2008 Regional

[redhawk2015]

Some questions.

6. If [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] then [unparseable or potentially dangerous latex formula]

13. Flight 123 flies 789 km from Sumwear Airport to Ennywear Airport on a bearing of 160 degrees. Flight 456 flies 789 km on a bearing of 290 degrees from Ennywear Airport to Nowear Airport. What bearing will flight 456 have to fly from Nowear directly to Ennywear?

17. The vertical asymptote and the oblique asymptote of [unparseable or potentially dangerous latex formula] intersect at point [unparseable or potentially dangerous latex formula]. Find the value of [unparseable or potentially dangerous latex formula].

Got as far as figuring out it was negative something by graphing, but didn't know where to go from there.

39. How many points of intersection occur when [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are graphed on a polar coordinate system?

Always miss the questions about polar coordinates. Any other info about them would be helpful.

42. Find the angle of rotation, [unparseable or potentially dangerous latex formula], (nearest degree), where [unparseable or potentially dangerous latex formula], such that the conic [unparseable or potentially dangerous latex formula] contains no [unparseable or potentially dangerous latex formula] term in its equation.

Is there a general procedure for solving these kinds of questions?

58. If [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], then [unparseable or potentially dangerous latex formula]

Again, is there a general method for solving these?

60. Tuff Teff has a dozen identical jawbreakers. How many ways can he put them into 6 bags such that each bag has at least 1 jawbreaker in it?

Thanks.

[Salvadoramerican]

6) remember [unparseable or potentially dangerous latex formula] so then [unparseable or potentially dangerous latex formula] now just do some plugging in

17) the verticle asymptote is x=-2 so find the slant one and insert x=-2 the slant is found doing long division and ignoring any extra

42) angle of rotation is found using [unparseable or potentially dangerous latex formula]

60) its [unparseable or potentially dangerous latex formula] its hard to explain but think of it this way their is 12 jawbrakers so place a space between all of them their are eleven spaces then their are 5 jawbreakers left over that can place in any of the eleven spaces. Its confusing but i hope it works

[nsguy1350]

6. Basic trick in NS as well.[unparseable or potentially dangerous latex formula]. This gives you 216 - 108 = 108.

13. Bearing = add 90 degrees.
[unparseable or potentially dangerous latex formula].
Use trig to find the angle after you find that.

17. The vertical asymptote is [unparseable or potentially dangerous latex formula]. The oblique asymptote can be found through long division or the polynomials, or, since you're dividing by a linear term, synthetic substitution.
[unparseable or potentially dangerous latex formula], I believe. I did that mentally, so that may not be correct. A check on my 89 confirms, so yes, that is correct.

Plug in x = 2 into x - 3 (ignore the [unparseable or potentially dangerous latex formula] term, it's not part of the oblique asymptote) to get -1. That is your y.

39. Graphing the polar graphs gives 3 intersection points, at many angle values. This is a four-petaled rose I believe, so you'll have points at x = 2, -2, and 0 on the rectangular coordinate system.
[unparseable or potentially dangerous latex formula] is just y = 0.

42. I believe you use the formula [unparseable or potentially dangerous latex formula], where A, B, and C are the coefficients of the [unparseable or potentially dangerous latex formula] terms, respectively. Not 100% sure on this, but I think this problem has been discontinued, anyways.

58. Basic calculus. You have to integrate and use plug in to solve for the constant of integration. Also, you can make the \prime in LaTeX look better by putting the carat (^) before it.
[unparseable or potentially dangerous latex formula]. Plugging in [unparseable or potentially dangerous latex formula], you get that [unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula].
Then, you must integrate again.
[unparseable or potentially dangerous latex formula].
Hmm.. did you forget the initial condition for f? You need to get rid of that pesky constant of integration, and you cannot without an initial condition.

60. I'm not sure, but I'd say this could work.
You can pick 6 out of the 12 jawbreakers to put in each bag, first. 12C6 = 924, so that's your first number,
Then, you have 6 choices for each remaining gumball, so [unparseable or potentially dangerous latex formula]? 43110144 choices? I'm not sure, again, but possibly, that might be it.

[Salvadoramerican]

I should've done NS

[redhawk2015]

Sorry nsguy...the question was wrong. It should be:

58. If [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula], and [unparseable or potentially dangerous latex formula], then [unparseable or potentially dangerous latex formula]

[Salvadoramerican]

Basicaaly what NSguy did is the same method to solve this but when its 3 so then [unparseable or potentially dangerous latex formula] where C=-5 then differentuate to [unparseable or potentially dangerous latex formula] where C=2. Solve from their

[Salvadoramerican]

NSguy explain number 13 i don't understand your method, normally i would use law of cosine to solve these kind of questions

[nsguy1350]

Law of Cosines works fine, maybe even better in this situation. Yea, you should probably go with that instead.
Alright, to finish 58,

[unparseable or potentially dangerous latex formula], Plugging in [unparseable or potentially dangerous latex formula],
[unparseable or potentially dangerous latex formula].
Then, you plug in [unparseable or potentially dangerous latex formula] to get [unparseable or potentially dangerous latex formula].

I usually NS these questions, so if you see a Math mistake, correct me please.