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Question Number 109369 Answers: 2 Comments: 0

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Question Number 109329 Answers: 0 Comments: 1

if all A,B be a set prove that( A^B = ∅↔A=∅ and B=∅) help me sir

$${if}\:{all}\:{A},{B}\:{be}\:{a}\:{set}\:{prove}\:{that}\left(\:{A}^{{B}} =\:\emptyset\leftrightarrow{A}=\emptyset\:{and}\:{B}=\emptyset\right)\: \\ $$$${help}\:{me}\:{sir}\: \\ $$

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Question Number 109337 Answers: 2 Comments: 0

x=cosθ, where ((3π)/2)<θ<2π, and that 2cosθ−sinθ=2, show that (√(1−x^2 ))=2(1−x). Hence or otherwise, find x and deduce that tan2θ=((24)/7)

$${x}=\mathrm{cos}\theta,\:\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\theta<\mathrm{2}\pi,\:\mathrm{and}\:\mathrm{that}\:\mathrm{2cos}\theta−\mathrm{sin}\theta=\mathrm{2}, \\ $$$$\mathrm{show}\:\mathrm{that}\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }=\mathrm{2}\left(\mathrm{1}−{x}\right). \\ $$$$\mathrm{Hence}\:\mathrm{or}\:\mathrm{otherwise},\:\mathrm{find}\:{x}\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{tan2}\theta=\frac{\mathrm{24}}{\mathrm{7}} \\ $$

Question Number 109264 Answers: 1 Comments: 0

Question Number 109262 Answers: 2 Comments: 0

f(x)+f(2x+y)+5xy = f(3x−y)+x^2 +1 for every x,y∈R . find f(10)

$${f}\left({x}\right)+{f}\left(\mathrm{2}{x}+{y}\right)+\mathrm{5}{xy}\:=\:{f}\left(\mathrm{3}{x}−{y}\right)+{x}^{\mathrm{2}} +\mathrm{1} \\ $$$${for}\:{every}\:{x},{y}\in\mathbb{R}\:.\:{find}\:{f}\left(\mathrm{10}\right) \\ $$

Question Number 109248 Answers: 0 Comments: 0

Question Number 109246 Answers: 5 Comments: 0

Question Number 109242 Answers: 0 Comments: 0

Question Number 109240 Answers: 1 Comments: 0

((♭emath)/(•••••)) use cayley − hamilton theorem to calculate A^(−1) for A= (((1 2 2)),((1 2 −1)),((−1 1 4)) )

$$\:\:\frac{\flat{emath}}{\bullet\bullet\bullet\bullet\bullet} \\ $$$${use}\:{cayley}\:−\:{hamilton}\:{theorem} \\ $$$${to}\:{calculate}\:{A}^{−\mathrm{1}} \:{for}\:{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{2}}\\{\mathrm{1}\:\:\:\:\:\:\mathrm{2}\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\mathrm{1}\:\:\:\:\mathrm{4}}\end{pmatrix} \\ $$

Question Number 109222 Answers: 1 Comments: 0

((…♭emATH…)/(≅≅≅≅≅≅)) (√(5+(√(10)))) = x.((√(5+(√(15)) )) +(√(5−(√(15)))) ) x =?

$$\:\:\:\:\frac{\ldots\flat{em}\mathcal{ATH}\ldots}{\cong\cong\cong\cong\cong\cong} \\ $$$$\sqrt{\mathrm{5}+\sqrt{\mathrm{10}}}\:=\:{x}.\left(\sqrt{\mathrm{5}+\sqrt{\mathrm{15}}\:}\:+\sqrt{\mathrm{5}−\sqrt{\mathrm{15}}}\:\right) \\ $$$${x}\:=? \\ $$

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