I'm trying to decide if simplifying sqrt(y^6) requires use of the absolute value bars. For example, the rule "nth root(u^n) = abs(u) when n is even" can be used to simplify sqrt(y^6) as sqrt[(y^3)^2]=abs(y^3). However, the rules of rational exponents can also be used to simplify sqrt(y^6) as...
Homework Statement
Use the method of separation of variables or an integrating factor to find a particular solution of the differential equation that satisfies the given initial condition.
y'=x-y+2 ; y(0)=4
2. The attempt at a solution
I've used an integrating factor of e^{x} to...
SORRY FOR THE LACK OF FORMATTING, I SPENT 30 MINUTES TRYING TO FORMAT AND IT KEPT GETTING MESSED UP.
Homework Statement
Evaluate by substitution.
Integral of dx/xln(x^2)
Homework Equations
integral of 1/u du = ln(u) + C
The Attempt at a Solution
u = ln(x^2)
du = 2/x...
1. Suppose we have two tanks, each with an inflow pipe and an outflow pipe and also connected to each other by pipes. At the start, tank A contains 40 gallons of clean water and Tank B contains 25 gallons of clean water. At t = 0 brine containing 0.5 lbs of salt per gallon begins to flow into...
Homework Statement
I am working on a problem and am wondering what 0/dt is.
The Attempt at a Solution
Is it just 0, or does it turn into something with t?
Homework Statement
In the ABC msgbox I would like the variable 'score' to appear after 'Your score was'. How do I do this?
Homework Equations
%tells the user their overall tv knowledge
score=A+B+C;
title1='Your TV Knowledge';
if ((A+B+C)<=24)&&((A+B+C)>=18)
ABC=msgbox('You are a...
Homework Statement
I need to do a final project for my Intro to MATLAB class and I have no idea what to do it on. Does anyone have any ideas for a program I could create? Other students are doing card tricks or games like MASH.
Well I can clearly see that a+b=b+a, (a+b)+c=a+(b+c), a(bc)=(ab)c, a(b+c)=ab+ac, and (b+c)a=ba+ca, and that there is an additive identity 0 st a+0=a for all a in R
So, I guess the non-obvious property is that there is an element -a in R such that a+(-a)=0, but is this property even true?
Homework Statement
Let R={0, 2, 4, 6, 8} under addition and multiplication modulo 10. Prove that R is a field.
Homework Equations
A field is a commutative ring with unity in which every nonzero element is a unit.
The Attempt at a Solution
I know that the unity of R is 6, and that...
I think so. Is this proof correct:
Let a\in Q, \epsilon rational, where \epsilon\in[r-a, s-a].
Then r-a<\epsilon<s-a, so r<\epsilon+a<s
So \epsilon+a\in[r, s] and \epsilon+a is irrational.
Therefore in any interval, there exists an irrational number.
Homework Statement
Prove that in any interval there exists an irrational z.
Homework Equations
The Attempt at a Solution
My professor wrote this for me when trying to explain how to prove this:
a \notin Q, \epsilon rational
[r, s]\in a
l([r, s])<\frac{\epsilon}{2}...
I just realized that I mistyped what I am trying to prove. It is supposed to be "prove that in every interval there exists an irrational z. That is why I was so confused with your proof. Thank you for all of your help, and I apologize for wasting your time. I will create a new thread about the...
I'll try to figure out how to prove this using your method, but I don't see where to go with your proof, or even why the things you've stated help to prove this.
If anyone else has something to say about the proof my professor stated, I'd still appreciate hearing it.