Racing Satellites

Two satellites are following the same orbit path, one is 1000 miles behind the other. If the front satellite is traveling at a speed of 17,000 miles per hour and the other satellite is traveling 17,500 miles per hour, how many miles will the front satellite travel before the second one catches up to it?

Solution to circle problem.

It turns out that circle #3 will be the only one shaded. The shading on the top circle moves one space counterclockwise each time. The shading on circle #5 moves two spaces counterclockwise each time. By the time you get to figure 5, circle #3 is the only one that is shaded.

What will the next figure look like?

Let's call the top circle #1. Then moving in a clockwise manner, we have #2, #3, #4, etc. If you were to draw the next figure in the pattern, what would it look like?

There may be more than one solution. Just be sure to explain your reasoning.

What does infinitely close mean?

In the last post we discussed .999..... We must remember that the 9's repeat infinitely...which means that they never end. Since the 9's repeat, the number .999... must be infinitely close to 1. If a number is infinitely close to another, can we distinguish between them?

Does 1 = 1?

In our Geometry class, we have been discussing the concept of infinity. What does in mean when we say that numbers are infinite? Can we really understand that? And further, if numbers are infinitely large, does there exist a number that is infinitely small? How do we deal with this "infinite smallness?"

The question that has come up in class is this:

Is .9999... = 1?

Solution to Problem of the Week 9/1/08

Many of you left some pretty good answers. But it looks like the best two solutions and explanations go to Josh M. and Kathryn I. Nice job, to the both of you. Here is the solution and explanation:

In this sequence there are two “sub-sequences.”

A, 2, C, 3, F, 5, K, 7, ___, ___...

A, 2, C, 3, F, 5, K, 7, ___, ___...


The first sequence is just a list of prime numbers. This tells us that the second blank would be 11.

The second sequence is dependant on the first. If A equals 1, B equals 2, etc… you can add the number value of the letter to the number that follows it in the sequence to get the number value of the next letter.
A = 1
A + 2 = 3
3 = C
Since K corresponds to 11 the next letter blank should be R.
(11 + 7 = 18; 18 = R)

ANSWER: R, 11

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