Re: [計量] 好幾題數學問題
先算幾題一看就知道答案的
: =====================================
: 1.For all real numbers,xy+x=5 and y^2+2y=19
: A: x / y+1 B: 1/4
y^2+2y-19=0 代公式解
y=-1+20^(1/2) or -1-^(1/2)
xy+x=5 x(y+1)=5
y代入上式可解得 x=[(5)^(1/2)]/2 or -[(5)^(1/2)]/2
x/(y+1)=1/4
答：C
: 2. How many ways can 2 identical red chairs and 4 identical blue chairs be
: arranged in a row?
: ANS: 15
: 3.(n+2)!-(n+1)!/n!= 有人可以告訴我算法嗎??或是有什麼訣竅 謝謝
: ANS: (n+1)^2
[(n+2)!-(n+1)!]/n!= [(n+2)!/n! - (n+1)!/n!]
=(n+2)(n+1) - (n+1)
=(n+1)[n+2-1]
=(n+1)^2
: 4. In the xy-coordinate plane, the vertices of the traingle ABC are
: A(15,1) B(9,3) C(4,5). What is the slope of the altitude to side AB?
: ANS: 3 但是我算的是-1/3,覺得好奇怪@@
altitude是指高的那條垂線
m1 = (1-3)/(15-9) = -(1/3)
m1 x m2 = -1
m2 = 3
註：兩直線互相垂直，其斜率相乘為-1
: 5. If the perpendicular bisector of the segment with endpoints A(1,2)and
: B(2,4) contains the point (4,C), then the value of C is?
: ANS:7/4 完全不知道怎麼算 ˊˋ
: 6. If a cube has an edge of length 10, then the length of the segment
: connecting the center of a face of the cube to any vertex not contained
: in the place of the face is?
: ANS:5√6
: 7. If a bowl cintains seven marbles, three red and four green, four marbles
: are drawn from the bowl at random without replacement. What is the
: probability that contains two red marbles and two green ones?
: ANS:18/35 但是我算出來是3/35 請問要怎麼算呢? 謝謝 ^^"
: 8. After the first term, each term in a sequence is 3 greater than 1/3 of the
: preceding term. If t is the first term of the sequence and t =/ 0, what is
: the ratio of the second term to the first term??
: ANS: t+9/3t
: 真的很不好意思我問好多題,再次感謝各位板友
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