问一道纠结的数学题 prep上的

sagamba

1.the  rate of  a certain chemical reaction is directly proportional to the square of the concentration of chemical Apresent and inversely proportional to the concertration of chemicalB present. If the concentration of chemical B is increased by 100 percent, which of the following is closet to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
40%increase? 50%increase?

2.what could be correct order? 1/x,2x,x*2
1)x*2<2x<1/x  2)x*2<1/x<2x 3) 2x<x*2<1/x
答案是1和2，不知道第二个是怎么解出来的

3. when a certain tree was first planted, it was 4feet tall, and the height of the tree increased by a constant amount each year for the next 6years, At the end of the 6th year,  the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
3/10  
2/5
1/2
2/3
6/5
这题我怎么算都是1/10,
请教各路牛人帮帮忙啦~十分感谢

piggycandys

1 is a chemistry question.

rate = n*[A]^2/[B]  If [B] becomes 2[B], then [A] has to become 1.41[A] to compensate that increase in B.

2.what could be correct order? 1/x,2x,x*2
1)x*2<2x<1/x  2)x*2<1/x<2x 3) 2x<x*2<1/x
答案是1和2，不知道第二个是怎么解出来的

Try x = 5/7

huangsiyan

3. when a certain tree was first planted, it was 4feet tall, and the height of the tree increased by a constant amount each year for the next 6years, At the end of the 6th year,  the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
3/10  
2/5
1/2
2/3
6/5

h(n) = 4 + a*n
h(6) = 4 + 6a
h(4) = 4 + 4a
h(6)-h(4) = (1/5)*h(4)
2a = (1/5)*(4 + 4a)
6a =4
a = 2/3

supermanlee

2.what could be correct order? 1/x,2x,x*2
1)x*2<2x<1/x  2)x*2<1/x<2x 3) 2x<x*2<1/x
答案是1和2，不知道第二个是怎么解出来的

在X<0 时， X^2一定大于2X和1/X, 所以 none of choice could be correct.
在X>1时，1/X一定小于2X和X^2, 所以none of choice could be correct.
在 1>X>0时候，X^2一定小于2X和1/X, 同时如果X>根号1/2, 那么2X>1/X (选项1), 如果X< 根号1/2, 那么2x>1/x (选项2).  
你可以在坐标图上画一下y=1/2 * X，和 Y= 1/X这两条线，或者解一下方程式，他们的交点是根号(1/2)
注意是could be, 也就是说可能就行不需要一定。

pfullsomer

1 is a chemistry question.

rate = n*[A]^2/  If becomes 2, then [A] has to become 1.41[A] to compensate that increase in B.

问一下哈 这1.41是不是指的是根2啊？

还有"1/5taller than" 我怎么觉得是比第四年多1/5的意思啊 求教求教~~

sagamba

牛人啊！
我一般做这题的时候狂带数~不如你这方法严谨！
谢啦哈！