( (√x)))=?

$$\mathrm{2}{x}+\sqrt{{x}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{8}{x}+\frac{\mathrm{1}}{\:\sqrt{{x}}}=? \\ $$

Question Number 170847    Answers: 0   Comments: 1

Question Number 170844    Answers: 2   Comments: 0

solve x^2 +(√(3βˆ’x))=3

$${solve}\:{x}^{\mathrm{2}} +\sqrt{\mathrm{3}βˆ’{x}}=\mathrm{3} \\ $$

Question Number 170843    Answers: 1   Comments: 0

Question Number 170838    Answers: 1   Comments: 0

if a<b, show that a<((mb+na)/(m+n))<b a,b,m,n are arbitrary constants

$$\mathrm{if}\:{a}<{b},\:\mathrm{show}\:\mathrm{that}\:{a}<\frac{{mb}+{na}}{{m}+{n}}<{b} \\ $$$${a},{b},{m},{n}\:\mathrm{are}\:\mathrm{arbitrary}\:\mathrm{constants} \\ $$

Question Number 170836    Answers: 2   Comments: 1

x^3 βˆ’ 2x^2 βˆ’ 5x + 6 = 0 Ξ±^3 + Ξ²^3 + Ξ³^3 = ?

$${x}^{\mathrm{3}} \:βˆ’\:\mathrm{2}{x}^{\mathrm{2}} \:βˆ’\:\mathrm{5}{x}\:+\:\mathrm{6}\:=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \:+\:\gamma^{\mathrm{3}} \:=\:? \\ $$

Question Number 170833    Answers: 1   Comments: 0

Solve { ((C_x ^y =C_x ^(y+1) )),((4C_x ^y =5C_x ^(yβˆ’1) )) :} or C_n ^k =((n!)/(k!(nβˆ’k)!))

$${Solve}\: \\ $$$$\begin{cases}{{C}_{{x}} ^{{y}} ={C}_{{x}} ^{{y}+\mathrm{1}} }\\{\mathrm{4}{C}_{{x}} ^{{y}} =\mathrm{5}{C}_{{x}} ^{{y}βˆ’\mathrm{1}} }\end{cases}\:{or}\:{C}_{{n}} ^{{k}} =\frac{{n}!}{{k}!\left({n}βˆ’{k}\right)!} \\ $$

Question Number 170832    Answers: 0   Comments: 9

Question Number 170831    Answers: 2   Comments: 0

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