Recent content by VietDao29

Hi Wildcat, Apart from the area method, there's still another way to tackle this problem. It's to use mid-segment of a triangle (it's the line segment that connects the two midpoints of any 2 sides of a triangle). There are 2 theorems about mid-segment you should remember is: Given \Delta ABC...

An identity is an equality that holds true for every value of the variable(s) in that equality. Example of an identity: sin2x + cos2x = 1. This equality holds true regardless of what value x takes. Try plugging in some random values for x to see. -------------------------- However, sin3x +...

Yes, I do. Can you show me your work, so that I can check it for you?

I think he's trying to derive the value of sin(θ), cos(θ), tan(θ), and cot(θ) using sin(2θ) = -8/17. Yes, this is true, if you have cos(2α), then finding sin(α), cos(α), tan(α), and cot(α) should be easy as a piece of cake, right? So the problem remains is, from sin(2α), how can you find...

There's one small error in your work: you assume that the limit does exist to apply L'Hopital's Rule, while the fact that this limit does exist, or not, is still unknown. @vrmuth: To solve these types of problem, we often divide both numerator, and denominator by x to the greatest power (in...

I did this problem by trial-and-error method. So here's how I would start. Firstly is to notice that there can only be two possible answers to this problem: + There's no such natural number. + If there happens to be some natural number a, which can be expressed as the sum of two cubes in two...

a - (b - c) = a - b + c. Or in general, if there's a plus sign in front of a pair of parentheses, then you don't have to change the sign of each elements in those prentheses. But if it's a minus sign, then you have to change the sign of every element in those parentheses. Like this: a + (b -...

No, that isn't enough, since the problem asks you to find N (\epsilon), such that: n > N ( \epsilon ) \Rightarrow |a_n - 1| < \epsilon Showing that \lim a_n = 1, doesn't have anything to do with pointing out the value N (\epsilon) the problem requires. They are 2 (quite) distinct processes. In...

Yes, that's correct. The CDF is the integral: F(x, \mu, \sigma^2) = \int \limits_{-\infty} ^ x f(t, \mu, \sigma^2)dt = \Phi \left( \frac{x - \mu}{\sigma} \right) = \frac{1}{2} \left( 1 + \mbox{erf} \left( \frac{x - \mu}{\sqrt{2}\sigma} \right) \right) There should be some table of value...

You had like 10 seconds to think about that. Yes, but did you mention that in the first post? How are we supposed to know that you did have 10 seconds to make that guess? And one more thing, didn't you think about that problem after the test? If you did, then it was not true that you only had...

If you interpret the problem to ask for the probability for each set of chit to have at least one number to be 5, and no number less than 5, then your result is correct. But looking at the problem, I think it asks for the probability such that each number in the set is no less than 5: "The...

Yup, that's correct. Congratulations. :) But, remember that F_S(x) = 0.2\sqrt{x} on the interval (0; 25), it takes other values elsewhere.

No, why are you squaring F(x)? To handle this type of problem, we often try to find the cdf of S first, then (if the problem asks further for pdf function) we can obtain it by differentiating the cdf of S. So, it goes like this: \begin{align*}F_S(x) = P(S \le x) = P(X^2 \le x) &= \left\{...

Imageshack is changing some of their policies. Can you move to another host like Photobucket or something along the line? To tell the truth, I cannot see your image. :(

Often, we often write "greater or equal to" sign (\ge) like this >=, to distinguish it from the "imply" sign (\Rightarrow). Well, you can think of (a + b)2, right? So what about (a - b)2? To solve the first part of this problem, you should also note that: the square of any real number is always...