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Question Number 153108 Answers: 1 Comments: 0

∫(dθ/(sin^2 θ(3−sin θ)))

$$\int\frac{\mathrm{d}\theta}{\mathrm{sin}\:^{\mathrm{2}} \theta\left(\mathrm{3}−\mathrm{sin}\:\theta\right)} \\ $$

Question Number 153109 Answers: 0 Comments: 1

∫(dx/(x^2 +2x+2(√(x^2 +2x−4))))

$$\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{4}}} \\ $$

Question Number 153019 Answers: 0 Comments: 0

Determine all functions f:R→(1;+∞) continuous such that f(4x) ∙ f(3x) = 2^x ; ∀x∈R

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{functions}\:\:\mathrm{f}:\mathbb{R}\rightarrow\left(\mathrm{1};+\infty\right) \\ $$$$\mathrm{continuous}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{f}\left(\mathrm{4x}\right)\:\centerdot\:\mathrm{f}\left(\mathrm{3x}\right)\:=\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:;\:\:\forall\mathrm{x}\in\mathbb{R} \\ $$

Question Number 153016 Answers: 1 Comments: 2

∫_0 ^2 xe^(4−x^2 ) dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{xe}^{\mathrm{4}−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$

Question Number 153012 Answers: 0 Comments: 1

Find all ordered pairs of real numbers (x,y) for which { (((1+x^4 )(1+x^2 )(1+x)=1+y^7 )),(((1+y^4 )(1+y^2 )(1+y)=1+x^7 )) :}

$$\:{Find}\:{all}\:{ordered}\:{pairs}\:{of}\:{real}\: \\ $$$$\:{numbers}\:\left({x},{y}\right)\:{for}\:{which} \\ $$$$\:\:\begin{cases}{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}\right)=\mathrm{1}+{y}^{\mathrm{7}} }\\{\left(\mathrm{1}+{y}^{\mathrm{4}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}\right)=\mathrm{1}+{x}^{\mathrm{7}} }\end{cases} \\ $$

Question Number 153009 Answers: 3 Comments: 2

montrer que: 2cos(π/2^n )=(√(2 +(√(2+...+(√2)))))

$${montrer}\:{que}: \\ $$$$\mathrm{2}{cos}\frac{\pi}{\mathrm{2}^{{n}} }=\sqrt{\mathrm{2}\:+\sqrt{\mathrm{2}+...+\sqrt{\mathrm{2}}}} \\ $$$$ \\ $$

Question Number 153006 Answers: 1 Comments: 8

prove that 4!!=8 please help

$${prove}\:{that}\: \\ $$$$\mathrm{4}!!=\mathrm{8} \\ $$$${please}\:{help} \\ $$

Question Number 152993 Answers: 3 Comments: 1

Question Number 152985 Answers: 0 Comments: 2

Question Number 152976 Answers: 0 Comments: 0

Question Number 152974 Answers: 0 Comments: 6

Question Number 153093 Answers: 1 Comments: 1

Find the solution of three variables equality system x, y, z . a^3 + a^2 x + ay + z = 0 b^3 + b^2 x + by + z = 0 c^3 + c^2 x + cy + z = 0 Thank you so much

$${Find}\:\:{the}\:\:{solution}\:\:{of}\:\:{three}\:\:{variables}\:\:{equality}\:\:{system}\:\:{x},\:{y},\:{z}\:. \\ $$$$\:\:{a}^{\mathrm{3}} \:+\:{a}^{\mathrm{2}} {x}\:+\:{ay}\:+\:{z}\:=\:\mathrm{0} \\ $$$$\:\:{b}^{\mathrm{3}} \:+\:{b}^{\mathrm{2}} {x}\:+\:{by}\:+\:{z}\:=\:\mathrm{0} \\ $$$$\:\:{c}^{\mathrm{3}} \:+\:{c}^{\mathrm{2}} {x}\:+\:{cy}\:+\:{z}\:=\:\mathrm{0} \\ $$$$ \\ $$$${Thank}\:\:{you}\:\:{so}\:\:{much} \\ $$

Question Number 152971 Answers: 0 Comments: 0

Question Number 152960 Answers: 1 Comments: 0

Find the values for b and c given that the quadratic expression x^2 +bx+c<0 {x:−1<x>3}

$$\:\: \\ $$$$\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{for}\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{given} \\ $$$$\:\:\:\:\mathrm{that}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{expression} \\ $$$$\:\:\:\:{x}^{\mathrm{2}} +\mathrm{b}{x}+\mathrm{c}<\mathrm{0}\: \\ $$$$\:\:\:\:\left\{{x}:−\mathrm{1}<{x}>\mathrm{3}\right\} \\ $$$$\: \\ $$

Question Number 153392 Answers: 0 Comments: 1

Σ_(k=1) ^n k^a =?

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{a}} =?\:\:\: \\ $$

Question Number 152950 Answers: 0 Comments: 1

((1/2))+((1/3)+(2/3))+((1/4)+(2/4)+(3/4))+...+((1/8)+(2/8)+...+(7/8))=?

$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}}\right)+\left(\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{2}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{4}}\right)+...+\left(\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{2}}{\mathrm{8}}+...+\frac{\mathrm{7}}{\mathrm{8}}\right)=? \\ $$

Question Number 152949 Answers: 1 Comments: 0

Question Number 152947 Answers: 1 Comments: 0

prove :: 𝛗=∫_(−∞) ^( ∞) (( e^( −(1/x^( 2) )) )/x^( 4) ) dx =^? (1/2) Γ ((1/2) )

$$ \\ $$$$\:\:\:{prove}\::: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:\infty} \:\frac{\:{e}^{\:−\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }} }{{x}^{\:\mathrm{4}} }\:{dx}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\:\Gamma\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:\right) \\ $$$$ \\ $$

Question Number 152946 Answers: 0 Comments: 1

((4038)/(1+(1/3)+(1/6)+(1/(10))+(1/(15))+...+(1/(1+2+3+4+...+2019)))) =?

$$\:\:\:\frac{\mathrm{4038}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{15}}+...+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+...+\mathrm{2019}}}\:=? \\ $$

Question Number 152942 Answers: 2 Comments: 1

Question Number 152940 Answers: 1 Comments: 0

In bottle manufacturing company, it was observed that 5% of the bottles manufactured were defective. In a random sample of 150 bottles, find probability that (a) exactly 3, (b) between 3 and 6, (c) at most 4, manufactured bottles are defective. [Take e = 2.718]

$$\:\mathrm{In}\:\mathrm{bottle}\:\mathrm{manufacturing}\:\mathrm{company},\:\mathrm{it} \\ $$$$\mathrm{was}\:\mathrm{observed}\:\mathrm{that}\:\mathrm{5\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bottles} \\ $$$$\mathrm{manufactured}\:\mathrm{were}\:\mathrm{defective}.\:\mathrm{In}\:\mathrm{a}\: \\ $$$$\mathrm{random}\:\mathrm{sample}\:\mathrm{of}\:\mathrm{150}\:\mathrm{bottles},\:\mathrm{find}\: \\ $$$$\mathrm{probability}\:\mathrm{that}\: \\ $$$$\:\left({a}\right)\:\mathrm{exactly}\:\mathrm{3}, \\ $$$$\:\left({b}\right)\:\mathrm{between}\:\mathrm{3}\:\mathrm{and}\:\mathrm{6}, \\ $$$$\:\left({c}\right)\:\mathrm{at}\:\mathrm{most}\:\mathrm{4}, \\ $$$$\:\mathrm{manufactured}\:\mathrm{bottles}\:\mathrm{are}\:\mathrm{defective}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\mathrm{Take}\:\:{e}\:=\:\mathrm{2}.\mathrm{718}\right] \\ $$

Question Number 152939 Answers: 1 Comments: 0

Q : If a , b are positive numbers and { (( a = 1 + (( 6a −2))^(1/3) )),(( b = 1 + (( 6b −2))^(1/3) )) :} then find the value of , a.b =? ... Compiled by m.n : (E lementary olympiad ). ■

$$ \\ $$$$\:\:\:\:\:\mathrm{Q}\::\:\:\mathrm{If}\:\:\:\:{a}\:\:,\:\:{b}\:\:\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}\:\:\mathrm{and} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\:\:{a}\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{6}{a}\:−\mathrm{2}}\:\:}\\{\:\:\:{b}\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{6}{b}\:−\mathrm{2}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:,\:\:\:\:{a}.{b}\:=? \\ $$$$\:\:\:\:...\:\mathrm{Compiled}\:\mathrm{by}\:\mathrm{m}.\mathrm{n}\::\:\left(\mathscr{E}\:{lementary}\:{olympiad}\:\right).\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$

Question Number 152937 Answers: 1 Comments: 0

Question Number 152935 Answers: 1 Comments: 0

Question Number 152918 Answers: 1 Comments: 0

Find the first derivative of y=x(√(16−x^2 ))+16sin^(−1) (x/4)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{derivative}\:\mathrm{of}\: \\ $$$${y}={x}\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }+\mathrm{16sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{4}} \\ $$

Question Number 152912 Answers: 1 Comments: 0

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