| GodOfWar_3ever said: 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 |
Thanks so much ;)
