District 2

[mathmajor]

I have a confusing question on the math test from District 2.

Cy Phy's physics class is trying to determine the magnitude of the sum if two forces, 220 and 180 lb, act on an object at an angle of 46 degrees. What is the magnitude of their sum? (Nearest lb)

[88bobcat]

[AuSmith]

[Kenon]

After thinking this over a ton, I can't help but go "huh". I think, though, after looking at the problem, the key is the word magnitude. One force acts up on it, and the other as AuSmith goes with it. The key here, though, is that the answer wants the magnitude of the resulting force vector.

Bobcat shows the right approach mathematically. The only thing is... the question is insanely confusing, especially if you know physics. Thinking logically kinda screws it up here.

[88bobcat]

[AuSmith]

Ya, I can't even recall how that made sense to me a few hours ago. I apparently forgot about the perpendicular component... and of course law of cosines works. Sorry, Bob.

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[datnguyen160]

Here are my questions from the district 2 test:
15. How many ways can a father, mother, son, and daughter be seated around a circular table with 4 chairs? 6. 10. 12. 18. or 24.

Well... this is going to be embarrassing to ask, but what's the difference between nPr, and nCr? How do I know what situation to use which one of them?

45. James the butler was offered a job for $8000 and a new car for a year of service. James quit after 7 months of service. he was given the car and $1600 for the 7 months of service. What was the dollar value of the car? 6400. 7200. 7360. 8000. 15360.
wordy, confusing problem?

Matrix problem: how do i find A^(-1), for A is a matrix? Isn't it the inverse of A?

Oh, also this one (I may be retarded for not knowing how to set up this problem):
4. Distance from A to B is 545 miles. Object 1 is leaving A toward B at 80mph. Object 2 is leaving B toward A at 65mph. How much farther will object 1 have driven than object 2 when they meet? 56. 73. 15. 45. 36.

[Kenon]

Ok, for 15 you asked what nPr and nCr is. I'll explain.

nPr is a Permutation. nCr is a Combination.

nPr basically says order matters. nCr is basically stating order doesn't matter.

Now, in 15, its important to diagnose what they mean by how many ways. The key here comes down to "I can rotate the view and see it as a different way". Oh snap, that actually throws some problems in it. We basically then don't care anything about position, but about the order. DID SOMEONE SAY PERMUTATION?

Too lazy to work it out.

(The answer's 6, right?)

45. Ok, so he worked for 7/12 months and got paid 1600+car/8000+car. So what we do here is that we detect how much money he would have earned in the 5 months (6400) and determine how much the car was worth based upon that. Pretty simple, really. Take the 1600 and divide it by 6400/5 and that is how many months you got that money in. 6.25 months are required for $8000. Thus the car was worth 5.75 months of the total working period. I figure you can work it from there easily.

Matrix. The inverse of a matrix is filled with the values required to make it equal the identity matrix. It is the inverse of A. I just use the calc for that.

4. Simple. Find the time it takes for them to hit each other, then take that time and find the difference between the speeds and multiply it by that time!