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Old 10-07-2009, 05:03 PM   #151
solsek
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Re: The Official Math/Physics/Whatever Homework questions thread

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Originally Posted by lastcardcharlie View Post
|a + bi| = sqrt(a^2 + b^2) = r and b/a = tan(theta).
Thanks for the fast reply. So I haven't taken a math class since my junior year of high school and now I'm a junior in college so please forgive me with all these dumb questions. The problem is 3 + 4i, and I just need to convert it to re^itheta. I get r = 5, and tan(theta) = 4/3. How do I convert this value in terms of pi? You don't need to give solutions, just a guide in the correct thought process and procedure would be great! This is for my physical chemisty class btw. Our assignment says to not use calculators and to simply everything.
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Old 10-07-2009, 05:21 PM   #152
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Re: The Official Math/Physics/Whatever Homework questions thread

Okay, hopefully someone can explain this to me. It is about solving a system of equations for three equations. Here is the example in the book: 2x+y-z=2
x+3y+2z=1
x+y+z=2
Solution: Begin by eliminating the term with x, this time from equations 2 and 3 as follows.
2x+y-z=2
-5y-5z=0
-y-3z= -2
My question is how did the book arrive at the last two equations?? There are a couple more steps to solve the problem, but I have to understand the first step before I move on. If anyone could help I would greatly appreciate it.
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Old 10-07-2009, 06:18 PM   #153
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Re: The Official Math/Physics/Whatever Homework questions thread

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...and tan(theta) = 4/3. How do I convert this value in terms of pi?
Sounds like theta is required to be in radians is all, since there's 2pi radians in a circle. I don't know if there's some cute way of doing it, or if you simply do tan^-1(4/3) in radian mode on your calculator.
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Old 10-07-2009, 06:25 PM   #154
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Re: The Official Math/Physics/Whatever Homework questions thread

Thanks, looks like its just a preference issue. Would leaving the exponent as i(tan-1(4/3))pi suffice as theta? Is that a standard notation?
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Old 10-07-2009, 06:30 PM   #155
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Re: The Official Math/Physics/Whatever Homework questions thread

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(#1): 2x+y-z=2
(#2): x+3y+2z=1
(#3): x+y+z=2

Solution: Begin by eliminating the term with x, this time from equations 2 and 3 as follows.

(#1): 2x +y -z = 2
-2*(#2): -2x-6y-4z=-2
(#1) - 2*(#2): -5y-5z = 0
(#1) - 2*(#3): -y -3z= -2
You're allowed to create new equations by

1) multiplying an old equation by a constant.
Idea: If Left Side = Right Side, then certainly
c*(Left Side) = c*(Right Side)

2) Adding two equations together (on both sides)
Idea: If A = B and C = D, then
A + C = B + D

So combining those ideas together, we can multiply an equation by a constant and add the resulting equation to an existing one. In the case above, we used this technique to cancel the x's in eqns #1 and #2.

Hope this helps.

-BW
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Old 10-07-2009, 06:30 PM   #156
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Re: The Official Math/Physics/Whatever Homework questions thread

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Thanks, looks like its just a preference issue. Would leaving the exponent as i(tan-1(4/3))pi suffice as theta? Is that a standard notation?
yes

edit: lol that i had to wait to post this, since the forum requires > 25 seconds between posts. Seriously, I got flagged for that in a math homework help thread. FML.

edit #2 -- siegmund is right. you added an extra pi and I missed it. theta = arctan(4/3).
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Old 10-07-2009, 06:31 PM   #157
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Re: The Official Math/Physics/Whatever Homework questions thread

theta=arctan(4/3) may well be acceptable. Not the extra pi. arctan(4/3) is a number -- about .927 radians, or 53.1 degrees, or 0.295*pi radians.

It doesn't look like their intention is for you to search for a rational equivalent.
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Old 10-07-2009, 06:41 PM   #158
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Re: The Official Math/Physics/Whatever Homework questions thread

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Would leaving the exponent as i(tan-1(4/3))pi suffice as theta?
Just i(tan^-1(4/3)). Note that this form does not specify whether theta is to be considered in radians or degrees. They're just different units of measurement, like miles and kilometres. x degrees = x(pi/180) radians.
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Old 10-07-2009, 09:07 PM   #159
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
Originally Posted by Wyman View Post
You're allowed to create new equations by

1) multiplying an old equation by a constant.
Idea: If Left Side = Right Side, then certainly
c*(Left Side) = c*(Right Side)

2) Adding two equations together (on both sides)
Idea: If A = B and C = D, then
A + C = B + D

So combining those ideas together, we can multiply an equation by a constant and add the resulting equation to an existing one. In the case above, we used this technique to cancel the x's in eqns #1 and #2.

Hope this helps.

-BW
Yes, thanks for clearing this up for me.
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Old 10-07-2009, 10:41 PM   #160
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Re: The Official Math/Physics/Whatever Homework questions thread

Thanks everyone for the help. Helped out a lot since I had 15 of these problem to work out.
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Old 10-07-2009, 10:51 PM   #161
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Re: The Official Math/Physics/Whatever Homework questions thread

Cool problem from my math test today. I had about 10 minutes to do it.

How many integers between 0 and 10,000 have digits that sum to 13?
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Old 10-07-2009, 11:07 PM   #162
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Re: The Official Math/Physics/Whatever Homework questions thread

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Cool problem from my math test today. I had about 10 minutes to do it.

How many integers between 0 and 10,000 have digits that sum to 13?
Spoiler:
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Old 10-07-2009, 11:37 PM   #163
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Re: The Official Math/Physics/Whatever Homework questions thread

Why for small angles does sin(theta) = theta? Can someone explain the reasoning behind, or point to a website that can show some graph/pictures why? I remember something about pendulums and why we can use sin(theta) = theta for solving for variables in a pendulum problem but I don't have the slightest idea how to explain it, our physics professor just said assume sin(theta) = theta for small angles and never explain why in detail.

Also quick question...pretty simple one, just want to make sure if I am on the right track - lol first assignment with no lectures about it and its due tomorrow

Simplify: 2e^(3ln(2)) = (2e^3)(e^ln2) = (2e^3)(2) = 4e^3

Sound about right?

Last edited by ManUTDFan; 10-07-2009 at 11:55 PM.
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Old 10-07-2009, 11:51 PM   #164
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Re: The Official Math/Physics/Whatever Homework questions thread

How much, if any, calculus do you know?

edit: the short answer is just -- graph y=x and y=sin(x), and see that they are very close near x=0. The longer answer can involve tangent lines, linearization, and/or Taylor series.

Last edited by Wyman; 10-08-2009 at 12:02 AM.
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Old 10-08-2009, 12:00 AM   #165
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Re: The Official Math/Physics/Whatever Homework questions thread

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How much, if any, calculus do you know?
If this is referring to me, I took calculus in high school and never bothered to take it in college (always putting it off until next semeter haha, bad idea, forgot everything). That was about 5 years ago and I am retaking it because some medical schools require college calculus ldo. Btw, what I am working on is like a "warming up math skills" homework assignment, the class isn't a calculus class, just uses math to derive certain equations that we will end up using.

edit: Thanks for the help, I will look up some of the long answer hints you gave me and see if I can jog my memory.
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Old 10-08-2009, 12:05 AM   #166
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Re: The Official Math/Physics/Whatever Homework questions thread

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Originally Posted by ManUTDFan View Post
Simplify: 2e^(3ln(2)) = (2e^3)(e^ln2) = (2e^3)(2) = 4e^3

Sound about right?
No. a^(bc) = (a^b)^c = (a^c)^b, whereas a^(b+c) = a^b * a^c.
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Old 10-08-2009, 12:07 AM   #167
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Re: The Official Math/Physics/Whatever Homework questions thread

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If this is referring to me, I took calculus in high school and never bothered to take it in college (always putting it off until next semeter haha, bad idea, forgot everything). That was about 5 years ago and I am retaking it because some medical schools require college calculus ldo. Btw, what I am working on is like a "warming up math skills" homework assignment, the class isn't a calculus class, just uses math to derive certain equations that we will end up using.

edit: Thanks for the help, I will look up some of the long answer hints you gave me and see if I can jog my memory.
The tangent line is a local approximation to a curve. ie "Near" the point of tangency, the curve "looks like" the tangent line. The tangent line to y=sin(x) at x=0 is y=x, so "near 0", we can approximate sin(x) by x.
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Old 10-08-2009, 12:12 AM   #168
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Re: The Official Math/Physics/Whatever Homework questions thread

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No. a^(bc) = (a^b)^c = (a^c)^b, whereas a^(b+c) = a^b * a^c.
Ahh, ok thanks.

Ended up getting 2e^(3ln2) = 2e^ln(2^3) = 2e^ln8 = 16


Appreciate all the help.
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Old 10-08-2009, 01:10 AM   #169
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Re: The Official Math/Physics/Whatever Homework questions thread

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How did you get that number? I left my answer in choose notation, and didn't add it up.
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Old 10-08-2009, 02:47 AM   #170
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Re: The Official Math/Physics/Whatever Homework questions thread

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How did you get that number? I left my answer in choose notation, and didn't add it up.
He's wrong. It's a tetrahedron with 4 corners chopped off.
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Old 10-08-2009, 08:53 AM   #171
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Re: The Official Math/Physics/Whatever Homework questions thread

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Old 10-08-2009, 09:10 AM   #172
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Re: The Official Math/Physics/Whatever Homework questions thread

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Spoiler:
561-81=480

=C(16,3)-4C(6,3)

As I said, it's a tetrahedron with 4 corners chopped off. DUCY?
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Old 10-08-2009, 09:14 AM   #173
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Re: The Official Math/Physics/Whatever Homework questions thread

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561-81=480

=C(16,3)-4C(6,3)

As I said, it's a tetrahedron with 4 corners chopped off. DUCY?
lol -- I am teh suck at adding. Yes, clearly 480.

And yes, I see why, and I'm a touch embarrassed I didn't notice that sooner.
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Old 10-08-2009, 12:27 PM   #174
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Re: The Official Math/Physics/Whatever Homework questions thread

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561-81=480

=C(16,3)-4C(6,3)

As I said, it's a tetrahedron with 4 corners chopped off. DUCY?
I did the math out, and I got to 480, but I don't quite understand the 4C(6,3) part. I had a much longer way to find a sum that adds up to 4C(6,3). I also don't understand the tetrahedron part. Would it be possible to explain this?

Thanks!
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Old 10-08-2009, 02:00 PM   #175
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Re: The Official Math/Physics/Whatever Homework questions thread

I am having trouble with this last problem in my homework set. The problem is

Integrate: e^(-4x^2)dx from -infinity to +infinity.

I tried looking up identities for integrating e^(-ax^2) but only managed to find one possible hopeful hint. I found that integrating e^(-ax^2) from 0 to +infinity has the solution of (pi/4a)^(1/2). So I just split the integral from -infinity to 0 and from 0 to +infinity (I get (pi/16)^(1/2) for the integral from 0 to +infinity). I am not sure how to evaluate the -infinity to 0 portion. Is there a better way to solve it?
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