Question and Answers Forum

AllQuestion and Answers: Page 610

Question Number 150718 Answers: 1 Comments: 0

Calculate: Li_2 (z) + Li_2 (1 - z) = ?

$$\mathrm{Calculate}: \\ $$$$\mathrm{Li}_{\mathrm{2}} \left(\boldsymbol{\mathrm{z}}\right)\:+\:\mathrm{Li}_{\mathrm{2}} \left(\mathrm{1}\:-\:\boldsymbol{\mathrm{z}}\right)\:=\:? \\ $$

Question Number 150792 Answers: 3 Comments: 0

if ((y+z)/x) = ((10)/3) and (x/z) = (3/4) find (x/y) = ?

$$\mathrm{if}\:\:\:\frac{\mathrm{y}+\mathrm{z}}{\mathrm{x}}\:=\:\frac{\mathrm{10}}{\mathrm{3}}\:\:\mathrm{and}\:\:\frac{\mathrm{x}}{\mathrm{z}}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\:\frac{\mathrm{x}}{\mathrm{y}}\:=\:? \\ $$

Question Number 150698 Answers: 2 Comments: 1

Question Number 150697 Answers: 1 Comments: 0

Question Number 150696 Answers: 1 Comments: 2

(1)∫ x tanx dx (2) ∫ ((√(tanx))+(√(cotx)))dx (3)∫ ((sinx+cosx)/( (√(sinx cosx)))) dx

$$\left(\mathrm{1}\right)\int\:{x}\:{tanx}\:{dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int\:\left(\sqrt{{tanx}}+\sqrt{{cotx}}\right){dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int\:\frac{{sinx}+{cosx}}{\:\sqrt{{sinx}\:{cosx}}}\:{dx} \\ $$

Question Number 150688 Answers: 3 Comments: 1

Question Number 150684 Answers: 0 Comments: 0

if a;b;c;d∈Z (b-a)(c-a)(d-a)(c-b)(d-b)(d-c) prove that the expression is divide into 12

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}\in\mathbb{Z} \\ $$$$\left(\mathrm{b}-\mathrm{a}\right)\left(\mathrm{c}-\mathrm{a}\right)\left(\mathrm{d}-\mathrm{a}\right)\left(\mathrm{c}-\mathrm{b}\right)\left(\mathrm{d}-\mathrm{b}\right)\left(\mathrm{d}-\mathrm{c}\right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{is}\:\mathrm{divide} \\ $$$$\mathrm{into}\:\mathrm{12} \\ $$

Question Number 150683 Answers: 1 Comments: 1

Question Number 150670 Answers: 3 Comments: 0

Solve the equation sin^3 x+sin^3 (((2π)/3)+x)+sin^3 (((4π)/3)+x)+(3/4)cos 2x=0

$$\:{Solve}\:{the}\:{equation}\: \\ $$$$\:\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{sin}\:^{\mathrm{3}} \left(\frac{\mathrm{2}\pi}{\mathrm{3}}+{x}\right)+\mathrm{sin}\:^{\mathrm{3}} \left(\frac{\mathrm{4}\pi}{\mathrm{3}}+{x}\right)+\frac{\mathrm{3}}{\mathrm{4}}\mathrm{cos}\:\mathrm{2}{x}=\mathrm{0}\: \\ $$

Question Number 150678 Answers: 2 Comments: 0

∫_0 ^2 ∫_0 ^(3−x^2 ) (3−x^2 −y)dy dx

$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}−{x}^{\mathrm{2}} } \left(\mathrm{3}−{x}^{\mathrm{2}} −{y}\right){dy}\:{dx} \\ $$

Question Number 150661 Answers: 0 Comments: 1

sin9x=sim5x+sin3x help

$$\mathrm{sin9x}=\mathrm{sim5x}+\mathrm{sin3x}\:\:\:\mathrm{help}\: \\ $$

Question Number 150656 Answers: 1 Comments: 0

Question Number 150655 Answers: 1 Comments: 0

Question Number 150654 Answers: 1 Comments: 0

Question Number 150647 Answers: 1 Comments: 0

Question Number 150646 Answers: 1 Comments: 0

Let 𝛌∈R fixed.Solve for real numbers: { ((ax + by = 2λ + 1)),((ax^2 + by^2 = 4λ + 1)),((ax^3 + by^3 = 8λ + 1)),((ax^4 + by^4 = 16λ + 1)) :}

$$\boldsymbol{\mathrm{L}}\mathrm{et}\:\boldsymbol{\lambda}\in\mathbb{R}\:\mathrm{fixed}.\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{2}\lambda\:+\:\mathrm{1}}\\{\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{4}\lambda\:+\:\mathrm{1}}\\{\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{8}\lambda\:+\:\mathrm{1}}\\{\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{by}^{\mathrm{4}} \:=\:\mathrm{16}\lambda\:+\:\mathrm{1}}\end{cases} \\ $$

Question Number 150652 Answers: 0 Comments: 5

If f(3x+1)+f(5x+1)=x^3 -2 Find f(1)+f(4)+f(16)=?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{3x}+\mathrm{1}\right)+\mathrm{f}\left(\mathrm{5x}+\mathrm{1}\right)=\mathrm{x}^{\mathrm{3}} -\mathrm{2} \\ $$$$\mathrm{Find}\:\:\mathrm{f}\left(\mathrm{1}\right)+\mathrm{f}\left(\mathrm{4}\right)+\mathrm{f}\left(\mathrm{16}\right)=? \\ $$

Question Number 150641 Answers: 2 Comments: 1

1+(√3^x )=2^x x=?

$$\mathrm{1}+\sqrt{\mathrm{3}^{\mathrm{x}} }=\mathrm{2}^{\mathrm{x}} \\ $$$$\mathrm{x}=? \\ $$

Question Number 150628 Answers: 1 Comments: 0

Question Number 150627 Answers: 1 Comments: 0

∫_0 ^1 (((−1)^(E((1/x))) dx)/x)

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(−\mathrm{1}\right)^{{E}\left(\frac{\mathrm{1}}{{x}}\right)} {dx}}{{x}} \\ $$

Question Number 150626 Answers: 1 Comments: 0

S(x)=Σ_(n=1) ^∞ ln(1+(1/n))x^n S(−1)= ?.. please help..

$${S}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right){x}^{{n}} \\ $$$${S}\left(−\mathrm{1}\right)=\:?.. \\ $$$${please}\:{help}.. \\ $$

Question Number 150609 Answers: 0 Comments: 0

I thought this as more basic: ((sinA)/a)=(1/(2R)) ((cosA)/a)=((b^2 +c^2 −a^2 )/(2abc)) ⇒ tanA=((abc)/(R(b^2 +c^2 −a^2 )))

$${I}\:{thought}\:{this}\:{as}\:{more}\:{basic}: \\ $$$$\frac{{sinA}}{{a}}=\frac{\mathrm{1}}{\mathrm{2}{R}} \\ $$$$\frac{{cosA}}{{a}}=\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{abc}} \\ $$$$\Rightarrow\:\:\boldsymbol{{tanA}}=\frac{\boldsymbol{{abc}}}{\boldsymbol{{R}}\left(\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} −\boldsymbol{{a}}^{\mathrm{2}} \right)} \\ $$

Question Number 150603 Answers: 1 Comments: 0

Compare: x=sin(165°) y=cos(165°) z=tan(165°)

$$\mathrm{Compare}: \\ $$$$\boldsymbol{\mathrm{x}}=\mathrm{sin}\left(\mathrm{165}°\right) \\ $$$$\boldsymbol{\mathrm{y}}=\mathrm{cos}\left(\mathrm{165}°\right) \\ $$$$\boldsymbol{\mathrm{z}}=\mathrm{tan}\left(\mathrm{165}°\right) \\ $$

Question Number 150601 Answers: 1 Comments: 0

Question Number 150600 Answers: 3 Comments: 0

xyz = 10 x + y + z = - 7 xy + xz + yz = 2 Find ((xy)/z) + ((xz)/y) + ((yz)/x) = ?

$$\mathrm{xyz}\:=\:\mathrm{10} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:-\:\mathrm{7} \\ $$$$\mathrm{xy}\:+\:\mathrm{xz}\:+\:\mathrm{yz}\:=\:\mathrm{2} \\ $$$$\mathrm{Find}\:\:\frac{\mathrm{xy}}{\mathrm{z}}\:+\:\frac{\mathrm{xz}}{\mathrm{y}}\:+\:\frac{\mathrm{yz}}{\mathrm{x}}\:=\:? \\ $$

Question Number 150599 Answers: 1 Comments: 2

lim_(x→0) x^x = ?

$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:=\:? \\ $$

Pg 605 Pg 606 Pg 607 Pg 608 Pg 609 Pg 610 Pg 611 Pg 612 Pg 613 Pg 614

Contact: info@tinkutara.com