2016 AMC 12B
Problem 1
What is the value of  when ?
Solution
By: Dragonfly
We find that  is the same as , since a number to the power of  is just the reciprocal of that number. We then get the equation to be
We can then simplify the equation to get 
Problem 2
The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of  and is closest to which integer?
Solution
By: dragonfly
Since the harmonic mean is  times their product divided by their sum, we get the equation
which is then
which is finally closest to .
Problem 3
Let . What is the value of    ?
Solution
By: dragonfly
First of all, lets plug in all of the 's into the equation.
   
Then we simplify to get
headfirstpython第2版pdf下载
   
which simplifies into
   
and finally we get 
Problem 4
The ratio of the measures of two acute angles is , and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the two angles?
Solution
By: dragonfly
We set up equations to find each angle. The larger angle will be represented as  and the larger angle will we represented as , in degrees. This implies that
and
since the larger the original angle, the smaller the complement.
We then find that  and 压力容器级别, and their sum is 
Problem 5
The War of  started with a declaration of war on Thursday, June , . The peace treaty to end the war was signed position of the day days later, on December , . On what day of the week was the treaty signed?
Solution
By: dragonfly
To find what day of the week it is in  days, we have to divide  by  to see the remainder, and then add the remainder to the current day. We get that  has a remainder of 2, so we increase the current day by  to get 
Problem 6
All three vertices of  lie on the parabola defined by , with  at the origin and  parallel to the -axis. The area of the triangle is . What is the length of ?
Solution
By: Albert471
Plotting points  and  on the graph shows that they are at kettle日志写入数据库 and , which is isosceles. By setting up the triangle area formula you get:  Making x=4, and the length of 如何快速进行二进制转换 is , so the answer is .
Problem 7
Josh writes the numbers . He marks out , skips the next number , marks out , and continues skipping and marking out the next number to the end of the list. Then he goes back to the start of his list, marks out the first remaining number , skips the next number , marks out , skips , marks out , and so on to the end. Josh continues in this manner until only one number remains. What is that number?
Solution
By Albert471
Following the pattern, you are
Time 1: Every non-multiple of 
小程序服务通知Time 2: Every non-multiple of 
Time 3: Every non-multiple of 
Following this pattern, you are left with every multiple of  which is only  .

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。