The math help thread

So if both numbers are greater than e, the larger being the exponent yields the largest term?
If a or b is > e, and the other is < e, what then?
If both are smaller than e?

Are we talking about the special e or just some variable?

Euler's Number
Its magical because the slope of y=e^x at any point is the y value of that point. Slope/y-value when x=0 is 1. When x=1, about 2.71818

So if both numbers are greater than e, the larger being the exponent yields the largest term?
If a or b is > e, and the other is < e, what then?
If both are smaller than e?

In general? Compare a/ln a with b/ln b.

Okay... I completely forgot how to do this and the notes I got aren't really helping.

For f(x) = 3x², find the slope of the secant line through the points (1, f(1)) and (1 + h, f(1+h)), h ≠ 0.

Also, is there a difference between the average rate of change and the slope of the secant line? I assume they're the same thing.

slope = (f(1+h)-f(1))/1+h-1

=(3(1+h)^2-3(1)^2)/h

=(3(1+2h+h^2)-3)/h

=(3+6h+h^2-3)/h

=6+h

slope = (f(1+h)-f(1))/1+h-1

=(3(1+h)^2-3(1)^2)/h

=(3(1+2h+h^2)-3)/h

=(3+6h+h^2-3)/h

=6+h

Ah thanks, I could have figured that out... but is nothing done with h, then? That's what threw me off when it comes to plugging numbers into x.

EDIT: Hold on, how did you go from (3(1+2h+h^2)-3)/h to (3+6h+h^2-3)/h?

Ah thanks, I could have figured that out... but is nothing done with h, then? That's what threw me off when it comes to plugging numbers into x.

EDIT: Hold on, how did you go from (3(1+2h+h^2)-3)/h to (3+6h+h^2-3)/h?

lol made an mistake.
(3(1+2h+h^2)-3)/h = (3+6h+3h^2-3)/h

final answer = 6+3h

h is a variable, so the slope would be different depending on what h is.

lol made an mistake.
(3(1+2h+h^2)-3)/h = (3+6h+3h^2-3)/h

final answer = 6+3h

h is a variable, so the slope would be different depending on what h is.

That's what I thought, got that as my final answer when I tried doing it. Thanks.

Looking for the inverse of the function. Argh.


EDIT: Nevermind, DO helped me fix it.

(y-4)x=2-3y should be the last line, if I'm doing it right. Your model only multiplies x by y.
Drawing a blank on what to do next....

Edit:
http://www.wolframalpha.com/input/?i=inv...F%28x-4%29
Not sure how to get there.

What does it mean to express a function in terms of x?

"The price p (in dollars) and the demand x for a particular steam iron are related by the equation x = 1,000 - 20p. Express the price p in terms of the demans x, and find the domain of this function."

p = (1000 - x)/20, it means that the function depends on what value u give to x.

Looking for the inverse of the function. Argh.


EDIT: Nevermind, DO helped me fix it.

Ha, that was a while ago too. Shows you how much I check this thread. Although, I guess I should check it more often, seeing as Mathematics is my minor and all. :3

p = (1000 - x)/20, it means that the function depends on what value u give to x.

How did you get that? >_>

How did you get that? >_>

Solve for p in terms of x.
x = 1,000 - 20p
- move the 1,000 to the other side of the equation
x - 1,000 = -20p
- divide both sides by -20
p = 50 - x/20

Factoring polynomials. Someone please help me before I break something.

4x^2 +81 - 36x

4y^2 + 16y + 16

Can someone explain in detail how this is worked out? No matter how much I look at this, I can't figure it out. And this is after spending all day + tutoring trying to figure out how the pineapple factoring works. I barely understand it at all, made worse by the fact that each new problem has something in it that makes it need to be done differently, or so it seems.

Factoring polynomials. Someone please help me before I break something.

4x^2 +81 - 36x

4y^2 + 16y + 16

Can someone explain in detail how this is worked out? No matter how much I look at this, I can't figure it out. And this is after spending all day + tutoring trying to figure out how the pineapple factoring works. I barely understand it at all, made worse by the fact that each new problem has something in it that makes it need to be done differently, or so it seems.

For the second problem...

Divide everything by 4 and you get

y^2+4y+4

Since you divided it all by 4, take that, place it in front...

4( )( )

Look for what adds to 4 for 4y and what multiplies to 4 for the final 4. In this case, 2x2 = 4 and 2+2 = 4. Enter each 2 in the brackets.

4(y+2)(y+2) = 4(y+2)^2

And the first one, a friend of mine did this.

Factoring polynomials. Someone please help me before I break something.

4x^2 +81 - 36x

4y^2 + 16y + 16

Can someone explain in detail how this is worked out? No matter how much I look at this, I can't figure it out. And this is after spending all day + tutoring trying to figure out how the pineapple factoring works. I barely understand it at all, made worse by the fact that each new problem has something in it that makes it need to be done differently, or so it seems.

I'd just use magic factoring on both....