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Question Number 179550 Answers: 2 Comments: 0

16cos^5 θ−cos 5θ = (5/2) 0<θ<2π θ =?

$$\:\:\:\mathrm{16cos}\:^{\mathrm{5}} \theta−\mathrm{cos}\:\mathrm{5}\theta\:=\:\frac{\mathrm{5}}{\mathrm{2}}\: \\ $$$$\:\:\:\mathrm{0}<\theta<\mathrm{2}\pi \\ $$$$\:\:\:\theta\:=? \\ $$

Question Number 179545 Answers: 0 Comments: 3

Find the probability that n people (n≤365) selected at random will have n different birthdays.

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{n}\:\mathrm{people}\: \\ $$$$\:\:\left(\mathrm{n}\leqslant\mathrm{365}\right)\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{will} \\ $$$$\:\:\mathrm{have}\:\mathrm{n}\:\mathrm{different}\:\mathrm{birthdays}. \\ $$

Question Number 179542 Answers: 1 Comments: 0

A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game . Find probability that the one who tosses second will win the game

$$\:\:\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{play}\:\mathrm{a}\:\mathrm{game}\:\mathrm{in}\:\mathrm{which}\:\mathrm{they} \\ $$$$\:\:\mathrm{alternately}\:\mathrm{toss}\:\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{dice}.\:\mathrm{The} \\ $$$$\:\:\mathrm{one}\:\mathrm{who}\:\mathrm{is}\:\mathrm{first}\:\mathrm{to}\:\mathrm{get}\:\mathrm{a}\:\mathrm{total}\:\mathrm{of}\:\mathrm{7}\:\mathrm{wins} \\ $$$$\:\:\mathrm{the}\:\mathrm{game}\:.\:\mathrm{Find}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{one} \\ $$$$\:\:\mathrm{who}\:\mathrm{tosses}\:\mathrm{second}\:\mathrm{will}\:\mathrm{win}\:\mathrm{the}\:\mathrm{game} \\ $$$$ \\ $$

Question Number 179529 Answers: 3 Comments: 0

(2−(√3))^x +(2+(√3))^x =4 x=?

$$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}} +\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} =\mathrm{4}\:\:\:\:\:\:{x}=? \\ $$

Question Number 179518 Answers: 0 Comments: 2

a−(1/b)=2cos((2π)/(13)) b−(1/c)=2cos((6π)/(13)) c−(1/a)=2cos((8π)/(13)) prove that (abc)^5 −(1/((abc)^5 ))=11

$${a}−\frac{\mathrm{1}}{{b}}=\mathrm{2}{cos}\frac{\mathrm{2}\pi}{\mathrm{13}} \\ $$$${b}−\frac{\mathrm{1}}{{c}}=\mathrm{2}{cos}\frac{\mathrm{6}\pi}{\mathrm{13}} \\ $$$${c}−\frac{\mathrm{1}}{{a}}=\mathrm{2}{cos}\frac{\mathrm{8}\pi}{\mathrm{13}}\:\:\:\:\:\:{prove}\:{that} \\ $$$$\left({abc}\right)^{\mathrm{5}} −\frac{\mathrm{1}}{\left({abc}\right)^{\mathrm{5}} }=\mathrm{11} \\ $$

Question Number 179517 Answers: 0 Comments: 0

22! ≡ x (mod 2024)

$$\:\mathrm{22}!\:\equiv\:\mathrm{x}\:\left(\mathrm{mod}\:\mathrm{2024}\right) \\ $$

Question Number 179515 Answers: 1 Comments: 0

Question Number 179513 Answers: 1 Comments: 0

F(x) = ∫ (1/x) (√((1−x)/(1+x))) dx F(1)=0 F((1/2))=?

$$\:\mathrm{F}\left(\mathrm{x}\right)\:=\:\int\:\frac{\mathrm{1}}{\mathrm{x}}\:\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\:\:\mathrm{F}\left(\mathrm{1}\right)=\mathrm{0}\: \\ $$$$\:\:\mathrm{F}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$

Question Number 179511 Answers: 2 Comments: 0

Evaluate ∫(x/( (√(2x^2 −4x−7)))) dx

$${Evaluate}\:\int\frac{{x}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{7}}}\:{dx} \\ $$

Question Number 179510 Answers: 1 Comments: 2

Evaluate ∫e^(4x) (√((1/e^(−2x) )+1)) dx

$${Evaluate}\:\int{e}^{\mathrm{4}{x}} \:\sqrt{\frac{\mathrm{1}}{{e}^{−\mathrm{2}{x}} }+\mathrm{1}}\:{dx} \\ $$

Question Number 179503 Answers: 0 Comments: 1

lim_(x→1) ((1/(tan^(−1) (x)−(π/4))) −(2/(x−1))) =?

$$\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)−\frac{\pi}{\mathrm{4}}}\:−\frac{\mathrm{2}}{\mathrm{x}−\mathrm{1}}\right)\:=? \\ $$

Question Number 179501 Answers: 1 Comments: 3

Question Number 179496 Answers: 1 Comments: 0

Evaluer ∫_1 ^2 ((sin (log(x)))/x)dx

$${Evaluer} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{sin}\:\left(\mathrm{log}\left(\mathrm{x}\right)\right)}{\mathrm{x}}\mathrm{dx} \\ $$

Question Number 179494 Answers: 1 Comments: 0

Evaluer ∫((1−logx)/(1+x))dx

$${Evaluer} \\ $$$$\int\frac{\mathrm{1}−\mathrm{logx}}{\mathrm{1}+\mathrm{x}}\mathrm{dx} \\ $$

Question Number 179482 Answers: 3 Comments: 1

Question Number 179478 Answers: 3 Comments: 0

Find ∫_( 0) ^( (1/6)) (1/(x^(−5) (36x^2 +1)^(3/2) )) dx

$${Find}\:\int_{\:\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{6}}} \:\frac{\mathrm{1}}{{x}^{−\mathrm{5}} \:\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx} \\ $$

Question Number 179458 Answers: 1 Comments: 2

Find the area of the triangle in the first quadrant between the x and y axis and the tangent to the relationship curve y=(5/x)−(x/5) and x dont equal 0 at (0,5)

$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{quadrant}\:\mathrm{between}\:\mathrm{the}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{relationship}\:\mathrm{curve}\:\mathrm{y}=\frac{\mathrm{5}}{\mathrm{x}}−\frac{\mathrm{x}}{\mathrm{5}}\:\mathrm{and}\:\mathrm{x}\:\mathrm{dont} \\ $$$$\mathrm{equal}\:\mathrm{0}\:\mathrm{at}\:\left(\mathrm{0},\mathrm{5}\right) \\ $$

Question Number 179453 Answers: 1 Comments: 0