The math help thread

[COLOR="Green"]I got this type of problem in calc today. I know the formula to use, but can't figure out what to do.

y=X^3, X[SIZE="1"]0[/SIZE]=3
Find the instantaneous velocity of the object at X[SIZE="1"]0[/SIZE].

The formula is:

lim...y={f(X) - f(X[SIZE="1"]0[/SIZE])} / (X - X[SIZE="1"]0[/SIZE])
X->X[SIZE="1"]0[/SIZE]

The numbers and equation for y are just placeholders, because they were on a test and I don't have it back yet. What exactly am I supposed to be doing here? :f6:[/COLOR]

That looks like the precursor to derivatives!

Using magical derivative magic, we find out that y' = 3x^2. y' also describes the slope of y at any point x, or in the case of movement, y' describes instantaneous velocity. Plugging in for x[SIZE="1"]0[/SIZE], we find that y' = 27.

Okay, doing it the proper way, using the formula for derivatives (which is a total PITA and impractical later on), we say that f(x) = y and plug in the numbers!

Code:

y' = lim(x->x[SIZE="1"]0[/SIZE]) [f(x) - f(x[SIZE="1"]0[/SIZE])] / (x - x[SIZE="1"]0[/SIZE])
y' = lim(x->x[SIZE="1"]0[/SIZE]) [x^3 - 27] / (x - 3)
y' = lim(x->x[SIZE="1"]0[/SIZE]) x^2 + 3x + 9
y' = 3^2 + 3*3 + 9
y' = 27

I'm a stupid algebra II student. 8D
I need a step by step showing of how to do;
x^2 - kx + 100 = 0
"Find the vale of k that would make the left side of the equation a perfect trinomial"

We are working these by completeing the square,
I tried that and got something like x-k/2 = -k/2 + 10i
....

Uh, I would assume k = 20 in that case.

(x - 10)^2 = x^2 - 20x + 100

As for a step-by-step treatment...

Code:

Perfect Trinomial = a^2 + 2ab + b^2
a = x
b^2 = 100
b = 10, since 10*10 = 100
2ab = 2 * x * 10

keeping in mind that the term 2ab can be negative. It doesn't matter much whether a or b is negative, since squaring any number (except i) is always positive.

If you can't recognize square values, then this can get pretty hard o.O