ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: ryley on June 23, 2009, 07:57:55 pm

Title: ryley's methods questions
Post by: ryley on June 23, 2009, 07:57:55 pm

In a practice test in class today, a question asked to find the values of p such that $y=px$ intersects $y=x^2+1$ twice. I was able to do this fine, but the next part asked to explain the geometric significance of this. Could someone please explain what is meant by geometric significance?

Thanks

ryley

EDIT:
Looking around, I found an answer to this identical question. It goes:

If $p=-2$ or $p=2$ , $y=px$ is a tangent, so there is one point of intersection
If $p>-2$ and $p<2$ , $y=px$ does not intersect with $y=x^2+1$
If $p<-2$ or $p>2$ , $y=px$ intersects twice with $y=x^2+1$

I think that is a correct response, as the question was worth three marks.

Title: Re: ryley's methods questions
Post by: TrueTears on June 24, 2009, 07:46:10 pm

Yeap I have thought about this and I have to agree with your answer, ie

If the gradient p is $\pm 2$ , the line is tangent to the parabola.
There is one intersection.

If p is greater than -2 and less than 2, the line misses the parabola.
There is no intersection.

If p is less than -2 or greater than 2, there are two intersections.

I think you would be awarded full marks for that.

Title: Re: ryley's methods questions
Post by: ryley on July 12, 2009, 07:07:11 pm

Another question, in exercise 15D, question 7, of the essentials book, could someone please walk me through it? I tried one way, but that choked my CAS and short of trial and error, I can't seem to see how to do it

EDIT: Resolved, see TrueTears post in another thread for procedure.

Title: Re: ryley's methods questions
Post by: ryley on August 22, 2009, 11:10:14 am

Just another quick question, if you have a continuous PDF defined by a hybrid function of two unique, non-zero functions, how do you work out the mean?

Thanks