Math Is Fun Forum

The acceleration of a body is given by the formula a = -(v^3/70) find the general equation for velocity. If the velocity was 7m/s when x = 0, dinf the position of the body when its velocity was 5m/s

How to write this as a partial fraction. I'm not sure how I would do this with more than two unknowns. Since I need to find a third numerator. I can't split it into three fractions with 3 variables as numerators and isolate them.

When you rearrange for a it doesn't matter if there are two t's on the other side. However if I wanted to isolate t I would have to get them both on one side and factor right? In this case is there any way to isolate t?

y=kx then dy/dx = k

if y= x^4 + 1/x -6x

then dy/dx = d/dx(x^4) + d/dx(x^-1) etc

so differentiation  sqrt(x) + 1/sqrt(x) w.r.t.x

d/dx(sqrt(x)) = 1/2sqrt(x),   d/x(1/sqrt(x)) = ?  I get -1/2x^-3/2 but the book says -1/(2xsqrt(x))

I really should learn to use Latex.

The other day I was doing polynomial division and thought "I have no idea why this works." There are only a few parts of math that I just do without knowing how it works. I realized that lots of people probably feel this way about the other topics. FOIL, BIDMAS, plug and chug the formula are not good enough if I want to write a basic proof or solve a problem with no immediately obvious solution.

The other day I taught a girl that the equal sign means the left and right side are equivalent like scales. It doesn't matter what you have on each side. The total is the same. She told me she didn't know this and that she thought it was just where the answer went. I had to explain to a guy that a minus number squared is the same as its positive squared though I didn't understand why. I think it's important to know these things.

So is there a method to learn so you can understand the subject conceptually?

I have been looking at sequences an series at the moment and their patterns don't always match mine. I'll describe the pattern in English and not know how to describe it mathematically. They will sometimes write a mathematical expression for the sequence and I wont know if it matches my word description. For example you could use

(x+1)^2  or x^2 +2x +1 as a formula for something. It's obvious to us that they will give the same result even though they look different. Also some methods may seem the same until you input values like 0 or -1/2 into the function so my word description may not work. Anyway does anyone know any resources where I can learn to write word descriptions of patterns in maths notation?

*what is it's origin?

*We are taught this in school but do we actually need to use it?

*Are there better ways to do algebra rather than remembering the acronym?

Someone told me that pretty much all the great mathematicians made their contributions before 30. The exception being Grigori Perelman. Do you agree or disagree with this and to what extent? Can you name any mathematicians that made decent contributions 30+?