Applied Mathematics

Can i just check if i have done this question right? Question:............ "Suppose that a linear transformation T is defined by a 4×5 matrix. Can T to be one to one? Can T be onto? Give reasons for your answers." This is my answer:............. Let the 4x5 matrix that defines transformation T be: A = [# * * * *] [* # * * *] [* * # * *] [* * * # *] #'s indeicate some possible pivot positions for the transformation T to be one to one, the columns oof matrix A have to be lineraly independent (by a particular therom). That is T is one to one iff Ax=0 has only the trvial solution. However, because there will alwa…

hows this.... 7a) Since the vectors are not multiples of eachother therefore they are linearly independent. b) it must be a linear combination of the two vectors. and the condition b4 - b1 = 0 has to hold. so am i completely wrong? :S Sarah

I cannot get my head around the following problem: An irregular six face die is thrown and the probability that in twenty throws it will give five even numbers is twice the probability that it will give five odd numbers, i.e.: P(5 even numbers is 20 throws) =2P(5 odd numbers in 20 throws) =2P(15 even numbers in 20 throws). How many times in 10000 sets of 10 throws would you expect it to give no even number? [Hint ] I do not fully understand it I think they are looking for a rnadom variable with a binomial distribution. Also I am A bit condused by P(5 even numbers is 20 throws) is that is maybe a typo and its su…

I am interested in modeling a photon as a particle that can accelerate, but I am not sure about where to begin. What I have been doing is this. I first define the position of the photon's center of inertia in a frame as follows: [math] \vec r = x \hat i + y \hat j + z \hat k [/math] Then velocity as follows: [math] \vec v = \frac{d\vec r}{dt} [/math] Now the magnitude of the photon's velocity is its speed in the frame. So this is a theory of a variable speed of light. I use the following formula for the speed of a photon in a frame: [math] |\vec v | = f \lambda [/math] I am not sure how to interpret photon frequency just yet, and ph…

For two events [math]A_1[/math] and [math]A_2[/math], if [math]A_1 \cap A_2 = \emptyset[/math] then we say that [math]A_1[/math] and [math]A_2[/math] are disjoint. Does disjointedness differ to mutual exclusiveness? Are they both the same or are they different?

This is from economics but it's mainly a math problem I'm dealing with. In this economic model we are dealing with two goods, textiles T and electronics E and two countries China C and Japan J. The lecturer put the images below up. The first image is a graph of the goods price ratio to the goods ratio. These is the relative supply curve. The countries are initially in autarky and after free trade both country J and country C move towards the world relative supply [math]RS^W[/math]. The second image below is the production possibilities frontier of country J, a graph of textile output to electronics output. What I want to know is whether the J and…

hey for this question i get A = [2/3, -4/3] [-1/3, 8/3] but is that the "Standard matrix for the linear transformation of T"? or are 'Standard' ones , ones which resemble an identity matrix? Cheers Sarah

hey just a query about this question.... for part c where it asks if it is wise to check if w in a lin. combination of the other vectors. well i suppose the answer is no, but if you check if v was a lin. combination of the other, then if u was a lin. combination of the others and then if z was a lin. combination of the others (which i think is the case for this problem) then you would be able to say whether of not the set is linearly dependent or not. what do peoples think? Cheers Sarah

Some of you have seen the formula for arc length: [math] S = R \theta [/math] Suppose that I have chosen my unit of distance to be the meter, and I have a rigid meterstick. Suppose, i have learned this: If I take a rope, and make a circle with radius one meter, that when I straighten out the rope, the length of the rope is greater than six meters, but less than seven meters. I can simply see that it is greater. Ok so, I then formulate the following question, which I now want answered: Suppose I use a compass, and describe a circle with radius one meter. As the arc length is slowly made in the sand, it gets longer and longer. I want to know wh…

I had this really easy Conditional Probability problem in class the other day but for some reason I just could not do it. I could not define the events properly and even though the answer is of no use to me now it has really been bothering me lately, so I was wondering if anyone could help me out? It went something like this: A short sighted man likes to throw a basketball at a hoop in his yard but he has rely on his son to report if he scored. The probability that he scores a goal is 0,6 and the probability that his son reports it correctly 0,8. If his son reports that the father has made a goal, what is the probability that he actually did so?

Ok i've attatched the shapes. Now what that is, is a square with 4 1/4 circles going through it. The aim is to find the shaded area and we know that the sides of the square are 10cm. Good Luck.

I'm sure its vry simple question but for sum reason I just cant solve it. 6cosx+5tanx=0 where x is equal or less than 2pie and equal or greater to -pie 3sinx-2cosx=0 then sinx/cosx=2/3, cosx can't =0 how can u move the sin's and cos's in one step like that and wt if it wz 3sinx+2cosx=0 then wt wd the eqn b? Cud ne1 give me sum pointers on how to solve identities, i seem to be having sum problems with them. Ne help wud b much appreciated. Thx.

Toss a die twice and take the sums. Let A be the event that the sum of the two numbers rolled is 6. Let B be the event that you roll a 6 on the first roll. Is there a negative relationship between A and B? I believe there is, but I'd like to have my working checked out. [math]AB = \emptyset[/math] and therefore [math]P(AB)=0[/math]. [math]A = \{(1,5), (2,4), (3,3), (4,2), (1,5)\}[/math] and therefore [math]P(A)=\frac{5}{36}[/math] [math]B = \{(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}[/math] and therefore [math]P(B)=\frac{6}{36}=\frac{1}{6}[/math] [math]P(AB) < P(A)P(B)[/math] [math]\frac{P(AB)}{P(B)}=P(A)[/math] [math]P(A|B) < P(A)[/math…

To calculate the angle of view in a pinhole camera the formula: [MATH]\theta = 2 tan^{-1}\frac{h}{2d}[/MATH] where: theta is the angle of view h is the height of the camera d is the depth of the camera To help visualize this, I will try some ASCII art showing the camera... y axis ______________ | | h | | |-------------|------------ z axis | | |_____________| d If you draw a line from the top left of the camera through the intersection of y and z and draw a line from the bottom left of the camera through the intersection of y and z the angle between these two lines (on the +z side)…

[math]x=\frac{m}{2p_{x}}[/math] and [math]x^{h}=\sqrt{u\frac{p_{y}}{p_{x}}}[/math]. How do I show that [math]\frac{\partial{x}}{\partial{p_{x}}}=\frac{\partial{x^{h}}}{\partial{p_{x}}}-\frac{\partial{x}}{\partial{m}}x[/math]?

Suppose that I have two particles in vacuum, and there is only one interaction force between them, and that force is a central force. Assume that at the beginning of time, the particles are a distance R apart, but are being pulled together by this one superforce S. How can I get the particles to orbit one another. Won't they just head right for the center of mass of the universe, collide, and then reflect or something in linear motion rather than circular motion? Put another way, exactly how does a central force end up making things orbit the center of mass. Regards

There is a semi-circle with diameter XY. Rectange PQRS is inscribed in the semi-circle with PQ=12 and QR=28. Square STUV has T on RS, U on the semi-circle and V on XY. The area of STUV is closest to.... Answer is 16. I just want to know steps to come up to this answer. I made a drawing on paint, it dznt look xactly like the one I have but it shd give u guyz and idea of the question. If someone can show me steps to get to this answer it wd b helpful alot. Thx.

Yeah, I was reading through my math book one day voluntarily, which is quite a surprise, and noticed an assignment that told you to draw a four (or was it five?) dimensional hypercube. So errr... What do they look like? And what about if it has five dimensions? And how do you add a dimension to a shape? The book had some minor explanations but I didn't quite get them.

Suppose you have a nine out of nine chance to be hit in the head by a flying hippo today, is it possible that you won't? I think it is. A thought experiment: You are taking a fill-in-the-blank math test, however, you have no idea what the problem is saying, or what the solution could be...So you guess. In theory, you chances of getting the right answer is one out of infinite. However, as practice has shown, people do in fact guess right ocassionally...How is this possible? And since it is indeed possible, that one out of infinite is not in fact zero, then perhaps it is also possible that .9 vinculum (sp?) is in fact, not 100%.

...are there any? Nathan

Hello. It's been over 30 years since my days at the university and have trouble thinking... I believe a catenary reflector has a focal area -locus?- instead of a focus point as a parabolic reflector has. Is it a circle ? The intention is to place a pipe of the same section at the locus of a catenary reflector trough, to be insolated and boil water circulating in it. The center of the locus must be centered between the ends of the catenary. The catenary lenght is 4 feet. What would be the correct catenary span or depth? Thanks, Miguel

Does any one know a good resource (preferably a website) that gives a deeper look about discrete Fourier Transform? For example, a way to know the properties of the output based on the knowledge of the properties of the input.

How do those work? Like 2 to the 2i power and stuff like that. And why does it work that way?

A few weeks ago I accidentally stumbled on a site with images of fractals. I have heard about those things before, but the images interested me so much that I decided I should try to create them personally. Well, Can anyone help me? Where should I start from? Links, books or any other kind of information on fractals is appreciated. Especially I am good at MATLAB and have a good (but instinctive) understanding of fractals and chaos theory. I know what the story is wholly about. But I am still unable to write few lines of code to generate them myself.

In the movie Pi, a character proposes that the Hebrew language consists entirely of mathmatics. If you've seen the movie you can stop reading the remainder of this paragraph. He gives us an example of how words are related: When the number of letters in the word for "mother"(4) is added with the number of letters in "father" (5) you get nine, which is the number of letters in the word for children. I haven't seen the movie in a few months so I don't remember if he gave any more examples. However, this same character also tells that he is searching for the true name of their god.....which they only know the number of letters in. (And I also can't remember.) Does an…