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Hippogriffs, here is a problem that may help you.
To get from 100 to 95, you multiply by 0.95 or 95% or 95/100
But to get back to 100 from 95, you multiply by 100/95 or a scary decimal.
Try to figure out what is the scary decimal???
When you get the answer, don't forget to look at it and write it down.
Think about the 0.95 that got you from 100 to 95
and then think about the new number that gets you back.
Do you see anything interesting???
One is less than 1, and one is bigger than one.
Which one is further from one, the big one, or the small one??
And from this we might be able to guess that the big reciprocal gets
bigger faster than the smaller reciprocal gets smaller.
Reciprocals are fun!! One is bigger than one, and one is smaller than one.
Bye!
I didn't go to those web sites, so here is maybe another way.
Allow the knowledge of a circumference being around 3 times the diameter (2π r)
If you don't approve of knowing this, then don't read on.
Imagine many concentric circles around the origin varying from really small to
a radius of one or r, if you want the general case. I'll use 1 for largest r.
Now the concentric circles are evenly spaced apart, and adding up their circumferences
times the distance between the circles should be about right.
Hence
Is there a method to finding the (x-2) factor of the cubic?
Or did Ricky divide by it because we had already known the root?
I'll have to learn what rational roots theorem and synthetic division is.
Woops, I forgot to read the 2nd page of responses in the thread...
so I erased my response...
...
Okay, now I've read everything, so I'm gonna be person #2.
And I must say mathsyperson was really on the ball to figure out this scheme!!!
Guess 5b (since ganesh called guess 4 guess 5): 3461
Nice job on the Graph Maker applet! I was examining the hyperbolic functions.
They are still a mystery to me, but I see the basic shape now.
Make units of water the x-axis, which goes to the right.
Make pennys the y-axis, which goes up.
Now imagine a point at the origin, what would this point mean??
It would mean that it is zero pennies for zero units of water.
But this is not true. You have to pay 1800 pennies even if you
don't use the water. So put a point 1800 up from the origin.
Does that make any sense??
Refresh my memory. What happens to the function y=x if you multiply
it by :italic(i)
Well these Calculus courses were each 7 weeks long, so Calculus III was
probably not as advanced as I made it sound.
I remember we used integration by parts and I remember learning some
of that stuff now that irspow figured out, where you rotate a function
around an axis to get surface area in 3-d, or to get volume.
But I still must relearn now to understand it.
Is this a 2-dimensional vector?
What is the coordinate system?
Yeah, that's what I meant. I guess I should have said you look from eyes that are
on your feet, but I forgot to say that.
Sounds like krassi_holmz wants Ganesh to give his original
replies to 7084 and 4532, so we can continue, and I would
like to play too. I always liked MasterMind, but was never
that good at it.
What is Cells?
Maybe you could have many smaller equations if you
broke them into categories of the polygons created??
That's great. I might order a used one. See, I forgot nearly all the calculus I ever
was taught in college in the late 80's due to lack of usage and never a great
understanding, mostly did it through just memorizing steps. Now I plan on
actually learning something, but I have no due date, as I'm not using the
information for anything except my own pleasure. Also, in my first year at
college I made a mistake by not starting with Calc I, I started with Calc III, since
I already had Calculus in high school (grade 12). I think I should have started
from scratch to see if you learn theory that you missed the first time around.
I'm not impressed that the laborers can't switch places each day because constraints
employers put like that simply induce things like carpal tunnel and other
repetitive injuries. Variety is a good thing.
If you walk around a board laying on
the ground, you can't see its length
if you are straight in line with it.
Call this the
Oh, thanks!
£ and p. How do you pronounce these? Pound? Cent? I am an ignorant New Englander over the Atlantic.
Thanks a lot, mikau, for the wonderful explanations about the
Maclaurin series. I am trying to learn new stuff, so I really
appreciate it. Who is the author of the Calculus book you are
studying from? Is it worth getting, do you think?
oh. I'll examine tomorrow. bye.
Okay, I get the product rule.
But what is that last equation you wrote?
Also, the math script isn't necessary unless you
like to type even more to get it to look cool.
As long as your understood.
But [m a t h]\frac{3}{4}[/m a t h] makes a 3/4 fraction.
You can google on LaTeX Math to learn it.
\int is integrate
_{x=0} makes x=0 a subscript, the underscore does that.
^{I'm tiny north east} makes writing a superscript.
I'm going to bed now, it's 1:45 am here. Bye.
Well I cheated after that and plotted the points with a tiny BASIC program.
And noted the minimum area was 4 at x=2
I'm rusty at calculus, but I want to learn it again years later.
So this is a product, so there is a rule for that.
What is the derivative of this?
dJ
Add 2 to both sides to solve for Yintercept.
Multiply both sides of equation by Xintercept so as to
solve for the area; you can divide by 2, if you want to
be exact.
Click on picture to see it bigger.