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  1. Replies
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    The age itself won't necessarily be (three...

    The age itself won't necessarily be (three hundred and something) or (thirty something), but the age reversed will be. One of the pieces of information we're given is that the units digit of Grandpa...
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    424

    Honestly, I think using a quadratic at all is a...

    Honestly, I think using a quadratic at all is a bit overkill for this problem. The answer practically falls directly into place if you think about it for just a bit, rather than treat as a "math"...
  3. Well, I see you've found the answer a different...

    Well, I see you've found the answer a different way (and I must admit that solution is far more elegant and nice... I only wish I'd thought of it myself :p), so I'm not sure how much this is worth......
  4. This is correct. There's absolutely no...

    This is correct. There's absolutely no expectation that a generic geometric series will sum to 1. This specific series, however, does. You seem to be at least a little bit familiar with the concept...
  5. Well, since you've shown no work of your own (and...

    Well, since you've shown no work of your own (and you've read the Read Before Posting thread that's sticked at the top of each sub-forum), I'm forced to assume that you have no work to share with us...
  6. This would be the definition of the binomial...

    This would be the definition of the binomial coefficient (read aloud as "n choose r"). It is:

    \sideset{_n}{_r} C = \displaystyle \binom{n}{r} = \dfrac{n!}{r! (n - r)!}

    What do you get when you...
  7. If I had to guess, I'd say that you "didn't find...

    If I had to guess, I'd say that you "didn't find anything" because there's nothing to be found. There's no question here! When you reply back, please include the full and exact problem text, ideally...
  8. No, there's definitely enough information to...

    No, there's definitely enough information to solve this problem. What you've done so far is great, but you've for some reason stopped five feet short of the metaphorical goal tape. So let's keep...
  9. Personally, I think Tkhunny's method is far...

    Personally, I think Tkhunny's method is far better, as it will get you to the answer much faster, but your method will absolutely work. The only problem you encountered was not being careful about...
  10. Hmm... How curious. I often find that expressions...

    Hmm... How curious. I often find that expressions written on this site are ambiguous or incorrect due to missing grouping symbols. However, in this particular case, the answer is incorrect because of...
  11. The general formula for the future value of an...

    The general formula for the future value of an investment subjected to compound interest is given by:

    F = P \left( 1 + \dfrac{r}{n} \right)^{nt}

    where F is the future value, P is the principal,...
  12. What you've done so far is good. That takes care...

    What you've done so far is good. That takes care of the easy part of plugging things in. Next comes the slightly more difficult (but not too onerous, hopefully) part of simplifying it down. Let's...
  13. If a value "satisfies a cubic equation" means...

    If a value "satisfies a cubic equation" means that when you plug that value to the cubic, you get a true equation. So let's do that now.

    (1 + 4i)^3 + 5(1+ 4i)^2 + k(1 + 4i) + m = 0

    This should...
  14. You're probably going to feel real silly when you...

    You're probably going to feel real silly when you see it, but your answer and the book's answer are the same, just written differently. Consider your final answer in fractional form: \dfrac{6.75}{4}....
  15. Well, the fact that you got a 3x3 matrix for C is...

    Well, the fact that you got a 3x3 matrix for C is a good sign that you might be on the right track. However, without seeing your answer or any of the work leading up to it, it is impossible to...
  16. Suppose the White family has the following ages:...

    Suppose the White family has the following ages:


    Mr. White: 39
    Mrs. White: 37
    Son 1: 13
    Son 2: 7
    Son 3: 3
    Son 4: 1
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    Your conclusion that A and B must be square...

    Your conclusion that A and B must be square matrices of the same size is correct, although perhaps an easier way to get there would be to consider the problem itself. We're asked to find any cases...
  18. Assuming that you were given literally no...

    Assuming that you were given literally no information other than what you included in your post, and thus you don't know anything about the variable's distribution, you won't be able to get an exact...
  19. Well, if you're doubting your solution, you can...

    Well, if you're doubting your solution, you can always check it to see if it meets all of the criteria.



    Let's quickly remind ourselves of the definition of "degree" in this context. The degree...
  20. Unfortunately, nothing you did on #12 is correct....

    Unfortunately, nothing you did on #12 is correct. You appear to have just arbitrarily decided that the triangle is a 30-60-90 triangle, but this is not justified. Instead, return only to the given...
  21. Typically a good place to start with problems...

    Typically a good place to start with problems like these is just to write down every piece of information you're given and then see what else you can deduce. For instance, you might note that...
  22. It looks like the problem statement is written in...

    It looks like the problem statement is written in black, and your work is in red. So the problem statement is:

    \left(P \vee \neg(\neg(\neg Q)) \right) \equiv \left( \neg Q \wedge P \right)
    ...
  23. Hm. A very interesting math puzzle. At first I...

    Hm. A very interesting math puzzle. At first I was completely stymied and thought maybe the trick was that there wasn't an answer. But then I carefully re-read the problem and saw that f(n) is the...
  24. Here's a big hint that will take you almost all...

    Here's a big hint that will take you almost all of the way: -C is notational shorthand for (-1)C.
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    I definitely concur with Subhotosh Khan that it...

    I definitely concur with Subhotosh Khan that it "looks like gibberish," but here's some of what I think it means.

    \frac{9}{3} + 2\% - (x + y) + dx - dy \frac{9}{3} + 2\% - (x + y) + dx - dy \cdot...
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