Mathematics

What is the smallest number that is divisible by 13 but when divided by the whole numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 yields a remainder of 1?

I have a project assigned for my differential equations class and i was looking for some help on how to get started. I'm supposed to solve the initial value problem: y' = f(x,y) y(x(0)) = y(0) by taking into account the method of Picard, which we discussed in class. the problem is : y' = x*y y(0) = 1 i need to show that y(x) converges to the true solution. Our prof wants us to use a math software package which I don't have much experience in. I do know fortran, but don't know if that's any help. Im looking for a recommendation on what software to use, maybe some help on the code, or a general overview of how the problem should be handled. thanks.

Leibniz said that the circunference of an infinite circle would be for us like a rect line. I would want some information about these ideas of Leibniz, and oher ideas that would be on the origins of calculus.

Hi, i need to do this for homework but I can't figure it out. If anybody could walk me through the solution that'd be great. (1978 AB 5) given (xsquared)-xy+(ysquared)=9 a. write a general expression for the slope of the curve b. find the coordinates of the points on the curve where the tangents are vertical c. at the point (0,3) find the rate of change in the slope of the curve with respect to x also, if anybody knows a free website with problems and solutions of AP AB calculus free response from the 1970's and 80's please let me know- thanks

Hi everyone. I want to inert a program in my portable calculator, a small one. Particularly, I want to use it to find the roots of equations with a degree as high as 4, involving trigonometry. In fact, there are many programs I can choose but I have no idea which gives me the answer the fastest. Iteration Method/False Position Method, or Regula Falsi/Secant Method/Iteration Method/ Newton's Method.

Hi everyone! This has been annoying me for a while now, you can have things like base 8, base 6, base 2, base 10 but how about something like base 2.5 for example, would that be valid? (Probably useless but there we go!) Also, would a negative base be valid and would an irrational base be valid too, such as base Pi for example? Cheers, Ryan Jones

Hi! I've got a question concerning neighbourhoods of points in 2- and 3-dimensional space. How can we explicitly show, using only the definition of a given metric, that the according neighbourhood is some figure? For example the three metrics are given: 1) [math]d(x,y)=\sqrt{\sum_{i=1}^{n}{(x_i-y_i)^2}}[/math]; 2) [math]d(x,y)=\displaystyle\max_i|x_i-y_i|[/math]; 3) [math]d(x,y)=\sum_{i=1}^{n}|x_i-y_i|[/math] If [math]a\in{\mathbb{R}}^2[/math] and the metric is 1), then it's clear: [math]d(a,x)=\sqrt{(a_1-x_1)^2+(a_2-x_2)^2}<\epsilon[/math] and it's clear that it's a circle...because one can rewrite:[math](a_1-x_1)^2+(a_2-x_2)^2<{\epsilon}^2[/math] …

How can i make a histodiagram in Excel by using Microsoft Windows Version 2002? Or how can i make it, which softwares? Thank you!

when finding the genotype ratio of Aa * Aa we could use binomial expansion (A+a)*(A+a) to get 1:2:1 ratio but how do we find AaBbCc * AaBbCc ?

so this is the problem: [math]d + e + f = A[/math] [math]d*e + d*f + e*f = B[/math] [math]d*e*f = C[/math] Where your trying to isolate d, e and f in terms of A, B and C. Is it impossible? I haven't been able to isolate anything... BTW I got this by figuring out what the factors of [math]x^3 + Ax^2 + Bx + C[/math] would be: [math](x + d)(x + e)(x + f)[/math] and the system of equations was how I'd figure out what the d, e and f's equaled. anyways, if it is possible to do, please help, this isn't homework or anything just trying to figure out this...

Can you find ANY point of a trigonomic function with only the radius, and an angle without using a system of equations to find the point of intersection between the circle's ray and its itself?

It's all about the n'th root of 2, and proving its irrationality (where n > 2). Suppose [imath]\sqrt[n]{2}[/imath] is rational. Then [imath]\sqrt[n]{2} = \frac{a}{b}[/imath] for [imath]a, b \in \mathbb{Z}[/imath]. So we must have that [imath]2 = \frac{a^n}{b^n} \Rightarrow a^n = b^n + b^n[/imath]. However, this is a contradiction of Fermat's Last Theorem, so it's irrational for n > 2. Just thought it was really neat.

http://www2.hkedcity.net/sch_files/a/kst/kst-07110/photo_album/200511/204962/507977820.JPG Addition: AD=e Anyone can help me with the above question please? P.s. If it's not shown immediately, please refresh it again.

as stated, is there a none intuitive way of solving [math] cos(x)=cos(x+pi/2) [/math] I know from experience that 7pi/4 and 3pi/4 are the solutions, but is there a way to derive it?

Hi all... I have a mass flow rate of 9800Kg/h substance through a heater. If the temperature of the substance is 0deg c and the min tem to be at 15deg c. Specific Heat Capacity: 1040 J/(kg*K) 1. how much heat do i need to apply? 2. How much power do i need to generate that heat? Anyone?

Im trying to increase my level of skill in math and wanted to know if there were any good books I may want to purchase or if their were any advice anyone could give me on how to be become better in math, any help will be greatly apprciated.

If I am given 3 points I am sure (but cannot prove) that there will be only 1 porabola that can satisfy all 3 of them. What formula would allow me to solve this porabola? The same applies for 4 points and a cubic (or more generally, n points and a polynomial of n-1 degree). Of course, no two points can share a y-value and not all the points can be in a straight line. I solved this problem for a circle given 3 points, althought the porabola has proven far more difficult. Could you please help?

A man walks into a hardware store. He buys 1 for a dollar, 20 for two dollars, and 300 for three dollars. What is the man buying? What's the solution?

hi, if you are given a triangle and there is a cirlcle circumscribing it. how do you find the radius of the circle?The triangle is not special.(not a right triangle or anything) is there a formula for this? thanks

I know what inverse functions are, but how do I find an inverse of something like this: y=(e^x)/(1+e^x). What I thought of doing which I'm not sure about is: y(1+e^x) = e^x y+ye^x = e^x (y/e^x)+y = 1 1/e^x +1 = 1/y e^x = y-1 x = ln(y-1) I think what I've done is ridiculously wrong..but yeah...

Proof is proof, or is it?

i was wondering if somebody had any ideas about this: the gradient of a horizontal line = 0 the gradient of a vertical line = infinity but the product of the gradients of perpendicular lines is -1 so does that mean that 0 x infinity = -1 ??? ... or is there something in the proof for the product of the gradients equalling -1 which excludes it for these values?

can anyone help me how to derive pie the value is commonly known as 22/7 and it is circumference by diameter. but is it broughty in no.???

I am trying to write a piece of software that will plot a relation (or implicit function). Is there a know easy solution to doing this or will I have to use approximation methods? At the moment I have it trying every number from -100 to 100 for both x and for y and shading the pixel according to the absolute error, it is very slow and as you can see from these casini curves the line width varies. Please let me know if you have any suggestions or know of any tutorial that might help.

Hello! We've got the following to prove by induction: a) [math]2n+1\le{2^n}[/math] b) [math]n^2\le{2^n}[/math] (It is assumed that 0 is a natural number) a) This inequality is not valid for [math]n=1,2[/math], so to prove the inequality one has to show its validity for all [math]n\ge{3}[/math]: 1) [math]A(3):7\le{8}[/math] (true) 2) Assume that [latex]A(n)[/latex] is true. [math]A(n+1): 2(n+1)+1\le{2^{n+1}}[/math] [math]2(n+1)+1=(2n+1)+2\le{2^n+2}\le{2^{n+1}}[/math], since for [math]2^n+2\le{2^{n+1}}[/math] we have [math]n\ge{1}[/math] Is there a difference if I make the induction step this way?: 2)[math]A(n+1): 2(2n+1)\le{2^{n…