# Search results

1. ### Combinatorial Probmlem

Hi, I was reading a models book and read about a study where 9 analysts were chosen at random. Out of this group, 3 were selected for 2 week training, 3 were selected for 3 week training, and 3 were selected for 5 week training. Now I believe this models course had the idea that the first...
2. ### I have variance of response. How can I find it's MSE?

To All, I did a study and my response is defined as y = b1x1 + b2x2 + e where e ~N(0,1). I have y~N(4,33). In my data results, I did an ordinary least squares regression model for y = b1x1+b2x2+ e. The ANOVA is telling me the mean of y is 4, but MSE is 1. So here is my question. If I...
3. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

Please help me prove this. I worked hard to make my notation somewhat easy to follow: If gcd ( ord_n(a) , ord_n(b) ) = 1 , then ord_n(a*b) = ord_n(a) * ord_n(b) Attempted proof: I can't see how to use the gcd condition. Which is bad news. I do realize the following. Let k1 =...
4. ### Show integrable is uniformly continuous

H = [a,b]\times[c,d] . f:H\rightarrowR is continuous, and g:[a,b]\rightarrowR is integrable. Prove that F(y) = \intg(x)f(x,y)dx from a to b is uniformly continuous. I initially ripped g(x) and f(x,y) apart and tried to show each was continuous. This failed. In short, I am...
5. ### Help me evaluate this limit

[SOLVED] Help me evaluate this limit Part a: Show that f(x,y) = \frac{x^{4}+y^{4}}{x^{2}+y^{2}} as (x,y) -> (0,0) Part b: Similarily, show that f(x,y) = \frac{\sqrt{\left|xy\right|}}{\sqrt[3]{x^{2}+y^{2}}} as (x,y)->(0,0) Lets work with Part a, shall we? I seemed to be...
6. ### 4 by 4 Inverse Matrix

Inquiry: Is there a standard equation for a 4 by 4 inverse? I know that one exists for 3 by 3, 2 by 2, but I cannot find one in my text nor in my searches online. I know I could find one by using the Jordan-Gaussian Method. But, I would be more comfortable with knowing a 4 by 4 general...
7. ### Can you help me evaluate this limit?

[SOLVED] Can you help me evaluate this limit? lim k -\sqrt{k^{2}+k} as k\rightarrow\infty I have evaluated the limit using computer technology and I know it should be -1/2. I have tried using something like the squeeze theorem but failed. My other attempt is to mutiply the limit by...
8. ### Prove ||B(x,y)|| = ||(x,y)|| for all x,y in R^2 (Rotations in R^2)

B = [cos\theta -sin\theta] ......[sin\theta cos\theta] for some \theta in R^{2}. (a) Prove that || B(x,y) || = || (x,y) || for all (x,y)\inR^{2} Question: What does B(x,y) and (x,y) notation mean? I have a result that says Let B=[b_{ij}] be an mxn matrix whose entries...
9. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

Question: Find two lines in R^{3} that are not parallel but do not intersect. My Thoughts: I have never seen this type of question before and the material in my text is unfortunately lacking. However, I was able to piece these thoughts together. The cross product of three vectors...
10. ### Show the angle between phi(t1)-phi(t0) is 0 or pi

Let a,b\inR^{m}, b\neq0 and set \phi(t)=a+tb. We must show that the angle between \phi(t_{1})-\phi(t_{0}) and \phi(t_{2})-\phi(t_{0}) is 0 or \pi for any t_{0},t_{1},t_{2},\inR with t_{1},t_{2}\neq. The 0,1, and 2 are supposed to be subscripts next to t, but my Latex is showing is as...
11. ### Find function is analytic on R and has Maclaurin expansion

Prove the function is analytic on R and find its Maclaurin expansion. (a) e^{x}cosx Well, I did some work. I can show that e^{x}=\sumx^{k}/k! cosx=\sum((-1)^{k}x^{2k})/(2k)! are analytic and have the above Maclaurin expression. My problem is multiplying these two...
12. ### Positive Radius of Convergence

Problem: Suppose that {a_{k}}^{\infty}_{k=0} is a bounded sequence of real numbers. Show that \suma_{k}x^{k} has a positive radius of convergence. Work: I have attempted to use the ratio test and failed. I am suspicious I can try the root test, but I am not sure how to work it...