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Question Number 170902 Answers: 0 Comments: 2

prove that sec((2π)/7)+sec((4π)/7)+sec((8π)/7)=−4

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

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 x−3y+13 = 0 and passes through the points (6, 3) and (4, −1).

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

Question Number 170889 Answers: 1 Comments: 1

Question Number 170878 Answers: 1 Comments: 0

Question Number 170868 Answers: 1 Comments: 0

Solve: ∣x − 1∣ + ∣x − 2∣ ≥ 4

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

Question Number 170856 Answers: 1 Comments: 2

in AB^Δ 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

⌊x⌋= log_2 (4^( x) −2^( x) −1)⇒ ⌊ 4^( x) ⌋=?

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

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 ^π sin^(2p) udu=∫_0 ^(π/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 +(√(3−x))=3

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

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 − 2x^2 − 5x + 6 = 0 α^3 + β^3 + γ^3 = ?

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

Question Number 170833 Answers: 1 Comments: 0

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

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

Question Number 170832 Answers: 0 Comments: 9

Question Number 170831 Answers: 2 Comments: 0

Question Number 170958 Answers: 1 Comments: 0

log _5 (x+3)=log _6 (x+14)

$$\:\:\:\:\:\:\mathrm{log}\:_{\mathrm{5}} \left({x}+\mathrm{3}\right)=\mathrm{log}\:_{\mathrm{6}} \left({x}+\mathrm{14}\right) \\ $$

Question Number 170824 Answers: 1 Comments: 0

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