簡單數學問題簡單數學問題

Tieria

2010-03-06 7:05 am

1. Which of the following statements is/are correct?
I. The centroid and the in-centre of an equilateral triangle are the same point.
II. The circumcentre of an isosceles triangle must lie outside the triangle.
III. The circumcentre and the orthocenter of a right-angled triangle must lie on the sides of the triangle.

The answer are I and III.

2. If the straight line L: 2x + 3y – 5 = 0 divides the circle C: x^2 + y^2 + kx – 8y – 2 = 0 into two identical parts, then k =

The answer is 7.

3. In a cabinet, there are three pairs of socks. One pair is yellow and two pairs are black. A boy takes two socks from the cabinet randomly without replacement. Find the probability that the two socks are of the same colour.

The answer is 7 / 15.

4. A man will continue throwing a dice until the number shown is 1. Find the probability that the man will stop throwing after three throws.

The answer is 25 / 216.

※試列明計算步驟※

回答 (1)

用戶10012

2010-03-06 3:46 pm

✔ 最佳答案

1. Circumcentre will not be inside the circle only if one of the angles of the isos. triangle is greater than 90 degrees.So II is wrong.
2.
Co-ordinates of the centre of the circle is ( -k/2, 4). Since 2x + 3y = 5 is the diameter because it cuts the circle in 2 equal halves, so (- k/2, 4) must be on this line. That is 2(-k/2) + 3(4) = 5, - k + 12 = 5, so k = 7.
3.
P(1st one black and 2nd one black) = (4/6)(3/5) = 2/5.
P(1st one yellow and 2nd one yellow) = (2/6)(1/5) = 1/15.
so probability for same colour = 2/5 + 1/15 = 7/15.
4.
P(not getting 1 in 1st throw) = 5/6
P(not getting 1 in 2nd throw) = 5/6
P(getting 1 in 3rd throw) = 1/6.
so probability of getting 1 in at least 3 throws = (5/6)(5/6)(1/6) = 25/216.

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