yeah i think that may have been it, ive just been doing heaps of exams lately, and 4th exam 2 of the day as well so i was fried haha.
would you be able to explain to me last question of graphs and relations http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf
why they subtracted the equations and made it equal 3
cheers man
Okay so this question. They're asking you to find WHEN they're 3km apart. To do this we can create an equation to find the distance between them. We can do this by subtracting the equation of Michael's Journey from Katie's journey. It's kinda hard to really articulate without printing this out and doing it via hand but I chucked them into CAS and found I have to use Michael's first journey equation.
We can conclude that if we subtract the distance of Michael's first journey from Katie's journey we will have an equation for the distance apart.
So dissecting this you can see we are subtracting the distance of Michael's first journey from Katie's journey and then equating it to 3 (Trying to find when the distance between is equal to 3)
BUT All we have found is when they are first 3km apart - now we need to find when they are last 3km apart. Now if you were to draw Katie's journey onto the graph given you'd see it is approximately 3km away at t=3. So we know it is approximately at t=3. To confirm we are going to have to subtract Katie's journey from the journey of Michael (This time it is rather easy as he's not moving so d=10 is the equation).
Dissecting this you can see we subtracted Katie's journey from the journey of Michael at t=3. Solving this:
So we can conclude they were first 3km away at 1.625km, They continued to get closer and closer and finally were 3km seperated again at 3km. So for 3-1.625 their radio transmitters would work.
Not gonna lie - this was a wierd question, first time I've seen something like this in a further exam. I guess it shows that only 3% of people got full marks for question 2.
In response to the post above I have done about 25 or 26 or something exams. Planning on doing another 5-10 in the time between English and Further.