By Vieta r + s = - 4/3 and r s = -12/3 = - 4
(r +s)^2 = r^2 + s^2 + 2 rs
(-4/3)^2 = ( r^2 + s^2) + 2 ( -4) you can finish, yah?
a/b = 4/3 b/c = 4/3
a = 4/3 b c = 3/4 b
a + b + c = 4625
4/3 b + b + 3/4 b = 4625
3 1/12 b = 4625
b = 1500 then a = 2000 and c = 1125
A different route:
(a+b)3 = ( a^3 + b^3 ) + 3 a^2b + 3 b^2 a
73 = ( 44 ) + 3 ab ( a+b) we know (a+b) = 7 .... sub that in to get:
7^3 - 44 = 21 ab
ab = 299/21
Now 1/a + 1/b = (a+b) / ab
= (7) / (299/21) = 147/299
6 out of 10 match a marble in the second bag so 6/10
now there are 6 x 6 possibles with 6 being a match 6/36
6 / 10 x 6/36 = 1/10
See below...... solve for 'x'
198 is found by tan 68 = 80/d then d = 198
Start with this:
(x^2 + y^2 ) 2 = ( x^4 + y^4) + 2 x^2 y^2 now remember x^2 + y^2 = 1 so
1 = 17/19 + 2 x^2 y^2 I think you should be able to finish from here, yah?
Note that c and a are the 'x' coordinates....
All you need to do is equate the two given parabolic equations, simplify and then use the Quadratic Formula to solve for the x's ( c and a )
-x^2 - x + 1 = x^2 - 3x - 3 <====== take it away !
Put the given equation into standard circle form by completing the square for x and y
(x+5)^2 + (y-3)^2 = 24 + 25 + 9
r^2 = 24+25+9 =58
Area = pi r^2 = 58 pi
