BMAD

Fair point

A tank contains 10 kg of salt dissolved in 3000 L of water. Brine containing 0.05 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 5 L/min. How much salt is in the tank after 1 hour?

There are three cars driving on a track. The track is a perfect circle (circumference unknown) and is not wide enough to allow any car to pass another. Currently, the lead car is going 55 MPH and the last car is going 45 MPH. While the car in the middle is going some speed between. At this moment there is x miles between the lead car and the middle car and x miles between the middle car and the slowest car where x is not 0 or 1 miles. If the car's maintained their speed up to the point where the lead car caught the slowest car (then everyone stops), would there ever be a point and time where the distance between any two pairs is again x miles (the pairs must be x distance apart at the same time)?

I appreciate it.

I see the issue, I was looking for L the total minimal length of PA,PB,PC while you found the length of DP. Nice job.

yes. PA + PB + PC = L I am not sure what 1.407 is referring to but i get a different answer.

hint: pythagoras is a straightforward approach

For those who can't access this image: There is a triangle BPC where on one line segment BC there is a point D such that BD=2 and DC=3. Extending through P is a line segment going from some point A to D which is a distance of 5 and perpendicular to BC. Find the minimum total distance of all the "cables" by placing p in an optimal place.

A point P needs to be located somewhere on the line AD so that the total length L of cables linking P to the points A, B, and C is minimized. What is the minimum value of L? My image won't upload so you can see it here: https://docs.google.com/file/d/0B0PFoZbqZhFCZUFicy10Q29od0U/edit?usp=docslist_api

Let F(x) = f(f(x)) and G(x) = (F(x))2 and f(4) =9, f(9)=2, f'(9)=15, and f'(4)=6 What is F'(4) and G'(4)?

Confirm

confirm

Here is a simple one: If two dice are rolled, the likelihood that the total on the two dice will be 5 is 1/9. Suppose two dice are rolled 50 times. Find the probability that exactly 6 rolls have a result of 5. Find the probability that 10 or fewer rolls have a result of 5.

In the image below, what does yes mean?

In the image below, what does yes mean?

integers a1, a2, a3, not all zero, satisfying a1 r1 +a2 r2 +a3 r3 = 0. this hint is for those Linear Algebra fans out there

x and y are of the three nonnegative real numbers r1 r2 r3

It's probably better to define a rhombus for each direction:

Informally, the proof is to take a square and let 2 opposite corner A and C run around the loop. Doing that, you rotate the square while trying to fit the 2 other corners B and D within the loop. If you start with A and C on a horizontal line, and B and D can fit within the loop, then after 1/4 turn, A and C are on a vertical line, where BD originally was and now B and D are outside of the loop. So, at some point (for some angle between AC and the horizontal), you go from "B and D both fit in the loop" to "B and D fit outside the loop". At that point, it should be possible to fit both B and D on the loop. There are plenty of loose ends, but it makes me feel such a square must exist.

Three nonnegative real numbers r1, r2, r3 are written on a blackboard. These numbers have the property that there exist integers a1, a2, a3, not all zero, satisfying a1 r1 +a2 r2 +a3 r3 = 0. We are permitted to perform the following operation: find two numbers x, y on the blackboard with x <= y, then erase y and write y - x in its place. Prove that after a finite number of such operations, we can end up with at least one 0 on the blackboard.

I came across this page which seems to contradict my proof. Any ideas where I went wrong? http://www2.stetson.edu/~efriedma/maxmin/

Winning is winning

How can you mirror player 1's first move in the center of paper? If player 1 places their point at (0, 0), place yours at (0, 1/infinity). I am confused as to how one can physically make that move

How can you mirror player 1's first move in the center of paper?

If a wagon wheel had 10 more spokes, the angle between the spokes would decrease by 6 degrees. How many spokes does the wheel have?