Algebra Problems, Math Problems

Problem of the Day: 2/9/13

The population of a bacteria sample doubles every hour. If there are 38,400 bacterial cells after 7 hours, how many cells were in the original sample?

Solution to yesterday’s problem:

My suggestion for this problem is to break the diagonal into parts that we can handle easily. This is how I divided it:


Now we have two 45-45-90 triangles and one rectangle. We instantly know that the middle segment is 4 cm, because it is the opposite side of the rectangle. As for the 45-45-90 triangles, we can use the Pythagorean theorem to solve for the two legs of the triangle, knowing that both legs are of equal length:





So the left and right segments of the diagonal are both 2\sqrt{2} centimeters. Adding those together, we get 4\sqrt{2} centimeters. Adding the middle segment, we find that the length of the diagonal is 4+4\sqrt{2} centimeters.


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