夫子,我是用向量(vector)來算的。 Let OA be a, OB be b, and OC be c.(all a,b,c are vector!) Let the position vector of center of mass be OG As this triangle is uniform, OG = (a+b+c)/3 (theory) Thus, for fulfilling question, a+b+c = 0 if b = bx * i + by * j, c = cx * i + cy * j. a = ax * i
so we have bx ^2 + by ^2 = 50 ^2 cx ^2 + cy ^2 = 40 ^2 bx + cx + ax = 0 by + cy = 0
By solving those system of equation, we have (bx, by) = ( -290 / 7 , +80 sqrt(6) / 7 ) (cx, cy) = ( -200 / 7 , -80 sqrt(6) / 7 )
Sorry for typing English rather than Chinese. If I have time, I will retype it by Chinese.
母雞、福特汽車、手帕。那些喚起性衝動的奇妙物品
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什麼東西能夠引發性慾呢?綜觀歷史,
有許多超乎想像的答案被記下來,母雞、汽車、手帕都成為性慾來源,這些怪怪的「性偏好」是如何性成的呢?又一定需要治療嗎?
The post 母雞、福特汽車、手帕。那些喚起性衝動的奇妙物品 appeared first on PanSci 泛科學.
B( -290 / 7 , +80 sqrt(6) / 7 ) ,
回覆刪除C( -200 / 7 , -80 sqrt(6) / 7 )
正解,不知你是用何方法求出?另外,願意留下大名嗎?
刪除夫子,我是用向量(vector)來算的。
回覆刪除Let OA be a, OB be b, and OC be c.(all a,b,c are vector!)
Let the position vector of center of mass be OG
As this triangle is uniform, OG = (a+b+c)/3 (theory)
Thus, for fulfilling question, a+b+c = 0
if b = bx * i + by * j,
c = cx * i + cy * j.
a = ax * i
so we have
bx ^2 + by ^2 = 50 ^2
cx ^2 + cy ^2 = 40 ^2
bx + cx + ax = 0
by + cy = 0
By solving those system of equation, we have
(bx, by) = ( -290 / 7 , +80 sqrt(6) / 7 )
(cx, cy) = ( -200 / 7 , -80 sqrt(6) / 7 )
Sorry for typing English rather than Chinese.
If I have time, I will retype it by Chinese.
You are welcome.
刪除That's OK for writing in English.
華人根華人說話,不應該用外語。
回覆刪除以下是更正版:
設向量OA為a,向量Ob為b,向量OC為c。
(註,a,b,c都是向量)
設三角形形心(重心)的位置向量(向徑)為OG
由於三角形是均勻的,所以OG = (a+b+c)/3
而另一方面,題目要求重心在原點,所以得出 a+b+c = 0
設 b = bx * i + by * j,
設 c = cx * i + cy * j.
設 a = ax * i
所以
bx ^2 + by ^2 = 50 ^2
cx ^2 + cy ^2 = 40 ^2
bx + cx + ax = 0
by + cy = 0
解以上方程組,可得
(bx, by) = ( -290 / 7 , +80 sqrt(6) / 7 )
(cx, cy) = ( -200 / 7 , -80 sqrt(6) / 7 )
就是這樣了。
嗯,四個方程式,四個變數,以第三及第四式代入一、二式,即可求解。
刪除你是學生嗎?