Forgot password? New user? Sign up
Existing user? Log in
If Earth somehow contracted to $\frac {1}{8 }$ of its current volume instantly (through some magical internal forces), while keeping its shape and mass, then how long would a day be?
Are you sure you want to view the solution?
Three unit circles are drawn tangent to each other with all their centers lying on line segment $OE.$
From $O,$ line segment $OD$ is drawn such that it's tangent to the rightmost circle.
If the length of the chord $AB$ is $\frac ab$, where $a$ and $b$ are coprime positive integers, then what is $a+b?$
Note: I did not create this problem; I simply solved it and decided to post it on here. Credit goes to my math teacher.
Are you sure you want to view the solution?
After paying for a newspaper with 4 quarters, the newspaper came out. But, to my surprise, my 4 quarters also came back out because the machine was broken. I quickly took note of how I paid for the paper: "4 quarters." After spending over a quarter of an hour at the machine, I paid for a newspaper in every possible way.
How many newspapers did I end up with?
Assumptions:
Are you sure you want to view the solution?
The 3 little pigs have recently established their own construction company.
Their new client is the wolf, now a real estate entrepreneur. The wolf would like to contract the pigs to build a house. The pigs provide the following conditions on their work:
Under the 3 pigs' conditions, what is the least amount of money (in $) the wolf can invest to complete this project?
Are you sure you want to view the solution?
The $x$-axis is a common tangent of the two curves $y = x^{2}$ and $y = x^{3}$.
Suppose the slope of the other common tangent (in sky blue) of these two curves is expressed as $\frac{p}{q},$ where $p$ and $q$ are coprime positive integers.
What is $p+q?$
Are you sure you want to view the solution?
Problem Loading...
Note Loading...
Set Loading...