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Engineer's Math Help Thread v.2
Topic Started: Sep 7 2011, 09:25 PM (963 Views)
Rockman
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hoighty-toighty

School has started back up, and most of you are back at it. I'm here to make your math related woes go away.
From doing your math homework, to simply getting help and understanding, just post it here.
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Jonnoley
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This is the best topic ever. Oh let me borrow your knowledge!

So yeah, I'm starting a university in a few weeks to do a physics degree, and had a browse through my textbook today only to realise I literally had no idea how the addition/subtraction/Scalar product of vectors work any more. :( I did it about a year ago in maths, and didn't need it last year, so it's all been completely forgotten.

So, if possible, could I have a quick reminded of the basics of vectors? I don't need too in detail, once I've remembered it should be fine.

Here's some gratitude up front: Thanks.
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Rockman
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hoighty-toighty

Jonnoley
Sep 7 2011, 10:14 PM
This is the best topic ever. Oh let me borrow your knowledge!

So yeah, I'm starting a university in a few weeks to do a physics degree, and had a browse through my textbook today only to realise I literally had no idea how the addition/subtraction/Scalar product of vectors work any more. :( I did it about a year ago in maths, and didn't need it last year, so it's all been completely forgotten.

So, if possible, could I have a quick reminded of the basics of vectors? I don't need too in detail, once I've remembered it should be fine.

Here's some gratitude up front: Thanks.
Vectors of ijk denote the direction based on Cartesian coordinates. A typical vector will have both direction and force with the multiplication of a scalar.

70(3i-4j+2k)
The first part 70 denotes a force as a scalar. Multiplying the 70 to each term will give you an answer that is combined in terms of direction and force.
i represents x direction
j represents y direction
k represents z direction.
Take away the z portion to just have 2 dimensions.
Addition of vectors is per direction. So all of the i terms can be added or subtracted from all of the second vectors i terms, and so on with the rest.

cos(angle) = F/ |F|
which states that the inverse cosign of a set of direction vectors, divided by the magnitude of the vector, equals the angle between them.
The magnitude is found by taking the squared root of the sum of the squared direction vectors. ie,
sqrt(3^2+(-4)^2+2^2)

Dot product of two vectors is found by multiplying each portion of the two vectors, and then summing the portions.
AxBx(i)+AyBy(J) ... etc is the dot product of two vectors A and B.
Also, AdotB = |A| |B| cos(theta).

The sum of all force vectors is equal to a resultant force.
In statics, the sum of all forces and moments are equal to zero, once an equilibrium representation is found.

Maybe this will help.
Edited by Rockman, Sep 7 2011, 10:51 PM.
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Jonnoley
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That is enormously helpful, thank you so much.
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Plush
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The gun that won that old Wild West

So, this is probably very simple for you, but I'm having trouble with it. I'm taking Pre-Algebra and I took a test today and made a 55 (F) but 99% of the class did terrible too so he let us take the test home and correct the ones we missed.

Here are some -

Use the distributive property to simplify each expression.

6.) 4(x - 3)

7.) 8(x + 6)

8.) -4(3x +5)

9.) -6(3x - 5)

--------------------------

Simplify each expression.

15.) 3(2c + 5c)

16.) 4(x + 3) + 8x

17.) 5(y - 7) - y + 7

18.) -2(2m- 1) + 4

19.) 8n - (n - 3)

20.) 20x - 6 (x + 5)

-------------

that's it. I'm embarrassingly bad at math, any advice would be appreciated too.
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Ani-Nation
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Stewbear here's an example problem

4(20 +7)
=4(20) + (7)
=80 + 28
=108

Hope that helped :X
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Cal
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I may not deserve to live, but I will protect those in my reach with my reverse blade!

--------------------------

Simplify each expression.

15.) 3(2c + 5c) = 21c

16.) 4(x + 3) + 8x = 12x + 12

17.) 5(y - 7) - y + 7 = 4y -28

18.) -2(2m- 1) + 4 = -4m + 6

19.) 8n - (n - 3) = 7n + 3

20.) 20x - 6 (x + 5) = 14x - 30

I could be wrong on all of them. I haven't done mathematics in a while. Kudos.
Edited by Cal, Sep 13 2011, 01:06 AM.


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Rockman
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hoighty-toighty

Oh, overly eager friends I have. lol.

Stewbear, here are some rules for any variable that may help you out in the future.

Let's use X for all of our problems.
There exists a 1 in front of X. Always. End of discussion. as you can multiple X by 1 any time.

So, when you're multiplying an integer say 3, by X. What you're really doing is 3(1(X)) 3 times 1 times X.
The 1 becomes a 3, but the one never goes away either.
When we do algebra, the most important step to realizing greater functionality is to multiply through both sides of an equation, 1. Because 1 times 1 is 1. 1 times anything is 1. So you are left with the original equation, even though you're multiplying it by 1. But 1 can come in many different forms. 3/3 is 1. so for instance:
3x = 4
(1)x = 4/3 Do you see where the 3 went?

When crossing the equal sign, you want to do the opposite of what you had. So say you want to move the three over, then you divide the number on the other side by 3.
Take for example:

3/x = 4
x = 3/4 because 3(1/x) = 3/x and 3/4 = 3(1/4)

Distributive properties, all you have to do is remember order of operations. Parenthesis first, multiplication and division second, addition and subtraction next.
15.) 3(2c + 5c) = 21c
Cal did this one by:
3*2c + 3*5c --> 6c + 15c = 21c
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Sheeves
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Hey Engineer, what's your occupation/degree? Just wondering
Mr. Popo: "I want you to put on a blindfold and catch this cat".
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Rockman
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hoighty-toighty

Sheeves
Sep 13 2011, 03:28 AM
Hey Engineer, what's your occupation/degree? Just wondering
I love it when people ask me that question. :lolz:
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+ Dan
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Better than Red.

I have a question Mr. Engineer, sir.

A particle is moving with constant acceleration in a straight line. It passes through three points, A, B and C with speeds 20m s^-1, 30m s^-1 and 45m s^-1 respectively. The time taken to move from A to B is t1 seconds and the time taken to move from B to C is t2 seconds.

Show that t1 / t2 = 2 / 3
Is it too late to tell you that I don't mind.


Keep Calm And Chupa No Pilau


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Rockman
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hoighty-toighty

Oh this is a semi-easy problem. Because its hidden in physics, it looks difficult. Its not.

All you need to do is prove a ratio of two things.
The math:
B-A = t1
C-B = t2
(B-A)/(C-B) = 2/3
Plug a,b,c, into the above equation, and you'll notice it equals 0.6666666667 when you hit enter.
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Sheeves
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Engineer
Sep 13 2011, 03:07 PM
Sheeves
Sep 13 2011, 03:28 AM
Hey Engineer, what's your occupation/degree? Just wondering
I love it when people ask me that question. :lolz:
<_< Lol okay, smartass. I figured you were an engineer of some sort. Is it mechanical, electrical, computer engineering or what? :)
Mr. Popo: "I want you to put on a blindfold and catch this cat".
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Optimus Banana
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What's an easy way to remember properties? Like in the problem
pie + 15 = 15 + pie
I have trouble remembering them.
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Rockman
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hoighty-toighty

About 37 Llamas
Sep 14 2011, 10:55 PM
What's an easy way to remember properties? Like in the problem
pie + 15 = 15 + pie
I have trouble remembering them.
You'll just have to get used to remembering them. The further advanced you get, the easier it is. I don't properly know every property by heart either. But I understand how to do most problems without reciting the property involved.

Knowing that anything + something is always going to be something + anything, is just extra information. Try not to get too bogged down into those details, but rather the function of addition.
There exists a function Sigma, or Summation, that allows a series of things to be added together, and it doesn't matter what those things are out to infinity. The property of addition always works regardless of how its being applied.

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<_< Lol okay, smartass. I figured you were an engineer of some sort. Is it mechanical, electrical, computer engineering or what? :)

Electrical Engineering.
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