Think about it this way: whenever you move the drill in one direction, you are sacrificing room on that side. At 2/3 you are sacrificing the most room while the other side can compensate. If you go further than 2/3 you create a 'dead zone'.
I've heard there's a proof out there of this, basically that (I think) you can use the intermediate value theorem to prove that an Nth-degree polynomial has no more than N roots.
I'm not in school anymore, just an interested engineer. Does anyone know where I can find this proof or any...
I'm trying to find a set of five (5) algebraic functions a(x), b(x), c(x), d(x), and e(x) that for every order they can be applied, will produce a unique result. That is, a(b(c(d(e(x))))) should be different from e(d(c(b(a(x))))) for every possible x. And every other unique ordering should...
Yes, I do remember from LA that no equation can be a linear combination of the others in order to get a unique solution. I believe what I am looking for is a linear regression.
HoI - Good to know! I had never heard of Diophantine equations before. In my situation I actually have about...
It seems what I am looking for is actually just a linear regression with multiple independent variables. Case closed (for now).
By the way, HallsofIvy, I saw that ;).
Thank you for reminding me that I'm actually expressing a system of equations. Let's start with a new example. Say the store is offering three bundles now:
4B+0G+3L=10
0B+2G+5L=16
6B+9G+2L=37
If you solve this, you get B=2, G=3, L=1. Now let's say the store offers another bundle...
Thanks for the help. I am afraid I don't completely follow, though I believe I do partially.
So for example, if the equations were:
2B + 1G + 3L = 10
4B + 2G + 6L = 20
These would be parallel planes, correct? And in this case, there would be infinitely many solutions?
If there were three...
This might go into stats, I'm not sure. But I'll throw it out there. You are at the grocery store and they have two product bundles:
Four bananas and three limes for $10.
Two grapefruits and five limes for $12.
You want to come up with a way to compute the average cost of a lime, the...
Yuqing - let me see if I have this right. I'm going to rewrite it slightly using integer division (floor(x/y)) and modulus. A foreslash (/) will indicate integer division, and a % will indicate modulus. N will be the number of elements in the "available list". The lists will have a...
Thanks awkward for the information. I actually had seen that already, but dismissed it on the basis that I figured using FNS would be too computationally intensive. That is, I would have to first convert the decimal representation to a FNS representation, then convert the FNS representation...
Say I have three elements: A, B, C. I can list all the permutations by going alphabetical in the first element, then the second, then the third, and so on, like so:
ABC
ACB
BAC
BCA
CAB
CBA
What I'm wondering, is given a number N, how do I decompose this into knowing what permutation it...
It's my impression that this is a matter of definition rather than proof: we've co-defined "prime numbers" along with this axiom in the same sense that we co-define the speed of light and the length of a meter.
That is, they are understood together.
Hi guys, it's 3 AM so don't judge me. I'm doing some accounting work with my student loans and I want you to confirm something for me:
If I have two loans:
$1,598 @ 6.8% F-APR
$6,680 @ 3.8% F-APR
Then the 'equivalent' single loan would be:
$8,278 @ 4.38% F-APR
Correct? I used a...
Inequalities are solved mostly the same as equalities; the only difference is you must flip the inequality when multiplying or dividing it by a negative number.
Most importantly, try getting it into some more usable forms. This isn't too useful:
These two are better:
Does that make some...
EDIT: Sorry, I didn't realize he said powers! My bad!
Using only addition, subtraction, multiplication and division, it is not possible with a finite number of these operations.
That's the answer I gave: populate the buckets with powers of two and put the remainder in one "overflow" bucket.
The customer may ask for any number of marbles, but they don't care how many buckets they get. You only care how many buckets you store.
You are the owner of a marble warehouse where you store marbles in buckets. You can fit any number of marbles in one bucket. Your job is to store X marbles in a minimal number of buckets. But, when a customer comes and asks for Y number of marbles, you must be able to hand over some buckets...
There are many different types of interpolations, all based on "what you know" at different points. Most are based on knowing the value of a function at different points. I am not aware of any that use derivatives at some points, but not others. You may just have to get creative and invent...
You can.
Your equation is correct - but remember that when you "undo" a logarithm, you effectively make each side of the equation the exponent of the base. So when you "undo" the log, the right side will have a^0, which is 1. Anything to the power of zero is one. Solving that quadratic will...
I think you just did some of your math wrong. You should not be getting 4 and -3 as solutions. I will update with some work in a moment.
\log_a (x+3) + \log_a (x-4) = \log_a (8)
\log_a ((x+3)(x-4)) = \log_a (8)
\log_a (x^2 - x -12) = \log_a (8)
x^2 - x - 12 = 8
So, what are the solutions...
When you "undo" a squared operation, it is not as simple as just removing the little "2" superscript.
Really? In my classes, we've always used \sqrt[]{x^{2}}=\pm x
When you are done, you can use http://www.wolframalpha.com" [Broken] to check your answer. You can type in things like "x/(x+y)=z, solve for x". It will also show you the steps in doing so if you choose "show steps".
Thank you guys so much! I get it now. Just an FYI, I was asking because I'm trying to use the drag equation, which when applied to an object of constant mass, is one such example of a velocity-dependent acceleration!