I put together a couple of equations for you not to actually solve for, but to break out X from. Some are first-degree equations, some are second-degree, and the difficulty varies quite a bit. Remember to post the solutions step by step as it's extremely easy to just cram the equations into an equation solver/breakout otherwise:
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
Yeah, that answer is correct, but do post the steps you managed to solve it through.
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
I don't know what on earth you did with #1, but here's some basic hints for it:
5x(75x+32y)=5xy
375x^2+160xy-5xy=0
x(375x+155y)=0
So it's a second-degree equation, and one x has to equal 0, but see if you can figure out what the other one equals.
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
Oops, 255 should be 225 isntead, except for that it's all good.
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
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Ugh, #5 is giving me a headache, I can't crack it. y=(x-y)(2xy)-x is about as far as I get, and it definitely seems like it's gonna be a fourth-grader, so feel free to help me out with this one a bit.
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
#1 should have the y in the numerator rather than the denominator. Oh, and the other root is 0.
#2 is correct.
#3 is correct.
#4 is correct.
#5 is incorrect. You can't turn (x+y)/(x-y)=2xy into
-(y-x)/(x-y)=2xy, trying to break out -1 would result in -(-y-x)/(x-y)=2xy.
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
yea, for #1 it's hard to write it with one line but it's (-155/375)y
and yes, my #5 is wrong, i have a full load of classes today, and as a matter of fact i'm going to "matrix theory" right now, i did that in sorta a rush (my excuse, obviously), so i'll try to work on it later.
It's sorta embrassing as an engineer to get algebra problems wrong, then again nasa crashed into mars cuz they forgot to convert :-P.
Cheers.
C. M. Ngan
Aerospace Engineering
University of Illinois at Urbana Champaign