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#3426 Re: Help Me ! » Another problem.. :) » 2005-12-15 17:49:23

I drew a rectangle with a diagonal in it and tried to keep the
diagonal a constant # like sqrt(200), but any # is fine.
Then I realized if height or width approaches 0, but is just
tiny bit over zero like 0.01, then you will get the
minimum area or product, but still have a diagonal length
of sqrt(200).   So the minimum product approaches zero,
I think.

#3428 Re: Help Me ! » I have another problem that involves some sort of substitution. » 2005-12-15 17:20:12

The x intercept must be greater than one.
Call x intercept J.
Here is the equation for the area.
Just find the J above one that makes the expression the smallest:


I arrived at this by drawing a picture and setting two
similar triangles proportions equal.
They are:

Sorry explanation so poor.

#3430 Re: Help Me ! » Finding the intersection of two functions. » 2005-12-15 15:03:59

I get (-2,-1) and (2,1) by graphing a sketch.


And I guess majicWaffle is right,
also (i, -2i) and (-i, 2i), whatever these complex thingys mean, I don't remember.

#3432 Re: Help Me ! » second order functions » 2005-12-13 10:28:37

The larger b is, then the parabola is bent more upward as you go right?
Just a guess.
If b is negative then the parabola is bent more downward as you go right?

#3433 Re: Help Me ! » Help!!!! » 2005-12-13 10:25:07

What about 2 and -5?  Negatives are probably disallowed, huh?

#3434 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-12-13 05:38:42

mathsyperson, how do you know the unaccounted for part is the broken off
piece?  ganesh said one-eight is above the water, but he didn't say one-eighth was
currently above the water with respect to the original size?
I think it's a trick question.

#3435 Re: Help Me ! » Effective Interest » 2005-12-13 05:10:02

I am guessing at the method, but here's how I got 3.4489379%.
.0575 ÷ 12
add one
raise to the 12th power (current result is effective rate about 1.059 or 5.9%)
Then work backwards with these ideas.
Subtract .024
raise to 1/12th power to get monthly rate
subtract one
multiply by 12
Bingo! You've got it.  0.034...

#3437 Re: Help Me ! » Math problem » 2005-12-13 04:51:34

Width is numerator; height of zeros is denominator,
so 1 is

      o

which means 1/1.

#3439 Re: Help Me ! » Find the Median » 2005-12-13 04:43:07

Just over a half because 75K is half of 150K and if you make the 150K smaller in
the denominator and the 75K bigger in the numerator, then the fraction gets
bigger.  That's why I say "over" a half.  76/147 is about 75/150.

#3441 Re: Help Me ! » Triangle related » 2005-12-12 11:33:08

Hi mathsyperson,
Yeah.  I think in retrospect, I just got extremely lucky in the curvy calculus stuff.
And also it occurs to me that maybe I was taught it back in 1985 or 6, but my
memory is so bad, I may have been reinventing something I'd seen before.
My major was Electrical Engineering, but I took a lot of Calculus courses, but
just barely passed somehow.  Now I am starting all over from nearly scratch again.

#3442 Re: Help Me ! » average within interval » 2005-12-12 07:32:41

Thanks, I got it.
But if you don't know the class width, you probably can't do it ahead of
time.  Like divide by

.
But that only works for y=constant?
What I mean is

so the 1/x is like dividing by the class width.
But it doesn't work if it is another function because
and then divide by class width.
But this is different than the following where I divide by
first:

And
clearly is not the same as
.
Sorry I left out the dx's in the equations; I don't understand what they are yet.  I know it is an incremental piece of x, but I don't know where it is
coming from.  Does it appear when you decide to take the integral with
respect to x?

#3443 Re: Help Me ! » average within interval » 2005-12-12 06:49:36

I don't understand.
What about y = x from 10 to 20, so the average should be 15?


So

Oh you mean divide by 10 and factor out the


before you do the integral?

#3444 Help Me ! » average within interval » 2005-12-12 04:31:22

John E. Franklin
Replies: 7

If you want the average y value (height) of a
function, then you can get the area under the
curve and divide by the interval width.
Well I was hoping to find a way to do this a
little differently, but I may need some help.
Instead of integrating first and then dividing,
I would like to do something in preparation
before the integration, so after the definite
integral, there will be no division.
If anyone can help.  Thank you.
If this can be done, I think it would help me
to grasp underlying principles better for
maybe other applications.

#3445 Re: Help Me ! » Steradian » 2005-12-11 15:39:38

I can't believe the progress you made!!!!!!
That's amazing.
(Google Latex math for graphical math symbols, notice _ for subscript and ^ for superscript, \frac{numerator}{denominator}, etc.  I just learned some today.
You've helped me a lot, and I also have been trying to do what you have done,
except I only got as far as the following, except I had the x and y axis
backwards from you:
Curved surface area of steradian = 1 =


Note that I am missing the 2 for 2
.
This is because I used the formula for the surface area of a cone and you
divide by two.
Cone Area Piece=dSlant 1/2 2 π y   (I'm rotating around the x-axis, so y is R base of cone)
y' is y prime or derivative in above; I'm very sloppy still; I need reform.
Where

and
, which I got
from a table, and then I gave up and read your post.
I must have made a mistake on the 2, but I thought I'd let you know just
in case.  I tried figuring out the rotation myself and must have failed by a
factor of two somehow.
...
I just examined what I did, and it turns out I was lucky to get as close as I
did because I should have used slices of cones, not the whole cone.
And slices of the cones would involve something I can't figure out yet.
It would be a slice of a cone at the base, incrementally thin.  Somehow the
1/2 goes away, don't ask me how.  But the surface area of a cone can be
shown "unfolded" as a bunch of triangles, and the area of a triangle has the
1/2 in it, that's a simple explanation I saw a few weeks ago.
...
But you are way ahead of me.
How come your formula didn't get really messy with the derivative
of the circle??  Your substition?  I'll have to try to learn all this when I can.
Bye.

#3446 Re: Help Me ! » Steradian » 2005-12-11 11:19:08

irspow wrote:

∫2πf(y)√1+(dx/dy)²  dy.

Tell me if this is the same thing?  This is way over my head unless I learn a lot.


which by the way was created with
     [ m a t h ] \int  2\pi f(y) \sqrt{1 + (dx/dy)^2} dy  [/ m a t h ]

irspow wrote:

The equation for that line will be y = H - (H/R)x, this is true for all cones.  This line intercepts the x axis at x = R.

     Now multiply your line function by (2 pi x) and then integrate from zero to R.  You will get:

     2pix(H - (H/R)x) = 2piH ∫x - x^2 / R dx  (remember to factor out constants?)

I finally figured out that you are making a series of hollow pipes that get
shorter and shorter as you approach R.
Thanks for teaching me so well!!!!!!
I am very grateful to everyone for spending so much time helping me.

#3447 Re: Help Me ! » Curvy line length calculus? » 2005-12-11 10:29:45

Thank you very much for the compliment.
You made my day!
I'll check out that link in a minute.
And yes, I did find it in a table, and I got 26.40253635
for the length from 0 to 5 for


I am still struggling with how calculus works, and it is
of great interest to me because I sometimes have to
resort to doing computer approximations by breaking
the problem into the tiny pieces and adding it up.
Newton was a
for sure!

#3448 Re: Help Me ! » Curvy line length calculus? » 2005-12-11 09:04:22

What is the length of the curvy line of a sine wave graphed from 0 to 2π radians?
I'll work on this and wish me luck...:)

#3449 Re: Help Me ! » Curvy line length calculus? » 2005-12-11 08:39:43

I cheated and used a standard mathematical tables integrals answer.
Plugging in 5 and 0, and subtracting revealed a line length of 26.40253635
This might actually be right, since it is a little longer than going
straight from (0,0) to (5,25), and that's because it is a parabola.
Maybe it's right!  Hurray!  Maybe it's not.  I'm not sure yet.

#3450 Re: Help Me ! » Curvy line length calculus? » 2005-12-11 03:26:36

This is probably all wrong, but I am learning to use LaTeX!!!

Even if this is wrong, I don't know how to integrate it? 
Anyone know where I can learn this one?
...
I found "Power Substitution" on internet.
I might learn this!
...
Well If I let

, it seems like a good
start, but then
gets just as messy as what I
started with, so that's no help...

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