# Mathematical Modelling, Vectors and Parametric Equations

1. Jun 7, 2015

### Nile Anderson

1. The problem statement, all variables and given/known data
Sorry to disappoint the math fanatics but no this is not a question that integrates all three topics at once but individual ones. I still need assistance though with the following more so in the reasoning behind them as I feel my logic is flawed.
https://scontent-mia1-1.xx.fbcdn.net/hphotos-xfa1/v/t34.0-12/11350393_1080048282023208_1468717877_n.jpg?oh=42c6757af8f078a9a8f525051260bde9&oe=5576CB04
https://scontent-mia1-1.xx.fbcdn.net/hphotos-xfa1/v/t34.0-12/11358829_1080048288689874_1045920915_n.jpg?oh=8a5bced9bb2de46109e19b8e50124969&oe=5575A90C
https://scontent-mia1-1.xx.fbcdn.net/hphotos-xpt1/v/t34.0-12/10003237_1080048292023207_149145089_n.jpg?oh=d49bf300e8c582b94ef1b70a47c9c616&oe=5575A4F2

2. Relevant equations
There are not really any relevant equations but look at my solutions below.

3. The attempt at a solution
I am pretty sure these are wrong
22D
28C
42C
43B

2. Jun 7, 2015

### Orodruin

Staff Emeritus
Please also state your reasoning behind your answers. Simply selecting on random does not really qualify as an attempt and it will be easier for everyone to see when/if you have the wrong idea.

3. Jun 7, 2015

### Nile Anderson

Sorry my good sir,
22) To be completely honest , the approach to this one is fuzzy for me as I have only done two variables at a time before this but i thought that i could square the x and y to get that x2 + y2 = r2cos2θ and then adding z squared would produce x2 + y2 +z2 = r2cos2θ + r2sin2θ= r2, is this correct , is there no simpler approach if so
28) This one was even trickier I imagined that is they were perpendicular then their dot product = 0 , but things got hairy when r.s came up , as I only had so far (r-s)(2r+3s)=0, I said r=s for one solution so r.s must me rs which makes no sense when I repeat it now .
42) I found the first derivative and assumed where it was greater than zero , the graph was increasing
43) I said it was 10 years between 1990 and 2000 and so it was zero to ten.

4. Jun 7, 2015

### Nile Anderson

Is this not satisfactory ?

5. Jun 8, 2015

### haruspex

For 43, you are right, but your explanation is a bit vague. Note the exact statement of the start and end times.
For 28:
Expand that and isolate r.s.

6. Jun 8, 2015

### Nile Anderson

Darn should have went with first instinct
(r-s)(2r+3s)=0
2r.r +3 s.r - 2s.r - 3s.s=0
2r2 + s.r -3s2=0
s.r= 3s2-2r2
Making A the answer, Thanks Mr. Haruspex Sir
About the integral one though, it was just basically an intuitive guess , I still don't understand why I would start at 0 and why end at 10 , why that would not work out to 11 years versus the 10 from 1990 to 1999 ( Because it is not the end of 2000), I am pretty clueless about that one, no intuition whatsoever

7. Jun 8, 2015

### Orodruin

Staff Emeritus
Exactly how many years are between Jan 1, 1990, and Jan 1, 2000? You are allowed to use decimals.

8. Jun 8, 2015

### Nile Anderson

10 years , yes ok but why do we start at zero , is that a general rule ?

9. Jun 8, 2015

### Orodruin

Staff Emeritus
No, this must be chosen according to how the time t=0 was selected, but this is not explicitly stated in the problem.