已知\(\Delta ABC\)中，\(\overline{AB}=5,\overline{BC}=9\)，且\(\displaystyle \frac{1}{tanA},\frac{1}{tanB},\frac{1}{tanC}\)成等差數列，試求\(\displaystyle tan^2 \frac{B}{2}=\)　　　。
[解答]
如附圖:

Screenshot from 2023-04-26 15-50-45.png (68.25 KB)

2023-4-26 15:53

已知\(x\)、\(y\)、\(z\)為三個實數且滿足\(\cases{x^2+y^2=18 \cr y^2+\sqrt{3}yz+z^2=13\cr x^2+xz+z^2=19}\)，則\(2xy+yz+\sqrt{3}xz=\)　　　。
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Screenshot from 2023-04-26 15-54-38.png (111.93 KB)

2023-4-26 15:55

已知\(\Delta ABC\)中，\(\overline{AB}=25,\overline{AC}=30\)，\(\angle B=2\angle C\)，且\(\angle B\)的內角平分線交\(\Delta ABC\)的外接圓於\(D\)點，且\(B\)、\(D\)為相異點。試求\(\Delta BCD\)的面積為　　　。
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2023-4-26 15:57

統計推論
A plant germination method is successful on average 4 times out of every 10. A horticulturist develops
a new technique which she believes will improve the number of plants that successfully germinate. She takes
a random sample of 50 seeds and attempts to germinate them. Suppose random variable X is defined as the
number of plants that successfully germinate. Using a 5% level of significance, find the rejection region for a
test to check her belief.
Ans：the rejection region is 　　　。
[解答]

Screenshot from 2023-04-27 10-02-22.png (33.74 KB)

2023-4-27 10:03

對! 嚴格來說{0<= X<= 13, X 為整數}, 只是X本來就是整數,也一定>=0