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AllQuestion and Answers: Page 770

Question Number 140816 Answers: 0 Comments: 0

Question Number 140815 Answers: 0 Comments: 0

Question Number 140813 Answers: 0 Comments: 0

Question Number 142208 Answers: 1 Comments: 0

Find the equation of the circle which is orthogonal to the circles x^2 +y^2 −7x−y=0 and x^2 +y^2 +3x−6y+5=0 and which passes through the point (−3,0).

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{orthogonal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{circles}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{7}{x}−{y}=\mathrm{0} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{6}{y}+\mathrm{5}=\mathrm{0}\:\mathrm{and}\:\mathrm{which}\:\mathrm{passes} \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(−\mathrm{3},\mathrm{0}\right). \\ $$

Question Number 142207 Answers: 2 Comments: 0

Question Number 142205 Answers: 0 Comments: 5

Question Number 142204 Answers: 1 Comments: 0

Question Number 140810 Answers: 0 Comments: 0

Find the natural value of x that satisfies the equation: (1/(6∙7)) + (1/(7∙8)) + (1/(8∙9)) +...+ (1/(x∙(x+1))) = (1/(12))

$${Find}\:{the}\:{natural}\:{value}\:{of}\:\boldsymbol{{x}}\:{that} \\ $$$${satisfies}\:{the}\:{equation}: \\ $$$$\frac{\mathrm{1}}{\mathrm{6}\centerdot\mathrm{7}}\:+\:\frac{\mathrm{1}}{\mathrm{7}\centerdot\mathrm{8}}\:+\:\frac{\mathrm{1}}{\mathrm{8}\centerdot\mathrm{9}}\:+...+\:\frac{\mathrm{1}}{{x}\centerdot\left({x}+\mathrm{1}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$

Question Number 140809 Answers: 1 Comments: 0

z^5 + (1/z^5 ) = ((205)/(16)) ∙ (z + (1/z))

$$\boldsymbol{{z}}^{\mathrm{5}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{z}}^{\mathrm{5}} }\:=\:\frac{\mathrm{205}}{\mathrm{16}}\:\centerdot\:\left(\boldsymbol{{z}}\:+\:\frac{\mathrm{1}}{\boldsymbol{{z}}}\right) \\ $$

Question Number 140805 Answers: 1 Comments: 0

find x 2cosh 2x+10sinh 2x=5

$${find}\:{x}\:\mathrm{2cosh}\:\mathrm{2}{x}+\mathrm{10sinh}\:\mathrm{2}{x}=\mathrm{5} \\ $$

Question Number 140803 Answers: 1 Comments: 0

Question Number 140798 Answers: 0 Comments: 1

Σ_(n=1) ^∞ (1/(n^3 (((4n)),(n) )))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{3}} \begin{pmatrix}{\mathrm{4}{n}}\\{{n}}\end{pmatrix}} \\ $$

Question Number 140793 Answers: 0 Comments: 0

∫(√((x+2)/e^x ))dx=...?

$$\int\sqrt{\frac{{x}+\mathrm{2}}{{e}^{{x}} }}{dx}=...? \\ $$

Question Number 140786 Answers: 0 Comments: 0

Question Number 140785 Answers: 0 Comments: 2

P-intersection point of bimedians in ABCD-convexe quadrilateral with a;b;c;d-sides, e;f-diagonals, E-point in plane, x;y;z;t-distances from, E-to A;B;C;D. Prove that... (1/4)(a^2 +b^2 +c^2 +e^2 +f^2 )+4PE^2 =x^2 +y^2 +z^2 +t^2

$${P}-{intersection}\:{point}\:{of}\:{bimedians}\:{in} \\ $$$${ABCD}-{convexe}\:{quadrilateral}\:{with} \\ $$$${a};{b};{c};{d}-{sides},\:{e};{f}-{diagonals}, \\ $$$${E}-{point}\:{in}\:{plane},\:{x};{y};{z};{t}-{distances} \\ $$$${from},\:{E}-{to}\:{A};{B};{C};{D}.\:{Prove}\:{that}... \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{e}^{\mathrm{2}} +{f}^{\mathrm{2}} \right)+\mathrm{4}{PE}^{\mathrm{2}} ={x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{t}^{\mathrm{2}} \\ $$

Question Number 140784 Answers: 0 Comments: 0

Let the i-j plane be the complex plane, with basic operations ij=−i ji=−j i^2 =−1 j^2 =−1 z=r+xi+yj w=s+pi+qj zw=rs+pri+qrj+sxi−px−qxi +syj−pyj−qy = (rs−px−qy)+(pr+sx−qx)i +(qr+sy−py)j wz=rs+sxi+syj+pri−px−pyi +qrj−qxj−qy = (rs−px−qy)+(pr+sx−py)i +(qr+sy−qx)j (little difference..) ⇒ zw−wz= (py−qx)(i−j) = 0 if py−qx= 0 z^2 = (r^2 −x^2 −y^2 )+(2rx−xy)i +(2ry−xy)j And if y=0 ⇒ z=r+xi z^2 =(r^2 −x^2 )+2rxi either way! (z^2 )z=r(r^2 −x^2 )+2r^2 xi +x(r^2 −x^2 )i−2rx^2 ⇒ (z^2 )z= r(r^2 −3x^2 )+x(3r^2 −x^2 )i z(z^2 )= r(r^2 −x^2 )+x(r^2 −x^2 )i +2r^2 xi−2rx^2 = r(r^2 −3x^2 )+x(3r^2 −x^2 )i so z(z^2 )=(z^2 )z = z^3 (so far so good) .....

Question Number 142200 Answers: 2 Comments: 0

Let p & q real positive number what the minimum of ((p^2 /q^2 ) +(q/p))^3 .

$$\:{Let}\:{p}\:\&\:{q}\:{real}\:{positive}\:{number} \\ $$$$\:\:{what}\:{the}\:{minimum}\:{of}\:\left(\frac{{p}^{\mathrm{2}} }{{q}^{\mathrm{2}} }\:+\frac{{q}}{{p}}\right)^{\mathrm{3}} . \\ $$

Question Number 140779 Answers: 1 Comments: 1

{ ((7x≡3(mod5))),((5x≡3(mod9))) :} solve for x

$$\begin{cases}{\mathrm{7}{x}\equiv\mathrm{3}\left({mod}\mathrm{5}\right)}\\{\mathrm{5}{x}\equiv\mathrm{3}\left({mod}\mathrm{9}\right)}\end{cases} \\ $$$${solve}\:{for}\:{x} \\ $$

Question Number 140774 Answers: 3 Comments: 3

Prove that ((1/( (√2)))+(5/(3(√6))))^(1/3) +((1/( (√2)))−(5/(3(√6))))^(1/3) = (√2)

$${Prove}\:{that} \\ $$$$\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} =\:\sqrt{\mathrm{2}} \\ $$

Question Number 140789 Answers: 2 Comments: 0

.......nice.....math.... calculate:: Θ:= Σ_(n=1) ^∞ (1/) =??

$$\:\:\:\:\:\:\:\:.......{nice}.....{math}.... \\ $$$$\:\:\:\:\:\:{calculate}::\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{}\:=?? \\ $$$$ \\ $$