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How would you prove this:
I'm confused on how you would prove them...
Is there a way to get Mathematica to solve a system over the integers?
I guess I can reduce down the equations a bit, but I'm not too sure if that'll help that much.
Hm... yes, I think that is correct.
I'm basically expanding out two functions and setting coefficients equal to each other...
Hm... why can't Mathematica not solve
Solve[{c, a+c^2 d, a^2+b+c d^2+c^2 e, a^2 b+ b^2+ d^2 e+c e^2, a^3+6 a b+d^3+6 c d e, a b^2+3 d e^2, b^3+e^3}=={h,f, f^2+g+h^2 t, f^2 g+g^2+h t^2, f^3+6 f g, f g^2, g^3+t^3}]
It just sits there loading! I'm trying to find the unknown variables... Is there something wrong with the syntax?
It then turns out that you can factor the remaining quartics into quadratics by having them factor over the extension of Sqrt[13+4 Sqrt[5]] and Sqrt[13-4 Sqrt[5]].
That's so cool!
I now have accomplished factoring
I learned that you can factor
Okay, thanks. I also realized \[Theta] will also work...
How do you add greek symbols such as
into your plots? Simply entering Theta doesn't work...Yes, I got the plot to work! (Yay!)
Although nothing showed up, implying I need to change the domain and range of the plot to get it to actually plot. Any ideas?
Never mind, I figured it out.
Yes.
I was using the online version of Mathematica, and I'm wondering if there is a way to delete your notebook cells...
I have the function
Plot3D[Sin[47^{64.9/Cos[90.469+x/y]}]{x,-5,5},{y,-10,10}]
And I want to graph it in 3D. But Mathematica won't graph it. It just doesn't seem to respond. What's going on? Am I doing something wrong with the brackets?
Yes.
How do you remember all of the commands? I have no idea what "ToExpression", "ToString i" and all those random i/n means.
As much as I can guess, you're telling Mathematica to find the number of digits with 1 from 1 to 999....
By the way, I got a 15 day trial of Mathematica. How do I use it? What are the commands?
I can't simply enter something like Solve[something here!] for a. Mathematica doesn't understand that...
But is there a way to represent v and u in terms of m and n?
For example:
So I'm wondering if it's possible to represent u,v in terms of m and n in:
Sorry that I didn't explain well enough...
(1) Catherine and Doris enter the first floor of the skyscraper, Taipei 101, and have to get to a meeting on a certain floor. The elevator is at the very top floor. It takes the elevator 1 minute to reach the first floor from the top floor, and 1 second to move up each floor. Alternatively, if you decide to walk up the stairs, while Catherine waits for the elevator and then takes the elevator up. They both arrive at the meeting at the same time. On which floor was the meeting held?
(2) Let x be a two-digit positive integer. Let y be the two digit integer that results from switching the order of the digits of x. Let z=x+y. How many possibilities are there for x such that z is a perfect square?
(3) The natural numbers 1,2,3,4,...,999 are written down in one long string. The string looks like this: 12345...998999. How many 1s appear in this string.
(1) seems similar to a classic speed distance problem, but I'm not too sure how to set up the equation.
I just don't know where to start on (3)
Sure, that works. But I'll need to solve for u in (1).
Eheu. Ego sum mortuus.
I just have a real quick question, but is the mathematical computing program Sage a good program to use to calculate messy Algebra? I'm just wondering!
I'm guessing you use Mathematica. Most people use Mathematica. But I'm wondering if Sage is a program that can rival that of Mathematica's, since I'm looking for a smart, and quick math-computations program. But would not like to pay money...
This is two separate questions:
(1)
Solve for u in(2)
Solve for v inI need help. Wolfram Alpha gives me the pounds symbols, which is something I don't understand and don't want. I want the exact solutions in terms of the other variables.
Given
Like... reduce the equation to another equation.
But I don't need values for m,n,s,t. I just want to simplify the above equation...
For
, we have to consider the cases when . Most notably, we have b=0, a=1 as the obvious ones.For the third problem,
which you can use Vieta's formula...This is an exponential decay...