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Question Number 190151 Answers: 2 Comments: 4

I saw this in a book (without explanation). Please show how. It is given that tan 2θ=(B/(A−C)) (A,B,C ∈R) . Find cos 2θ.

$${I}\:{saw}\:{this}\:{in}\:{a}\:{book}\:\left({without}\:{explanation}\right).\:{Please}\:{show}\:{how}. \\ $$$${It}\:{is}\:{given}\:{that}\:\mathrm{tan}\:\mathrm{2}\theta=\frac{{B}}{{A}−{C}}\:\:\left({A},{B},{C}\:\in\mathbb{R}\right)\:.\:{Find}\:\mathrm{cos}\:\mathrm{2}\theta. \\ $$

Question Number 190140 Answers: 2 Comments: 1

Question Number 190138 Answers: 1 Comments: 0

Question Number 190137 Answers: 2 Comments: 0

{ ((fog^(−1) (x)=3x+2)),((gof(x)=2x−1)) :} find f(x)=? and fof(3)=?

$$\begin{cases}{\mathrm{fog}^{−\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{2}}\\{\mathrm{gof}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}}\end{cases} \\ $$$${find}\:\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=?\:\:\:\mathrm{and}\:\:\:\:\mathrm{fof}\left(\mathrm{3}\right)=? \\ $$

Question Number 190134 Answers: 0 Comments: 0

Question Number 190131 Answers: 1 Comments: 0

if: x^2 +y^2 +z^2 + 14 = 2(x + 2y + 3z) find: T=((xyz)/(x^3 +y^3 +z^3 ))

$$\:\mathrm{if}:\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{14}\:=\:\mathrm{2}\left(\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{3z}\right) \\ $$$$\:\mathrm{find}:\:\:\mathrm{T}=\frac{\mathrm{xyz}}{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} }\: \\ $$

Question Number 190129 Answers: 1 Comments: 0

Question Number 190115 Answers: 1 Comments: 0

if: (a+b)(a+1) = b find: P = (√(a^3 +b^3 −3ab))

$$\mathrm{if}:\:\:\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}+\mathrm{1}\right)\:=\:\mathrm{b} \\ $$$$\:\mathrm{find}:\:\:\mathrm{P}\:=\:\:\sqrt{\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} −\mathrm{3ab}} \\ $$

Question Number 190106 Answers: 0 Comments: 0

Question Number 190104 Answers: 1 Comments: 0

In AB^Δ C : II_( a) ^( 2) =^? 4R ( r_( a) − r ) I : incircle center I_( a) : excircle center corresponding A R: circumcircle radius r: incircle radius r_( a) : excircle radius corresponding A

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{In}\:\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{II}_{\:{a}} ^{\:\mathrm{2}} \:\overset{?} {=}\:\mathrm{4}{R}\:\left(\:{r}_{\:{a}} \:−\:{r}\:\right) \\ $$$$ \\ $$$$\:\:\:\:\mathrm{I}\::\:{incircle}\:\:{center} \\ $$$$\:\:\:\mathrm{I}_{\:{a}} \::\:{excircle}\:{center}\:{corresponding}\:{A} \\ $$$$\:\:\:{R}:\:{circumcircle}\:{radius} \\ $$$$\:\:\:\:\:{r}:\:{incircle}\:{radius} \\ $$$$\:\:\:\:\:{r}_{\:{a}} \::\:{excircle}\:{radius}\:{corresponding}\:{A} \\ $$

Question Number 190100 Answers: 1 Comments: 1

Question Number 190098 Answers: 0 Comments: 0

Question Number 190095 Answers: 1 Comments: 0

Question Number 190094 Answers: 2 Comments: 0

Question Number 190093 Answers: 2 Comments: 3

prove that : c= ( (√5) +2)^( (1/3)) − ((√5) −2)^( (1/3)) is a rational number.

$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$${c}=\:\left(\:\sqrt{\mathrm{5}}\:+\mathrm{2}\right)^{\:\frac{\mathrm{1}}{\mathrm{3}}} \:−\:\left(\sqrt{\mathrm{5}}\:−\mathrm{2}\right)^{\:\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{is}\:\:\:\mathrm{a}\:\:{rational}\:\:\mathrm{number}. \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 190091 Answers: 1 Comments: 0

1. Find sin52° + sin8° − cos22° 2. If a^2 + (1/a^2 ) = 6 find a^3 + (1/a^3 ) 3. Find ((tan32° + tan13°)/(1 − tan32° ∙ tan13°))

$$\mathrm{1}.\:\mathrm{Find}\:\:\:\mathrm{sin52}°\:+\:\mathrm{sin8}°\:−\:\mathrm{cos22}° \\ $$$$\mathrm{2}.\:\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }\:=\:\mathrm{6}\:\:\:\mathrm{find}\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} } \\ $$$$\mathrm{3}.\:\mathrm{Find}\:\:\:\frac{\mathrm{tan32}°\:+\:\mathrm{tan13}°}{\mathrm{1}\:−\:\mathrm{tan32}°\:\centerdot\:\mathrm{tan13}°} \\ $$

Question Number 190082 Answers: 1 Comments: 0

Question Number 190079 Answers: 0 Comments: 1

F(t)=(4t^3 ,2cos(2t),3e^(3t) ) find F ′(t) F ′(t)=(12t^2 ,-4sin(2t),9e^(3t) ) is my answer correct?

$$ \\ $$$$ \\ $$$$\:{F}\left({t}\right)=\left(\mathrm{4}{t}^{\mathrm{3}} ,\mathrm{2}{cos}\left(\mathrm{2}{t}\right),\mathrm{3}{e}^{\mathrm{3}{t}} \right) \\ $$$$\:{find}\:{F}\:'\left({t}\right) \\ $$$$\:{F}\:'\left({t}\right)=\left(\mathrm{12}{t}^{\mathrm{2}} ,-\mathrm{4}{sin}\left(\mathrm{2}{t}\right),\mathrm{9}{e}^{\mathrm{3}{t}} \right) \\ $$$$\:{is}\:{my}\:{answer}\:{correct}? \\ $$

Question Number 190076 Answers: 2 Comments: 0

Question Number 190075 Answers: 1 Comments: 0

Question Number 190073 Answers: 0 Comments: 0

Question Number 190067 Answers: 2 Comments: 0

Question Number 190061 Answers: 1 Comments: 0

Question Number 190056 Answers: 1 Comments: 0

Solve : { ((y′(t)=[tanh(y(t))]^(−1) )),((y(0)=2)) :} tanh is hyperbolic tangent function.

$${Solve}\:: \\ $$$$\begin{cases}{{y}'\left({t}\right)=\left[{tanh}\left({y}\left({t}\right)\right)\right]^{−\mathrm{1}} }\\{{y}\left(\mathrm{0}\right)=\mathrm{2}}\end{cases} \\ $$$$ \\ $$$${tanh}\:{is}\:{hyperbolic}\:{tangent}\:{function}. \\ $$

Question Number 190052 Answers: 1 Comments: 0

Evaluate ∫∫_A (x+y)^2 dxdy over the area bounded by the ellipse (x^2 /a^2 ) + (y^2 /b^2 ) = 1 Anybody?

$$\mathrm{Evaluate}\:\int\int_{\mathrm{A}} \left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \mathrm{dxdy}\:\mathrm{over}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{ellipse}\: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Anybody}? \\ $$

Question Number 190047 Answers: 0 Comments: 1

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