Mathematics

The area of a triangle with vertices (a,b), (c,d), and (e,f) is (sorry, I don't know how to put it into vertical bars for determinants) +/- .5 determinant of A where A is a b 1 c d 1 e f 1 and the symbol +/- indicates that the appropiate sign should be chosen to yield a positive area. How can one prove this? I think I have a method for proving it, but it seems too tedious and long to do.

I'm trying to prove that, hopefully this comes out right, [math]\sum_{r=0}^{n}{(-1)}^{r}{_n}C{_r}{(n+1)}^n = n![/math] Can anyone help? The pattern is from 1 4 9 3 5 2 1 8 27 64 7 19 37 12 18 6 1 2 1 etc.

How do I prove that lim x->a [xf(x) ] = cL, given that Lim x->a f(x) = L?

Hi, I have never really been a math type of person and am taking a intro to math course at uni. I am asked to solve an equation in the same format as the one below and indicate clearly the method used. The trouble is I have no idea how to do it [math] {6}/{y} + {8}/{y^2} = -1 [/math] I would really appreciated any help. Thanks edit: I don't know how to make fractions with latex

[math]w = \frac{K^{\frac{1}{4}}}{K^\frac{1}{2}}\frac{p}{2} \left(\frac{w}{2r}\right)^\frac{1}{2}[/math] [math]r=\frac{1}{8}[/math] and [math]w = \frac{1}{2}[/math] What is K in terms of p? The answer is [math]K=4p^4[/math] but I want to see the working out because, for some reason, I got [math]K=2p^2[/math].

Who, invented the mathematical idea of cross product, and in what year? Why did they invent it, and how did they do it? Thank you

how would i show that the values of x at which sinxe^(-sinx) has stationary points form an arithmetic sequence. I've so far worked out dy/dx=cosxe^-sinx(1-sinx)=0 so cosx.e^-sinx= and sinx=0 arcsin0=pi,2pi,3pi,4pi,etc so cospi.e^-sinpi=0 cos2pi.e^-sin2pi=1 cos3pi.e^-sin3pi=0 cos4pi.e^-sin4pi=1 therefore it is a repeating sequence and common difference 1,-1 but i don't think this is correct as again (im not sure how to solve (cosxe^-sinx(1-sinx)=0)) any ideas? thanks for any help

I've spent two hours trying to do this, but I cant figure a way out . We've just started the Gr. 12 Geometry and Discrete Mathematics and so far we've done dot product/cross product of vectors in 2,3 dimentions in cartesian and algebraic form Any help would be greately appreciated

Hi there If i had a function in the format cos(ln(x+1)) =0 how would i go about trying to solve for the solutions (roots) I can see there are three roots but i'm not sure how to solve it. ps. how do you solve secx(2sec^2x-1)=0 as ih happens i know it has no solutions, but how would i go about showing this. where can i look this stuff up thanks guys!

e^i(pi) + 1 = 0 if we modify it like so e^(i(pi)) = -1 e^(i(pi))^2 = 1 i^2(pi)^2 = ln1 = 0 so -pi^2 = 0 which is obviously wrong... so why?

since i began posting on this site, i have seen more than one thread like "what is sin, cos, ...?". so, somewhat inspired by daves two calculus lessons, decided to post the relevent parts of my trig notes. it was a one semester class, so it will probably be really basic. note: i will not cover graphing and inverse trig function. i will begin by introducing a unit of measurement of angles, because i find them much easier to work with. that unit is radian. the name will make sense after the description. we have a circle whose center is at the origin. as we all know, the circumference of a circle is [math]C=2{\pi}r[/math]. assume the radius of the circle is one. the circ…

I tried \newcommand but clearly that's been disabled. Is there some way to quickly write Einstein notation? [math]\eta_{\rho\sigma} = \Lambda^u{}_{\rho} \Lambda^v{}_{\sigma} \eta_{uv}[/math]

Im a total idiot and i can't find a pyramid or a triangular prism that was a surface area that is less than its volume by a 40 cm margin.. If you could find a triangular prism/ pryamid that has no more than 320 cm squared and at the same time has a volume of over 360 cm cubed....i would really apprieciate it thank you soo much

I have a question about something i read here. Why did they choose not to define vector division exactly? They said something about non-uniqueness, and I don't follow. To help me refresh my memory, suppose that we have two lines in an xy plane. For the sake of reality, let the plane be a real plane in real space. An equation for any line in the plane will have the following form: Ax+By+C=0 Suppose we have two lines. [math] A_1 x + B_1 y + C_1 = 0 [/math] [math] A_2 x + B_2 y + C_2 = 0 [/math] We can rewrite the equations as follows: [math] A_1 x + B_1 y = - C_1 [/math] [math] A_2 x + B_2 y = - C_2 [/math] We can rewrite this in …

[math]\lim_{n\to\infty}(1+\frac{1}{n})^n=e[/math] how was this discovered? where did e originally come from?

Is there a way to use latex to make a matrix? And for that matter a determinant? Thank you

http://www.math.harvard.edu/archive/21b_fall_03/goodwill/ a problem that Will Hunting (Matt Damon) solves in the movie it's kind of interesting, a simple 4-point graph, the adjacency matrix for it

Hey I have this question due for thursday and cant figure anything out, (btw no calculus knowledge is required) A) Express the number 25 as a product of two complex conjugates, a + bi and a - bi in two different ways with a and b both natural numbers. b) Find another perfect square that can be expressed as a product of two complex conjugates, a + bi and a - bi in two different ways, with a and b both natural numbers. c) describe the most efficient method for finding numbers that satisfy the above relationship.

pi is probably the strangest number on the planet. On one hand, Pi is defined as a ratio... that of the Circumference of a circle to its diameter. However, as far as I know, it is a nonrepeating infinite decimal, therefore making it an irrational number, correct? So how is it that you can take a ratio, and get an irrational number out of it?

Hi, ive just done a Anova on a set of data...ive got the results but i have no idea how to examine the data to get answers? can anybody help me? i have df,f and sig!!

Sorry if you've heard this before. Three guys need to get a room for the night. The room costs $30 so they each chip in $10. After they get upstairs, the desk clerk realizes he made a mistake and the room should have only been $25, so he sends a bell hop up with $5 to give back to them. The bell hop decides that he's only going to give each guy $1 and keep the other $2 for himself, so that's what he does. So if each guy pays $10 and gets $1, then it's like they only payed $9. So 9 * 3 = 27. Add the $2 that the bell hop has and you get $29 for the room. Where did the other dollar go? I'm pretty sure I know it, but I'm not to sure of my explaination (whi…

(n+2)^3 =n^3+3(n^2)(2)+3(n)(2^2)+2^3 =n^3+6n^2+12n+8 Could sum 1 tell me how this method cud b used for other exponents such as (n+2)^4 or (n+2)^5. So plz xplain to me this method of expanding, plz show the pattern if there is one.

Is it possible to derive the formula for a traveling wave using classical Newtonian mechanics? Here is the formula I want to derive: [math] A(x,t) = A_0 sin(kx-\omega t ) [/math] Thank you

Ok, so on this other forum I go to, one of the users asked for help explaining exponents to her kid and how the work for his homework. Most of it I could cover, but one thing I couldn't. We all know negative exponents, and simple stuff like 1/(x^-2) = x^2, and it's easy enough to simply state the rule, but my question is *why* is that rule the way it is? I mean, what's the derivation behind it? I hate to say "it just is that way, kid", but it's been a hell of a long time since I took Algebra, and I don't remember the reasoning for it. So, basically, what I'm after is a logical explanation for the way negative exponents work, that I can present in a form a kid t…

I've been trying to figure out how to know what units can be used with each other in equations such as P=E/t. After reading about the MKS, CGS, and FPS unit systems, I think I understand now, but Im not sure. 1) From what I understand, the MKS, CGS, and FPS unit systems are collections of units that can be used in equations with only other units from the same collection. So if you use MKS, you can use meters with kilograms, but not meters with grams to get the right answer. In MKS you can use kelvin but not celsius, you can use watts but not statwatts, etc... Im I understanding right so far? 2) If I was to use a set of units that aren't a part of MKS, CGS or FPS…