Recent content by ivybond

I am sorry I failed to mention that this question was given in the Algebra 2 class to somebody I know. Using vectors is the fastest way to go (I did not check my answer though :redface: ), but I don't think they covered it in the class. Thanks anyway!

Question: Find the area of triangle ABC that has the coordinates A(1, 3, 0), B(0, 2, 5), and C(-1, 0, 2). ------------------- One way to do that is to find the lengths of ABC sides and use Heron's formula. Not pretty nymbers! You can find the distance h between C and AB. Area A(ABC) =...

Triangle ABC is equalateral according to the lemma, and so is triangle A_1 B_1 C_1 by constructing. P.S. This problem (and another one you posted on the Calculus forum) strikes me as an olympiad kind. Where did you get them? Art of Problem Solving is probably a better place to get help...

I have not proven this lemma (it'll be your contribution): If pont D is a fixed distance from the ABC plane, SA is min when triangle ABC is equalateral and point D projects onto its center. ======================= Projection of the inscribed sphere S onto the ABC plane is a circle with center...

http://www.csulb.edu/~acaproj/Spring98/uchida.html

You don't need to "get the intersecting points of the two graphs", you want to find their number. Helpful apprach - solve an easier problem first: how many points of intersection do these graphs have y=4 sin(x) and y=x / 25 ? Graph "by hand" and see the pattern.

Hey, upon further research (and splitting the "splits"), I found that "either of a and b" is a legitimate expression: it does mean either a, or b, or both (like in OR operator in Boolean logic)!:approve: In r = \frac {p}{2^a 5^b} either of three scenarious (a=0, b=0, both a=0 and b=0) is...

Stand corrected, sorry. Actually, I changed my post before seeing yours having realized my mistake.:redface:

Splitting hairs I think either of a and b is more precise, and p does not have to be prime.

harmonic mean could be calculated slightly easier: \frac{v_1 v_2}{\frac{v_1 + v_2}{2}}

My favorite word: VISUALIZE. For generic inequality f(x) > g(x): h(x) = f(x) - g(x). Find the intervals where a graph y=h(x) is above the x-axis (you'll have to find/estimate the roots of the y=h(x) and points where h(x) is undetermined). Try \frac{x+2}{x}\leq \frac{1}{2-x} Could you post...

x = \frac \pi {10} 3x = \frac \pi {2} - 2x

Yes, that's right. Start working with the smaller numbers and make a list of subsets, number of which you are asked to find. (I showed a partial list for one example). It's too bad your teacher did not write any comments or suggestions. Maybe you could find some book with a concise...

Let's deal with the easier one first. Is the order in which you answer questions important? In other words, is answering questions A, B, C the same as C, B, A? I hope I understand the question right and rephrase is correctly: How many ways are there to choose a set of three letters out of a...

Reducing numbers often helps. Try solving a "smaller" question first, listing all possible arrangements first, and comparing their number to one you calculated. -------------- You are taking a test with 5 questions A, B, C, D, E, you only have to answer 3, how many ways are there to do it...