understanding

1. Help understanding this proof: E is a subset of f^(-1)(f(E))

\text{Let } f: X\rightarrow Y, \text{ where } X \text{ and } Y \text{ are sets.} \text{Prove that }E \subseteq f^{-1}(f(E)) \text{ } \forall E \subseteq X. PROOF: \text{Let } x \in E. \text{Then, }y = f(x) \in f(E), \text{ so } x \in f^{-1}(f(E)). \text{ Hence } E \subseteq f^{-1}(f(E)) How...
2. Clarification to improve my understanding

I was given this question to do; Find the ranges of values of k for which the equation x^2 +(k-3)x +k = 0 has roots of the same sign I have been able to do it with help. I was advised to use b > \sqrt{b^2 - 4ac} > 0 and b < - \sqrt{b^2 - 4ac} < 0 to solve it. Also, i was told...
3. Understanding point processes

Hi everyone I'm using a 3D design software and I want to fill a 3D space (a cube) using different point processes, other than the Poisson point process, but I'm having a hard time understanding how to construct them. The link below, starting at page 28, describes two Neyman Scott processes...
4. Difficulty understanding a problem.... HELP

The Problem is... N(t)=(200000)/[1+999e^(-0.4t)] Use logarithmic differentiation to find the time to the point of inflection. I know that in order to find the point of inflection I must set the second derivative equal to 0. And I believe I have solved for the first derivative, but I need...
5. A problem I am having difficultly understanding...

Having trouble with this whole question. A line by line breakdown would be very appreciated <3
6. Understanding an Equivalence Relation proof

Hey guys, I asked this question before but now I got the answer from my prof, but I don't really get the answer. A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c (mod 2) and b = d (mod 3) Here's what I don't get: From the definition, isn't reflexive (x, x)...
7. Not understanding the physics difference between first moment and second moment.

I know the second moment is known as the moment of inertia, and the first moment is used to find the centroid, but I'm not quite sure if I understand the conceptual understanding of the moments themselves. Here is what I think: The first moment respect so some axis is the average weighted...
8. Understanding the formula for 'Whole-organism metabolic rate'

Hi guys, I'm doing a PhD in Media Arts with the aim of create virtual worlds inspired by the closed systems inherent in metabolic ecology. I'm not great at math, so I'm having trouble understanding how to use these formulas. If someone could help me understand these formulas, it would be...
9. Help understanding formula

Im not used with 2 sums and having problem with bernoulli numbers. This is the formula : https://upload.wikimedia.org/math/2/5/8/2584486d5134ca1e52bb0b6a806a4a3a.png If n = 0 then: 1/(0+1) * ((-1)^0 * (0+1)^0 * choose(0,0)) If n = 1 ((1/(0+1)+(1/1+1)) * ((-1)^0 *...
10. Understanding Arithmetic and Geometric series, help?

Below are a few examples i pulled from by book, i was wondering if i could get some help with so i can have a better understanding on how to solve the rest. 8+3-2-7-12-....-87 1a) What Kind of series is this? Arithmetic, Geometric, or Neither? Why? 1b) Use the appropriate formula to find...
11. Learning to Think Mathematically

I'm in High School, and in studying for the ACT Math exam, I discovered that the secret to doing well on it is not simply to know the Math, but to understand the Math. For example, if you know how to solve an equation, but you don't readily think of what the next step could be to simply an...
12. Expanding Logarithmic Expressions. Not Understanding This One.

I was working through a logarithm packet for practice and I got this one: log3(9x3)1/5 ,where 9x3 to the 1/5 is 9x3 root 5 (I think 1/5 is equal to radical 5, correct me if I'm wrong (Itwasntme)). After expanding, I got 1/5(2log3(3)+3log3(x)) However, the...
13. Need Help understanding a portion of this Probability Problem

What is the probability of getting a total of 7 or a total of 11 when a pair of fair dice is tossed? [My SOLN] A = { (1,6), (2,5), (3,4), (6,1), (5,2), (4,3) }, 6 possible outcomes B = { (6,5), (5,6) }, 2 possible outcomes P(A) = 1/6, P(B) = 1/2, [Now in my book it says that P(B) =...
14. understanding Kakuktani’s fixed point theorm problem

I have an exercise as part of game theory that requires that I understand what compactness means. Kakuktani’s theorm as stated in my text says Let X be a compact convex subset of R^n and let f:X->X be a set-valued function for which all x in X the set f(x) is non-empty and convex AND the...
15. Need help understanding the following question

Indicate which of the following statements are true and which are false, justify your answers as best you can. a.Every integer is a real number. I answered that as true, because every whole numbers are considered real numbers, i think. b. 0 is a postive real number. I answered...
16. Understanding mutual independance

My book has this example that i'm trying to understand. If possible, I want explained how the conclusion is reached, as my intuition is incorrect. Mutually independent states collection of events, A1, A2, . . . , An, any subcollection, Ai1, . . . , Aim , P(Ai1∩ · · · ∩ Aim ) = P(Ai1 ) · · ·...
17. Understanding Set Proofs

No need in solving the problem, although I wouldn't mind, but I need some help understanding the symbols and such. I have this. A ⊆ B ^ A ⊆ C => A = ∅v (B ∩ C =! ∅) (same as picture) I understand the first half, but not the second. What does => mean? And what am I supposed to do with...
18. Help with understanding distance rate problem.

Here is a distance rate problem I found on the web which I've solved but have a question about. "2 cyclists begin at the same place and at the same time on a circular track travelling in the same direction. One is travelling 3mph faster than the other and he "laps" the slower cyclist at the...
19. Help understanding Altimeter topic

On wikipedia here is a topic about Radar Altimeter: https://en.wikipedia.org/wiki/Radar_altimeter There's a bit that I don't understand. I don't get how exactly this: becomes this: Same thing with this: any help?
20. Not understanding Logarithms.

1st problem. log2^(2x-1)=32 so then i make it log2^2x-1=2^5 so then i do 2x-1=2 and then x= 3/2 but that doesnt solidify the statement? Because x has to be 3 that is what I put on the answer for my exam. Also log4(8x-16)=3 I had no idea how to do this on the final exam... the teacher...