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You probably see your mistake now, you have typed - 1/h, when you mean - 1/a
So in the overall numerator, there are two fractions subtracted, get like denominators.
Then subtract their numerators.
Then you'll see (-h/x(x+h))/h and the h's cancel and the limit can be taken. Good Luck!
Anchor, the very first definition of derivative means delta y divided by delta x, which means rise over run or slope.
limit where delta goes to zero. You forgot the f(x + h) and f(x), the f makes it the y part.
So 1/(x+h) - 1/x all divided by h is how you start off.
I'll work on it...
Making a hash table for arctan will be funny to use, because the slope changes by leaps and bounds between 88 degrees
and 89.99 degrees. But with a little thought, it would probably still be a good idea. Just need to create a
binary tree instead of a hash table, so you can test less or greater or equal, and get down to the right element to
use quickly. That's what I would do for the arctan().
On k + 89, I was below with this 3 times correction still by factor of 1.062801932.
So with the new correction factor, it's kind of dumb, but, you'll laugh, but...
percentage that it was from machine B knowing first that the piece is
defective = 35% ((4 x 3)/(5 + 4 + 2)) * correction factor, where correction factor = (5 + 4 + 2)/(3*(.35 x 4 + .25 x 5 + .40 x 2))
On k + 89, I meant to multiply by 3, but then I still would be wrong.
I wish there was a theorum to get the number that is close to this 3.
I'll have to work on that. The 3 multiplier would be like having 4 + 4 + 4 in the numerator.
I know it is wrong, but I feel the need to research this further.
Once you find a segment that crosses over the y value of interest, you can do this:
Call the bottom point A and the top point B. Call the dividing horizontal point C.
Cx = Ax + HeightToDivideLine*(Bx - Ax)/(By-Ay)
Cy = Ay + HeightToDivideLine
No prob.
That sounds pretty nice and methodical, M.IsFun! One tiny thing though, (0,0) to (0,25) is vertical, not flat, but luckily, no intersection in the example.
slope = (By - Ay) / (Bx - Ax)
Cx = Ax + 50 cos(arctan(slope))
Cy = Ay + 50 sin(arctan(slope))
I get everything except the N and the ss usage.
What if the piece is shaped like two mountains beside one another connected at the bottom, and then
if you cut in up too high, you end up with THREE pieces??
When you said simple polygon, do you mean, this could not occur?
Oh, I think you said there are upper and lower parallel lines, can you explain this a little more.
What would you do with a stair case with many parallel lines, how do you tell which is the top and bottom, check every one?
Math is good in the grocery store to compare prices, figure out weight watcher points.
To figure out weight watcher points without the little slide rule they give you, you figure how many
50's can you squeeze into the calories. For example a 110 calorie cereal would be just over 2 points, at first.
but then you read the total fat, and for every 3 grams of fat, you add a 1/4 point more, so 12 grams of fat adds
another point to this. Finally, you look up the dietary fiber, and for every gram of dietary fiber, you can SUBTRACT
(because it is good for you) about 1/5th (or a 1/4 if it is easier in your head) of a point.
See at weight watchers, based on your weight and other criteria, you are assigned to eat a certain number of points
each day inorder to lose weight at a reasonable pace.
I don't know what ≡ means in krassi's topic.
That's neat. Maybe the spread sheet could be used to play interactive games whereby anyone can change the values in the boxes. What if you want to play Chinese checkers, and then you need a hexagonal closest 2-D packing arrangement, though.
I don't know anything about servers, but it seems that you would have a file global to all participants, and only one could make
changes to the information at a time. So you could have an interface that might allow users to click and drag game pieces around on a board and draw something. The next user would start where the last one left off, hence accessing the same file.
We are very lucky to have you as our Administrator, as you are very curious about everything, and this makes for a wonderful site as this surely is!
Also, you don't need to know 3 x 6 if you know 4 x 5 because
3 x 6 = (3+k)(3+k+1) - k(k+1), where k=floor((6-3)/2).
So now you only have to memorize the twins, really called squares, and
the numbers that are right beside each other, also called consecutive numbers.
Click on picture.
The little black dots are each one unit apart.
So the graph goes a little below the x-axis,
but not much.
This was created with Just BASIC.
Memorize the twin's first:
3 x 3 is 9
4 x 4 is 16
5 x 5 is 25
6 x 6 is 36
7 x 7 is 49
8 x 8 is 64
9 x 9 is 81Memorize the ODD's times the EVEN'S below:
odd's |
|
3 | 12 18 24
|
|
5 | 20 30 40
|
|
7 | 28 42 56
|
|
9 | 36 54 72
|__________________________
4 6 8
e v e n 'sAfter that you can figure out the rest
with the Less-Than-A-Twin way.
Say you need to know 3 times 9.
It is 27, but you don't know that,
so you check that 3 and 9 are both
odd, and they are, so find the number
that is right between 3 and 9.
It is 6. Now 3 and 9 are three away
from the middle number 6. So we
have to subtract three three times
from the middle number times the middle
number. So 6 times 6 is 36 because
you have to memorize the twins.
And 3 times 9 is this 36 minus 3 minus
3 minus 3. I subtracted 3 three times
because 3 and 9 are three away from
the middle.
Here is an easier one.
Say you want to know what 4 times 8 is.
Both numbers are even, so we can
figure it out. The middle number is 6
again. And 4 and 8 are two away from
6. So now we subtract 2 from 6 x 6 two
times. So 36 minus 2 minus 2 is 32, and
that is 4 times 8. 4 x 8 = 32.
Here is the easiest one.
Say you want to know 7 x 9. They are
both odd and the middle number is 8.
7 and 9 are one away from 8, so subtract
one one time from 8 times 8.
So 8 x 8 you have to memorize because it
is a twin. So 8 x 8 minus one is 63.
So 7 x 9 is 63.
memorize the ODD's times the EVEN'S below:
odd's |
|
3 | 12 18 24
|
|
5 | 20 30 40
|
|
7 | 28 42 56
|
|
9 | 36 54 72
|__________________________
4 6 8
e v e n 'sFirst memorize these ones:
six times six is thirty-six, seven times seven is forty-nine, eight times eight is sixty-four, and nine times nine is eighty-one.
Next memorize these ones because the answers are one below the answers of the other ones I just did.
five times seven is thirty-five, six times eight is forty-eight, seven times nine is sixty-three, eight times ten is eighty.
Next memorize these ones because they are three less than the ones I just did.
four times eight is thirty-two, five times nine is forty-five, six times ten is sixty, seven times eleven is seventy-seven.
Also if you know that 5 times 5 is 25, then you automatically know 3 times 7 is 21 because it is four less.
This is the difference of two squares. (5 times 5) minus (2 times 2). You see 3 and 7 are two away from 5, so 2 times 2 less than 25.
So that's why you should know 4 x 4 = 16 because then you automatically know that 3 x 5 is one less.
And 4 x 6 is one less than 5 x 5.
And 8 x 10 is one less than 9 x 9.
So learn the same numbers multiplied by self first.
So 2 x 9 is 11/2 times 11/2 subtract (11/2 - 2)^2.
The ^ sign means to multiply by same number.
So for 2 x 9, it is too hard to use this method because 2 and 9 are not both even numbers.
Also 2 and 9 are not both odd numbers.
2 and 9 are one of each, so memorize those ones.
3 x 6 is double 3 x 3 or 9 x 2 is 18.
Good Luck!
If you are looking for the slant of the line perpendicular to this line, then it is negative one over slope of this line.
The slant of a line is the same anywhere on the line.
This is not true for a more complicated curve. So the slope of the perpendicular line to this one is
three.
Are you asking what is the probability f(x) is over 100 or just x? Because if it just x, then the function doesn't matter, you said it was a random continuous variable, so 1/2 of the time x is > 100 and 1/2 of the time x < 100 since x can go from negative infinity to postive infinity.
I am imagining two pulleys, the smaller one on the left, close together because they are separated by only 4 cm when they are 32 and 40 cm in diameter. The string goes from the top of one pulley to the top of the other pulley.
What is cross over and at what angle from the line drawn from center to center of pulleys are the endpoints you wish to
measure from?