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Type: Posts; User: ksdhart2

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1. ## Thread: Help finding limit (somewhat urgent)

by ksdhart2
Replies
1
Views
63

### The trouble with multivariable limits is that...

The trouble with multivariable limits is that there are literally infinitely many paths one can take to approach the limit point. Showing that a given limit exists means finding a systematic proof to...
2. ## Thread: T substitution: Why is the derivative of sinx in terms of t NOT cos x in terms of t?

by ksdhart2
Replies
8
Views
135

### Whoops! Yes, I missed a minus sign out front of...

Whoops! Yes, I missed a minus sign out front of the whole thing. It should really be -\dfrac{2(t^2-1)}{(1+t^2)^2}. Flipping the order of the terms in the numerator would achieve the same effect....
3. ## Thread: T substitution: Why is the derivative of sinx in terms of t NOT cos x in terms of t?

by ksdhart2
Replies
8
Views
135

### The catch is that you've changed the variable....

The catch is that you've changed the variable. It's true that \dfrac{d(sin(x))}{dx} = \dfrac{d}{dx} \left( \dfrac{2t}{1+t^2} \right) = \dfrac{1-t^2}{1+t^2} = cos(x). However, \dfrac{d(sin(x))}{dt} =...
4. ## Thread: Probability using cards

by ksdhart2
Replies
4
Views
77

### Personally, I think the question is a bit poorly...

Personally, I think the question is a bit poorly written and ambiguous. If we interpret it to mean "Find the probability that a card drawn at random will be both red and black," then you're correct...

by ksdhart2
Replies
3
Views
115

6. ## Thread: finding the ratio of students in one class to another using average test scores

by ksdhart2
Replies
3
Views
87

### Very good! The only minor criticism I have is...

Very good! The only minor criticism I have is that you're missing some grouping symbols. For now, it's clear what you meant from context, but in the future it may not be as clear and could result in...
7. ## Thread: Geometric Sum Question

by ksdhart2
Replies
3
Views
240

### Oh, hey, sorry about the delay. For some reason I...

Oh, hey, sorry about the delay. For some reason I didn't get notified of your response. If I hadn't happened to manually check out of curiosity, it may have gone forever unnoticed. I'll have to...
8. ## Thread: Geometric Sum Question

by ksdhart2
Replies
3
Views
240

### Well, you say you can't reproduce the answer,...

Well, you say you can't reproduce the answer, which directly implies you've tried at least one method. That's excellent! Trying things is usually the best way to learn. Unfortunately, we cannot...
9. ## Thread: Trying to Understand Logarithm Property: Prove e^{ln(x)} = x

by ksdhart2
Replies
2
Views
137

### A good place to start is to refresh yourself with...

A good place to start is to refresh yourself with the definition of logarithm. The definition means that if b^y=x then log_{b}(y)=x. Perhaps consider a few concrete examples. 2^3 = 8 implies that...
10. ## Thread: lim [x->2^+] [8/(x^2 - 4) - x/(x - 2)]: tried multiplying common denom's, then....

by ksdhart2
Replies
8
Views
301

### Everything you did is fine, up to this point: ...

Everything you did is fine, up to this point:

\dfrac{8(x-2)-x(x^2-4)}{(x^2-4)(x-2)}

In the next step, you made an error when expanding the denominator. This is what you should have gotten:
...
11. ## Thread: Finding the Min and Max of a range when I know the 25th, 50th, and 75th Percentiles

by ksdhart2
Replies
1
Views
107

### Unfortunately, what you're seeking is not...

Unfortunately, what you're seeking is not possible. Consider the data set {118, 119, 119, 137, 137, 137, 140, 140, 140, 155, 155, 160, 160, 173, 173, 173, 191, 191, 200}. This meets all of your...
12. ## Thread: Discrete Math: In how many ways can 30 ident. balls be put in 7 distinct boxes, s.t.

by ksdhart2
Replies
13
Views
635

### Oh dear. I seem to have majorly messed up here....

Oh dear. I seem to have majorly messed up here. Sorry about that. Upon further reflection I see now that my proposed solution of 730 would only be valid if the balls were in some way distinguishable...
13. ## Thread: Discrete Math: In how many ways can 30 ident. balls be put in 7 distinct boxes, s.t.

by ksdhart2
Replies
13
Views
635

### It's not immediately obvious what you mean by...

It's not immediately obvious what you mean by "1st one," but I'll guess that you probably mean part (1a). Assuming that's the case, your proposed answer is not correct. Since you've not shown any...

by ksdhart2
Replies
1
Views
206

### Those sure are some very nice homework problems...

Those sure are some very nice homework problems you have there. But what are your thoughts? What have you tried? Please re-read the Read Before Posting thread that's stickied at the top of each...
15. ## Thread: unique value dice probability

by ksdhart2
Replies
5
Views
306

### From my perspective, it looks like your main...

From my perspective, it looks like your main problem isn't really that you're "bad at probability" or even bad at math. Rather, the problem is that you don't have a clearly defined problem. I'll be...
16. ## Thread: dollar and cent coins were mixed up. banker needs help!

by ksdhart2
Replies
7
Views
462

### Your only flaw here is that you've subjected...

Your only flaw here is that you've subjected yourself to rounding errors. 199/98 is not exactly equal to 2.03061224, and neither is 5/98 exactly equal to 0.05263158. As far as I can tell, there's no...
17. ## Thread: Simplify trig expressions: cos-1(cos(47pi/12), arcsin(tan(-pi/6)), csc-1(cos(2017pi/2

by ksdhart2
Replies
2
Views
259

### Those sure are some very nice homework problems...

Those sure are some very nice homework problems you have there. But given that this is a tutoring website (note that the name is "Free Math Help," not "Free Homework Solutions" :p), we'd like to see...
18. ## Thread: Question about probability: Peta deals with a hand of 10 cards...

by ksdhart2
Replies
2
Views
244

### The reason why you can't use the binomial formula...

The reason why you can't use the binomial formula here is that it only works if the probability of each event is constant. That's not the case here. You've correctly identified that the probability...
19. ## Thread: Compute number of distinct divisors of 98000 = 2^4 * 5^3 * 7^2.

by ksdhart2
Replies
4
Views
789

### Often times when I'm stuck on a math problem, I...

Often times when I'm stuck on a math problem, I find it immensely helpful to consider a smaller/simpler version of the problem, to help me get a feel for what's going on. Then I can attempt to scale...
20. ## Thread: how to explain why ax = bx will always have at least one solution?

by ksdhart2
Replies
2
Views
209

### Truthfully, I'm not really sure what more you...

Truthfully, I'm not really sure what more you want in order to consider it a "professional" solution/explanation. The problem asks you to explain why there's at least one solution, and you've done...
21. ## Thread: Need help finding the rule to this pattern: 3, 4, 3, 4, 5, 3, 4, 5, _, _, _, _, _, 7

by ksdhart2
Replies
5
Views
613

### It seems to me like all of your work so far has...

It seems to me like all of your work so far has been focused solely on trying to find a common difference between the terms, to which end you've discovered there doesn't appear to be any such...
22. ## Thread: Tangents and the Derivative of V=(4/3)* π * r^3 at a point (r = 4)

by ksdhart2
Replies
9
Views
550

### What you've done so far is fine, and if you...

What you've done so far is fine, and if you continue to simplify and evaluate the limit you will get the correct answer. But I think it would be way easier to differentiate first, and then plug in...
23. ## Thread: find x if the numbes 3-x, x, and 1-3x form an arithmetic sequence.

by ksdhart2
Replies
7
Views
397

### Actually, Denis, the problem text specifically...

Actually, Denis, the problem text specifically instructed OP to "find x," directly implying that they were meant to come up with a numerical solution rather than an expression in x.
24. ## Thread: find x if the numbes 3-x, x, and 1-3x form an arithmetic sequence.

by ksdhart2
Replies
7
Views
397

### I can infer from context that you've not shown...

I can infer from context that you've not shown any work because you're stuck at the very beginning and have none to show. That's perfectly alright. The key words to pick out of the problem text are...
25. ## Thread: 100 animals 100dollars

by ksdhart2
Replies
10
Views
675

### As it turns out, there's four unique solutions to...

As it turns out, there's four unique solutions to this problem. You identified one such solution, which should suffice (although I have seen teachers refuse to accept any answer except their...
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