Difference between revisions of "AMC 12C 2020"
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| − | ==Problem 8 | + | ==Problem 8== |
| − | The real value of <math>n</math> that satisfies the equation <math>ln(n) + ln(n^{2} - 34) = ln(72)</math> can be written in the form < | + | The real value of <math>n</math> that satisfies the equation <math>ln(n) + ln(n^{2} - 34) = ln(72)</math> can be written in the form <cmath>a + \sqrt[b]</cmath> where <math>a</math> and <math>b</math> are integers. What is <math>a + b</math>? |
Revision as of 12:56, 20 April 2020
Contents
Problem 1
What is the sum of the solutions to the equation 
?
Problem 2
How many increasing subsets of 
contain no 
consecutive prime numbers?
Problem 3
A field is on the real 
plane in the shape of a circle, centered at 
with a a radius of 
. The area that is in the field but above the line 
is planted. What fraction of the field is planted?
Problem 4
What is the numerical value of 
?
Problem 5
cows can consume 
kilograms of grass in 
days. How many more cows are required such that it takes all of the cows to consume 
kilograms of grass in days?
Problem 6
candy canes and 
lollipops are to be distributed among children such that each child gets atleast 
candy. What is the probability that once the candies are distributed, no child has both types of candies?
Problem 7
Persons 
and 
can plough a field in days, persons and 
can plough the same field in 
days, and persons and can plough the same field in 
days. In how many days can all of them plough the field together?
Problem 8
The real value of 
that satisfies the equation 
can be written in the form
\[a + \sqrt[b]\] (Error compiling LaTeX. Unknown error_msg)
where 
and 
are integers. What is 
?
