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Mathematics 45 Online
OpenStudy (iwanttogotostanford):

is this right?

OpenStudy (loser66):

nope the first entry is correct but the second one is not.

OpenStudy (loser66):

yup

OpenStudy (iwanttogotostanford):

@Loser66

OpenStudy (loser66):

yup

OpenStudy (loser66):

Can you see the relationship among the elements?

OpenStudy (iwanttogotostanford):

yeah i think it is B or D but I'm not sure

OpenStudy (loser66):

ok, so test B

OpenStudy (loser66):

\(a_n=3*(4^{n+1})\) Now, if I pick -12, that is \(a_2\) right?

OpenStudy (iwanttogotostanford):

yes

OpenStudy (loser66):

So, \(a_2= 3*(4^{2+1})=3*4^{3}=192\neq -12\)

OpenStudy (loser66):

Now, test D, you do

OpenStudy (loser66):

If you hate someone, do you want to hit him?

OpenStudy (loser66):

If someone scares you, do you want to hit him?

OpenStudy (iwanttogotostanford):

no

OpenStudy (loser66):

hahaha...

OpenStudy (iwanttogotostanford):

whats the point of these? can i please have help with my math

OpenStudy (loser66):

That is why you do not want to hit the problems scare you. To me, if I don't know how to solve it, I hit it as many times as I can if it helps me to master the process. I want you to practice. Just test D by yourself

OpenStudy (iwanttogotostanford):

ok i tested D on my paper and it came out wrong again

OpenStudy (loser66):

If D doesn't work, Test A, Test C until you get the answer I am done

OpenStudy (iwanttogotostanford):

ok i tested all of them and got C!

OpenStudy (loser66):

Bingo. You will go to standford!!

OpenStudy (iwanttogotostanford):

yay- thank you!!!

OpenStudy (iwanttogotostanford):

@Loser66

OpenStudy (loser66):

As usual, tell me your opinion first

OpenStudy (iwanttogotostanford):

I believe it is D @Loser66

OpenStudy (loser66):

why?

OpenStudy (iwanttogotostanford):

Substitute a = 25 and b = 15 in the ellipse equation. x2/(25)2 + y2/(15)2 = 1 x2/625 + y2/225 = 1

OpenStudy (loser66):

When they ask you about the vertices and foci at the same time, they meant the major vertices.

OpenStudy (iwanttogotostanford):

ok

OpenStudy (loser66):

So that, if foci are on the y -axis, then the vertices MUST on the y-axis also. for D) foci are \((0,\pm 15)\) so, \(c=\pm 15\), and \(c=\sqrt{a^2+b^2}=\sqrt{625+225}=29.15\neq 15\)

OpenStudy (loser66):

I give you my trick

OpenStudy (loser66):

the number under y^2 is 625, right? and 625 >225, right? so, the foci are on the y axis. ok?

OpenStudy (loser66):

So, the foci is under the form of (0, something)

OpenStudy (loser66):

hahaha...such a good future Standford student!!!

OpenStudy (loser66):

you got my medal for that correct answer

OpenStudy (loser66):

hey, greedy guy!! I am busy now. just 1 more!!

OpenStudy (loser66):

shoot

OpenStudy (loser66):

for cos, it is ALWAYS symmetric about x -axis.

OpenStudy (loser66):

and you need know the rules: About x-axis: both \((r, \theta), (r,-\theta)\) are on the graph. Let's test \(r= 5 cos (5\theta) \), if \(\theta =-\theta\), we have \(cos (\theta)=cos (-\theta)\) Hence \(r = cos(-5\theta)\) So, \((r,-\theta)\) is also on the graph. About y-axis: (-r, -theta) must be on the graph. now cos (-5theta) = cos 5theta = r and \(r\neq -r\), so it is not about y-axis. About origin (-r, theta) Must be on the graph. \(-r = - 5 cos (5 theta)\neq r\) Hence not about origin Conclusion: just about x-axis.

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