1)
If the initial # of members = x
720/x = y ----> From this, 720 = xy
720/(x-2) = [y (plus) 4] ----> From this 720 = (x-2)[y(plus)4] = xy (plus) 4x - 2y - 8
Since they're both equal to 720,
xy = xy (plus) 4x - 2y - 8
0 = 4x - 2y - 8
2y = 4x - 8
y = 2x - 4 Substitute this in 720 = xy and we get,
720 = x(2x-4)
720 = 2x2 - 4x
Divide everything by 2,
360 = x2 - 2x
x2 - 2x - 360 = 0
(x plus 18)(x - 20) = 0
Therefore, x = -18 or x=20
Since -18 cannot be taken, the # of members is 20 before, 18 after.
2)
Don't know if you've done this at school but to check the roots of a quadratic equation, you can use this thing called the discriminant (Think thats what its called)
Discriminant = (coefficient of the "x" term)2 - 4(coefficient of the x2 term)(coefficient of the constant term)
If its equal to 0, then the equation has real, equal roots.
If its more than 0, then there are 2 real, different roots.
If its less than 0, the roots are not real... I think
Anyway, we have to consider the discriminant to be equal to 0.
Coefficient of the,
x term - -5
x2 term - p
constant term - p
Therefore, for the equation to have real roots,
(-5)2 - 4(p)(p) = 0
25 - 4p2 = 0
25/4 = p2
p = 5/2 or p = -5/2
3)
I don't understand what you're saying....
I'm gonna assume one root is 2 plus 3 sqr.5 and the other is 2 - 3 sqr.5
So the equation is -
(x-[2 plus 3sqr.5])(x-[2 - 3sqr.5]) = 0
x2 -[2 - 3sqr.5]x - [2 plus 3sqr.5]x plus [2 plus 3sqr.5][2 - 3sqr.5] = 0
x2 - 2x plus 3sqr.5x - 2x - 3sqr.5x plus (22 - 3^2(sqr.5)^2) = 0 (^2 = squared btw)
x2 - 4x -4 plus 4 - 45 = 0
x2 - 4x - 41 = 0
God I hope that correct....
4)
If the boat is travelling at x km/h,
[65/(x - 5)] plus [55/(x plus 5)] = 15
[65(x plus 5) plus 55(x - 5)] that whole thing divided by (x plus)(x-5) = 15
Divide both sides by 5 to get
[13(x plus 5) plus 11(x - 5)] that whole thing divided by (x plus)(x-5) = 3
[13x plus 65 plus 11x - 55] divided by x2 - 25 = 3
24x plus 10 = 3x2 - 75
3x2 - 24x - 85 = 0
x2 - 8x - 85/3 = 0
x2 - 8x plus 16 - 133/3
(x - 4)2 = 133/3
x - 4 = sqr.(133/3)
x - 4 = 6.658
x = 10.658
There are bound to be some mistakes cause typing this shit in and no plus symbols is pain in the ass
