✔ 最佳答案
(1) Let original speed = 100 km/h. Let distance = 100 km
so time taken = 1 hr.
New speed = 100(1 - 15%) = 85 km/h.
so new time = 100/85 = 1.17647 hr.
so % change in time = (1.17647 - 1)/1 x 100% = 17.647% increase. (B).
(2)
In 1 day, Mr Chan can finish 1/m parts of the job.
In 1 day, Hong can finish 1/n parts of the job.
So in 1 day, two together can finish (1/m + 1/n) parts of the job.
1/m + 1/n = (m + n)/mn.
So it takes mn/(m + n) days to complete the job. (D).
(3)
Since the circle touches both the x and y axis, so the x and y co - ordinates of the circle is the same and equal to the radius. Let radius be r, so center is (r,r).
Radius = sqrt [ ( r - 2)^2 + (r - 1)^2] = sqrt [ (r - 8)^2 + (r - 9)^2]
That means
(r - 2)^2 + (r - 1)^2 = (r - 8)^2 + (r - 9)^2
Solving the equation, r = 5. So center is (5,5)
So equation of circle is (x - 5)^2 + (y - 5)^2 = 5^2
x^2 + y^2 - 10x - 10y + 25 = 0 (B).
Let me take a rest and answer to others later.
2012-12-18 21:38:03 補充：
(4) Put y = 0 into the equation of the circle, x^2 + 2x - 8 = 0, (x - 2)(x + 4) = 0, x = 2 or - 4.
So the co-ordinates of A and B are (2,0) and ( - 4,0). From the equation of the circle, we know center of circle is (- 1, 4), so area of triangle ABC = [2 - (- 4)](4)/2 = 12 (B).
2012-12-18 21:43:58 補充：
(5) Sub. y = mx into equation of circle, x^2 + (mx)^2 + 6x - 2(mx) + 2 = 0
(1 + m^2)x^2 + (6 - 2m)x + 2 = 0. Since the line and the circle do not intersect, so delta < 0. That is (6 - 2m)^2 - 4(1 + m^2)(2) < 0. (3 - m)^2 - 2(1 + m^2) < 0. 9 + m^2 - 6m - 2 - 2m^2 < 0. - m^2 - 6m + 7 < 0.
2012-12-18 21:45:38 補充：
(m + 7)(m - 1) > 0. So m < - 7 or m > 1. (D)
2012-12-18 21:51:21 補充：
(6) Let y = f(x) be represented by a quadratic function with vertex ( 2, 4). So f(x) = (x - 2)^2 + 4. f(2x) = (2x - 2)^2 + 4 = 4(x - 1)^2 + 4. 3f(2x) = 3[4(x - 1)^2 + 4] = 12(x - 1)^2 + 12.
3f(2x) - 2 = 12(x - 1)^2 + 12 - 2 = 12(x - 1)^2 + 10. So the new vertex is (1, 10) (A)
2012-12-19 08:10:23 補充：
(7) If a, b and c are negative, only (D) is correct. For example a = - 2, b = - 3 and c = - 4.
