Mathematics

Hello, I was doing my math team practice packet, and in the writers choose section, I had three questions on the problems. Lets see, for the first question was this: How many integers (10<x<100) are increased by nine when their digits are reversed. So my answer was eight numbers; the numbers 12, 23, 34, 45, 56, 67, 78, and 89, and I know that is right. I had to do it all out by hand, until I noticed a pattern which was you take the last digit of the number, make that the first digit of the next number, and have the number in the tens place be one less than the one in the ones. It took me about five minutes to reach that conclusion. Now my question would…

Hello everyone Pretty stupid: I was wondering how you can write "the derivative of a function f(x) in a" (to use in proofs), using [math]\frac{d}{dx}[/math], not just [math]f'(a)[/math]: [math]\frac{df}{dx}_{x=a}[/math]? [math]\frac{d}{dx}f(a)[/math]? [math]\frac{df}{dx}(a)[/math]? [math]\frac{df}{dx}_a[/math]? Something else? Can someone help me on this one? Thanks. Function.

Does (a+b)1/2 equal a1/2 + b1/2 - (2ab)1/2? If you have ( (a+b)2)1/2, then because of the binomial theorem, then (a+b)2=a2+b2+2ab. Inserting this into the equation, then you get (a2+b2+2ab)1/2, which gives you a+b, since a2+b2+2ab=(a+b)2. If you set x=a2 and y=b2, then you have (x+y+2x1/2y1/2)1/2, which gives you x1/2+y1/2. This is also equal to x1/2 + y1/2 + (2x1/2y1/2)1/2 - (2x1/2y1/2)1/2, since (2x1/2y1/2)1/2 and -(2x1/2y1/2)1/2 cancel out. What if you removed 2x1/2y1/2 from the square root? Then, would you get x1/2 + y1/2 - (2x1/2y1/2)1/2?

I have worked on a number system, that works, in order to label points of a perimeter and be connected to produce vertical symmetry, mostly. I find more relevance in using an odd number of points, dispersed evenly around a geometric perimeter. I gravitate to the results in triangle perimeters, since it is applicable to create other shapes with its multiplication. i.e. Four triangles equals a square, five a pentagon, and six triangles making up a hexagon, and so fourth. In compounding triangles into grids that use the symmetric numbering system, there is formation of wave patterns and very interesting results. I am not, but an enthusiast for math. I have no crident…

I did a google search of this, and didn't get far... How would you find the sine of, say pi/2 radians.(Of course, this is 1, just wanted to keep things simple). I'm sure that some caculators have an algorithm to find the sine of a number, and how did people find it out back when they didn't have caculators. Just curious... And I am just talking about finding the sine, and the others with just one number, the number you are finding the ratio with. Say I wouldn't give you any other information, no other angles or lengths. Thank's for your time

I want to know why people have such a hard time dividing by 0. Basic concept: in A/B=C, when B gets larger, C gets smaller. When B gets smaller, C gets larger. So A/0.1=10A and A/0.0001=10000A.... Obviously when B becomes infinitely small (0), C is an infinite multiple of A. Logical proof: if I want to save $100 and I save $0/month, how long until I reach my goal? 100/0=inf, therefore an infinite amount of time will pass and I will never reach my goal. Objection A: But, if A is negative, you'll net "negative infinity". Answer: yea. What's wrong with that? -A/.0001=(-10000A). Still works. objection B: if a/0=inf and b/0=inf but a and b are different…

I shall be grateful if someone can recommend me some book(s) that gives comprehensive knowledge on Mathematical Modeling of Mechanical Systems. Mostly books on Mathematical Modeling give the knowledge with respect to Controls. In other words, they only discuss differential equations; however, differential equations might not be the only branch of mathematics that is used to define any mechanical system.

If you theoretically had negative lengths, what are some ways they would differ from positive lengths?

Would the arctangent of y/x give you the angle in radians?

The problem states that: [math]y_0 \neq 0[/math] [math]|y - y_0| < \frac{\epsilon|y_0|^2}{2}[/math] And I must use those to prove that: [math]y \neq 0[/math] [math]|\frac{1}{y} - \frac{1}{y_0}| < \epsilon[/math] My professor told me to utilize the inverse triangle inequality: [math]|a| - |b| \leq |a - b|[/math] Solving the first part was easy - I changed one of the expressions and used the triangle inequality: I change [math]|y - y_0|[/math] to [math]|y_0 - y|[/math] Then I use the inequality: [math]|y_0 - y| \geq |y_0| - |y| < \frac{|y_0|}{2} => -|y| < \frac{|y_0|}{2} - |y_0| => -|y| < -\frac{|y_0|}{2} => |y| > \frac{|y_0|}{2}[/math] So…

I'm curious as to the nature of numbers and have come up with a little concept. I've recently found a new love for maths so ive been going over some geometry, trig, algebra, calc etc and have a few basic questions. What dimension are numbers? Based on the fact logic works in binary i concluded they are 2D but have no idea. The euclidean geometry is 2D? can all shapes be expressed in these terms? i know there is 3D geometry but it too is express in mathematical terms which seems to impose its only a 2D manifistation of 3D reality by the use of logic. In my mind right now i see numbers as 2D, shapes as 3D and reality as 4D. Each heirarchy can be expresse…

I think most know as two Fibonnaci numbers are divided together, dividing the smaller one by the larger one, you get closer to the golden ratio as the two Fibonnaci numbers get larger and larger. Here is the equation that I want to use for this example: (Correct me if this is an incorrect way of doing this). Since at the limit of infinity there would, in fact, be a fraction, but of immeasurable magnitude, that would exist, therefore making this not an irrational number? I am not saying it isn't an irrational number, but I want to be sure of my logic on irrational numbers. Or would this immeasurable magnitude of the fraction make this an irrational number? …

there is a guy named Niels Abel. he tried and failed to solve the quintic - polynomial degree five. find it, solve it. it is trivial.

If you theoretically had negative lengths, what are some ways they would differ from positive lengths?

What do sin∅ and cos∅ tells us in cross product and dot product I mean what is the significance of them & from where it came ?

I had wondered if looking for Pi in a different base other than "10" would produce finite or repeating decimals. So using the formula circumference/diameter I started with the normal base 10, as a control, putting 23.12/7.36 into the WolframAlpha engine, of course getting 3.14..... (infinitely non-repeating as usual). And then I changed it from base 10, entering "23.12/7.36 in base 5". I also tried it with all other bases from 1-20, also 100, and a few in between. Oddly, every single result had the numbers repeating after only less than fifteen digits. Cap'n Refsmmat advised me just input "pi in base (anything)" to see what happens. And of course doing that…

Hello everyone I've seen 2 definitions for [math]e[/math] (one on the internet, one I have proven myself): [math]e=\lim_{n\to\infty}{\left[1+\frac{1}{n}\right]^n}[/math] and [math]e=\lim_{n\to 0}{\left[n+1\right]^{\frac{1}{n}}}[/math] Now, is there a proof that these two are equal? (I'd first like to know if I can change the first expression to something in the form of [math]n\to 0[/math].) Thanks! Function

Hello everyone My book gives us a proof for the rule of de l'Hôpital and to do this, its first statement is: [math]\frac{f(x)}{g(x)}=\frac{f(x)-f(a)}{g(x)-g(a)}[/math] However, I don't agree with this... Or I have no idea where that comes from... e.g.: [math]f(x)=6x^3+2x^2+4[/math] and [math]g(x)=8x^2+3x+1[/math] [math]\frac{f(3)}{g(3)}=2,243...\neq\frac{f(3)-f(7)}{g(3)-g(7)}=5,951...[/math] What's wrong with this? Thanks. Function Nope, wait.. I oversaw that [math]f(a)=g(a)=0[/math] Sorry (...again..)

Why does a negitive times a negitive equal a positive

Hello! Well as the titel says, I need help with a math problem I can't get a grip of. I have thought of this problem for around 1-2 hours and just can't understand it. Some tips: Use derivate For which numbers on a doesn't the curve (y = x ^ 3 + ax ^ 2 + x) has any extreme points? The answer to this question is -√3 < a < +√3 Regards!

Question : 1.How to solve this question (steps) 2.How to analyse this question Please help me it is emergency, I don't know how to analyse this problem.

Why does a negitive times a negitive equal a positive

Here is proof that a+bi=-a+bi: Using the distributive proprty, we can write a+bi as i(a/i+b). a/i is also equal to ai, so then it becomes i(ai+b). That equals ai2+bi, and i2=-1, so therefore it makes -a+bi. Equation form of proof: a+bi=i(a/i+b)=i(ai+b)=ai2+bi=-a+bi Proof that a/i=ai: Because i2=-1, we can write a/i as a/-11/2. a is also sq.root(a2), or a2/2, so it is also a2/2/-11/2. Since a1/2/b1/2=(a/b)1/2, we can write this as (a2/-1)1/2, which is also equal to -a2/2. -a2/2 =a2/2i, or just ai. What do you guys think?

There is a website named tauday.com and it was mad by a guy who thinks τ should be the circle constant. I agree with him, but what do you guys think?

I've found an exact equation for e without pi e=(cos(1/2)+i*sin(1/2))^(2/i) does this mean that e is not a transcendental number?