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

Quote:
 Originally Posted by lastcardcharlie |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.

 10-07-2009, 05:21 PM #152 Never Win veteran     Join Date: Jun 2009 Posts: 2,317 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.
10-07-2009, 06:18 PM   #153
lastcardcharlie
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by solsek ...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.

 10-07-2009, 06:25 PM #154 solsek Carpal \'Tunnel     Join Date: Feb 2008 Posts: 6,003 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?
10-07-2009, 06:30 PM   #155
Wyman
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Never Win (#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

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

Quote:
 Originally Posted by solsek 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).

 10-07-2009, 06:31 PM #157 Siegmund Pooh-Bah     Join Date: Feb 2005 Posts: 4,105 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.
10-07-2009, 06:41 PM   #158
lastcardcharlie
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by solsek 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.

10-07-2009, 09:07 PM   #159
Never Win
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Wyman 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.

 10-07-2009, 10:41 PM #160 solsek Carpal \'Tunnel     Join Date: Feb 2008 Posts: 6,003 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.
 10-07-2009, 10:51 PM #161 Myrmidon7328 old hand     Join Date: Dec 2007 Posts: 1,960 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?
10-07-2009, 11:07 PM   #162
Wyman
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Myrmidon7328 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:

 10-07-2009, 11:37 PM #163 ManUTDFan centurion   Join Date: Oct 2006 Posts: 139 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.
 10-07-2009, 11:51 PM #164 Wyman Carpal \'Tunnel     Join Date: Mar 2007 Location: Redoubling with gusto Posts: 12,023 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.
10-08-2009, 12:00 AM   #165
ManUTDFan
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Wyman 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.

10-08-2009, 12:05 AM   #166
Wyman
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by ManUTDFan 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.

10-08-2009, 12:07 AM   #167
Wyman
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by ManUTDFan 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.

10-08-2009, 12:12 AM   #168
ManUTDFan
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Wyman 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.

10-08-2009, 01:10 AM   #169
Myrmidon7328
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Wyman Spoiler: 561? Or am I teh suck at adding?
How did you get that number? I left my answer in choose notation, and didn't add it up.

10-08-2009, 02:47 AM   #170
thylacine
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Myrmidon7328 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.

10-08-2009, 08:53 AM   #171
Wyman
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Wyman Spoiler: 561? Or am I teh suck at adding?
Spoiler:

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

Quote:
 Originally Posted by Wyman Spoiler: I counted numbers like 0076 (but I was smart enough to not count it twice). I guess this means I counted all the 2 and 3 digit numbers twice, so I should be taking 81 away. So uhh how about 460?
561-81=480

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

As I said, it's a tetrahedron with 4 corners chopped off. DUCY?

10-08-2009, 09:14 AM   #173
Wyman
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by thylacine 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.

10-08-2009, 12:27 PM   #174
Myrmidon7328
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by thylacine 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!

 10-08-2009, 02:00 PM #175 solsek Carpal \'Tunnel     Join Date: Feb 2008 Posts: 6,003 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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