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Type: Posts; User: Dr.Peterson

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  1. Replies
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    I was wondering if you might have done that,...

    I was wondering if you might have done that, though it didn't seem likely!

    So it's

    x^2 + y^2 = 5
    y - x = 3

    You can still do exactly what was suggested: solve one equation for one variable,...
  2. Depending on how much you have learned about...

    Depending on how much you have learned about quadratic equations, there are several ways you might approach this.

    One is to use the discriminant, or equivalently the quadratic formula. What can...
  3. The notation is somewhat ambiguous, but I would...

    The notation is somewhat ambiguous, but I would say that their interpretation is at least as valid as yours, and certainly consistent with how a programmer would look at it.

    If you want to express...
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    It's not all that hard to solve, at least if you...

    It's not all that hard to solve, at least if you do it the way I suggested, and if you know the quadratic formula; but the answer is not pretty, so it is quite possible that the problem was copied...
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    One way to simplify this is to first take the...

    One way to simplify this is to first take the square root of both sides of the first equation. But be careful! You need to use plus-or-minus, because there are two square roots. (This caution will...
  6. If you typed it in just as you show here, it...

    If you typed it in just as you show here, it would definitely be unhappy.

    Assuming you are supposed to use t in place of theta, your last line should look like this, where I am being careful to...
  7. Sometimes there are shortcuts for this process,...

    Sometimes there are shortcuts for this process, but in general, you just replace x and y with their expressions in terms of r and theta (were you taught those?), and then do whatever is needed (in...
  8. You are correct about the evaluation; so choice...

    You are correct about the evaluation; so choice (c) does produce an odd number at least for a=2.

    Can you convince yourself that its value will be odd for any integer a? Why?

    And can you see why...
  9. If you're asking about how to evaluate this...

    If you're asking about how to evaluate this expression, you have to follow the order of operations: apply the exponent first (to just the base, 2), and then multiply the result by the multiplier (the...
  10. I get the same result by a different method. ...

    I get the same result by a different method.

    Either the problem itself is wrong, or you copied something wrong. Please check!

    If it said, "the sum of the units digit and twice the tens digit,...
  11. The solution has to be expressed in different...

    The solution has to be expressed in different ways, depending on what you have learned. That's part of the reason we require you to show some work: so we can see what kind of work you know about. We...
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    I think there's a mistake in the problem. If it...

    I think there's a mistake in the problem. If it said the parallel sides (not the non-parallel sides) were 8 and 10, then one of the answers would be an obvious way to solve it. I don't think any of...
  13. Poll: Please tell us what you expected to get, and why...

    Please tell us what you expected to get, and why you typed that. What are you trying to accomplish?

    We can't know what is going on without that background.
  14. First, to make sure I'm reading the slightly...

    First, to make sure I'm reading the slightly fuzzy picture, you are asked to calculate \displaystyle \left(f^{-1}\right)'(0) + \int_0^ef^{-1}(x)dx, right?

    The main thing to know is that you don't...
  15. Have you tried drawing this graph by hand, to see...

    Have you tried drawing this graph by hand, to see how it happens?

    What point do you plot for theta = 0? How about theta = pi? Try some other angles as well. You should see what I was talking about...
  16. If you don't know about the pigeonhole principle...

    If you don't know about the pigeonhole principle (which you can look up), then can you tell us why you are working on this problem? If it is for a class, what methods do you know that might be used?...
  17. How are you using the word "solve"? It isn't...

    How are you using the word "solve"? It isn't clear what your goal is, but I don't think you're actually solving an equation to find x.

    Are you asking what the graph will look like? Are you...
  18. The only way to learn how to visualize something...

    The only way to learn how to visualize something is to experience it! You do have to try graphing this (and a few more) in order to really know what to look for. Make a table of values and plot it....
  19. That's right. The first term is 2 and the common...

    That's right. The first term is 2 and the common ratio is 3, so an = 2*3n-1. You can check it by putting n = 1, 2, 3, 4 into the formula.
  20. This looks like a pigeonhole type problem. Are...

    This looks like a pigeonhole type problem. Are you familiar with that method?

    Can you make 8 "pigeonholes" that a 9th "pigeon" won't fit into without sharing space?
  21. Your problem is very common, and there is a...

    Your problem is very common, and there is a simple solution.

    The key here is knowing which of x-y and x+y represents which speed; and to get that right, it helps a lot if, rather than just...
  22. The answer to the first is not 105.1, as you can...

    The answer to the first is not 105.1, as you can see by doing the check (substituting b with 105.1 and evaluating). Why do you think it is? Did you copy the equation exactly as given, or does what...
  23. What help do you need? Please show whatever...

    What help do you need?

    Please show whatever work you have done; for example, did you find the length of the side of the square? Do you see how that is related to the circle?
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    I don't think I can tell you why (or even...

    I don't think I can tell you why (or even whether) the majority of teachers would skip that particular step. That's up to them. Most likely it would be because they are talking to students whom they...
  25. In general, the formula for a geometric sequence...

    In general, the formula for a geometric sequence is an = arn-1. Here a is the first term (corresponding to n=1), and r is the "common ratio" between terms.

    In your example, you can just recognize...
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