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AlgebraQuestion and Answers: Page 268

Question Number 83590 Answers: 0 Comments: 3

transform the ellipse (x^2 /a^2 )+(y^2 /b^2 )=1 to the polar equation r= ((a(1−e^2 ))/(1+ecosθ)) a: semimajor axis e: eccentricity

$t r a n s f o r m t h e e l l i p s e \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 t o$ $t h e p o l a r e q u a t i o n r = \frac{a (1 - e^{2})}{1 + e c o s θ}$ $a : s e m i m a j o r a x i s$ $e : e c c e n t r i c i t y$

Question Number 83570 Answers: 2 Comments: 3

Find the locus of a point which moves such that its distance from the line y = 4 is a constant k.

$Find the locus of a point which moves such that its$ $distance from the line y = 4 is a constant k .$

Question Number 83554 Answers: 1 Comments: 0

Question Number 83543 Answers: 1 Comments: 2

Question Number 83542 Answers: 2 Comments: 0

Question Number 83621 Answers: 2 Comments: 1

∣ x+(1/x)∣ < 4 find the solution

$∣ x + \frac{1}{x} ∣ < 4$ $find the solution$

Question Number 83512 Answers: 1 Comments: 0

find the solution ((4x^2 )/((1−(√(2x+1)))^2 )) < 2x+9

$find the solution$ $\frac{{4 x}^{2}}{{(1 - \sqrt{2 x + 1})}^{2}} < 2 x + 9$

Question Number 83477 Answers: 0 Comments: 1

a^b +b^a =1 a=? , b=? a≠b≠0

$a^{b} + b^{a} = 1 a = ?, b = ?$ $a \neq b \neq 0$

Question Number 83473 Answers: 1 Comments: 0

solve in R sin(πln(x))+cos(πln(x))=1

$s o l v e i n R$ $s i n (π l n (x)) + c o s (π l n (x)) = 1$

Question Number 83378 Answers: 0 Comments: 2

x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 find x^4 +y^4 +z^4 =?

$x + y + z = 1$ $x^{2} + y^{2} + z^{2} = 2$ $x^{3} + y^{3} + z^{3} = 3$ $f i n d$ $x^{4} + y^{4} + z^{4} = ?$

Question Number 83373 Answers: 0 Comments: 4

Question Number 83372 Answers: 0 Comments: 1

Question Number 83370 Answers: 0 Comments: 3

Question Number 83341 Answers: 1 Comments: 1

Find the maximum and minimum of the expression 𝚺_(i=1) ^n a_i x_i with 𝚺_(i=1) ^n (x_i −b_i )^2 =c^2 , where a_i , b_i and c are constants. (extracted and modified from Q83331)

$F i n d t h e m a x i m u m a n d m i n i m u m$ $Double subscripts: use braces to clarify$ $\underset{i = 1}{\sum^{n}} {(x_{i} - b_{i})}^{2} = c^{2}, w h e r e a_{i}, b_{i} a n d c a r e$ $c o n s t a n t s .$ $(e x t r a c t e d a n d m o d i f i e d f r o m Q 83331)$

Question Number 83264 Answers: 1 Comments: 2

Question Number 83262 Answers: 1 Comments: 0

Question Number 83229 Answers: 0 Comments: 4

Question Number 83050 Answers: 0 Comments: 1

Question Number 83049 Answers: 0 Comments: 0

Question Number 82991 Answers: 1 Comments: 2

Question Number 82952 Answers: 1 Comments: 0

Show that: y + (√(y^2 − 1)) ≥ 1 and 0 < y − (√(y^2 − 1)) ≤ 1 if y ≥ 1

$Show that : y + \sqrt{y^{2} - 1} ⩾ 1 and 0 < y - \sqrt{y^{2} - 1} ⩽ 1$ $if y ⩾ 1$

Question Number 82897 Answers: 1 Comments: 2

Question Number 82881 Answers: 1 Comments: 2

(√(√(...(√(6561))))) = 3^8^x (60 times) find x

$\sqrt{\sqrt{. . . \sqrt{6561}}} = 3^{8^{x}} (60 times)$ $find x$

Question Number 82873 Answers: 1 Comments: 2

Question Number 82843 Answers: 1 Comments: 0

show that (((1+(√3) i)^4 (1+i)^8 )/((cos100°−i sin100)^3 ))=−256

$s h o w t h a t$ $\frac{{(1 + \sqrt{3} i)}^{4} {(1 + i)}^{8}}{{(c o s 100 ° - i s i n 100)}^{3}} = - 256$

Question Number 82877 Answers: 1 Comments: 1

1)find xy∈R 2)find x,y∈Z (x+2yi)^6 =8i

$1) f i n d x y \in R$ $2) f i n d x, y \in Z$ ${(x + 2 y i)}^{6} = 8 i$

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