4U Maths Question Thread

[Mei2016]

Hi,

I'm stuck on a few questions from paper 1999
Q2c) why is Re(z)= -1 an empty circle?
Q2e) isn't turning anticlockwise x i, and turning clockwise x -i ?
So answer should be -->AP= -Z(1)i? [But ANS is -->AP =Z(1)i]

(I tried to upload the pics of the question, but it didn't work)

Mod edit: Merged posts. Try to keep everything together

[RuiAce]

Hi,

I'm stuck on a few questions from paper 1999
Q2c) why is Re(z)= -1 an empty circle?
Q2e) isn't turning anticlockwise x i, and turning clockwise x -i ?
So answer should be -->AP= -Z(1)i? [But ANS is -->AP =Z(1)i]

(I tried to upload the pics of the question, but it didn't work)

Mod edit: Merged posts. Try to keep everything together

Are we talking about the 1999 HSC exam? Because Q2c) of that does not have Re(z).

If the diagram failed to upload, what paper are you trying to refer to

[Mei2016]

Yep, it's the HSC 1999 paper. So you have to sketch the region on the Argand diagram so the x-axis would be Re(z) and the y-axis would be Im(z) right?

(I'm new to the site, so this is taking me a while...)

[RuiAce]

This is the 1999 paper

Q2c) says to sketch the region bound by |z-i|≤2 and 0≤arg(z+1)≤π/4

[Mei2016]

sorry, that question seems so dumb now...
I get it now; just needed a quick scan of the textbook  ....
sorry for wasting your time 

[Mei2016]

What about Q2e) ?

Also, for Q6bvi) I followed through i to v) but when I got up to vi) what's U, U(o) and V? and also, T(o) is the total time if air resistance is ignored so this should be smaller than T (which if the total time with air resistance-I think) ? >>because an object falling with no air resistance will fall quicker than an object falling against air resistance. [But the ANS is T(o) > T]

Thanks.

[RuiAce]

Hi,

I'm stuck on a few questions from paper 1999
Q2c) why is Re(z)= -1 an empty circle?
Q2e) isn't turning anticlockwise x i, and turning clockwise x -i ?
So answer should be -->AP= -Z(1)i? [But ANS is -->AP =Z(1)i]

(I tried to upload the pics of the question, but it didn't work)

Mod edit: Merged posts. Try to keep everything together

Regarding 2e) That is an anticlockwise rotation. Keep in mind the direction of the vector.

PA is a clockwise rotation.

However, AP is an anticlockwise rotation.

[RuiAce]

What about Q2e) ?

Also, for Q6bvi) I followed through i to v) but when I got up to vi) what's U, U(o) and V? and also, T(o) is the total time if air resistance is ignored so this should be smaller than T (which if the total time with air resistance-I think) ? >>because an object falling with no air resistance will fall quicker than an object falling against air resistance. [But the ANS is T(o) > T]

Thanks.

[Mei2016]

Thanks so much for your help Rui! That made the question a lot clearer. I get it now. Previously, I was really confused with all the Ts, Us, and Vs and I was visualising the fall of the object downwards only. So T which is with air resistance is 'pushed' against by the air downwards while it's travelling upwards resulting in a lower maximum height compared to T(o) which is without air resistance, thus allowing it to have a greater max height. So T(o)>T.

Thanks again. 

[znaser]

Hi, how do u solve this question?
In how many ways can 5 different red roses and 3 different white roses be planted in a straight line next to a fence so that no 2 white roses are together?
I personally did: 8! - 6! x 3! but this equates to 36 000 and the answer is 14 400. Can you please also tell me wat is wrong with my working out. Thanks

[RuiAce]

Hi, how do u solve this question?
In how many ways can 5 different red roses and 3 different white roses be planted in a straight line next to a fence so that no 2 white roses are together?
I personally did: 8! - 6! x 3! but this equates to 36 000 and the answer is 14 400. Can you please also tell me wat is wrong with my working out. Thanks

Can't exactly follow your logic how 6!3! eliminates the cases when the white roses are planted together in your working.

[znaser]

Can't exactly follow your logic how 6!3! eliminates the cases when the white roses are planted together in your working.

Thanks! Well I did 6! x 3! as the white roses being together as you would consider the 3 roses as a group and therefore there would be 6! ways of arranging them with the 5 roses and 3! ways of themselves being arranged in their own group. My wording is not probably the best but that's how I usually tackle these sorts of questions and I'm not sure why this method doesn't get me to the answer like it usually does. Do u know y that is the case?

[jamonwindeyer]

Thanks! Well I did 6! x 3! as the white roses being together as you would consider the 3 roses as a group and therefore there would be 6! ways of arranging them with the 5 roses and 3! ways of themselves being arranged in their own group. My wording is not probably the best but that's how I usually tackle these sorts of questions and I'm not sure why this method doesn't get me to the answer like it usually does. Do u know y that is the case?

I follow you! That covers cases with all three white roses together, but if you think carefully, it actually doesn't cover two at a time. So, you aren't subtracting enough cases, which is why your answer is higher than it should be

I love the method you use, and often it works really well, just not in this case, you need to be very careful with probability!

[Mei2016]

Hi znaser,

I might be wrong, but I'm pretty sure that with your method, for the white flowers; it's just 6x3! as if you imagine the 3 flowers as a bunch, you can order them with only 6 choices and not 6! choices.

So instead, the answer should be 8!-3!x6= 40284, unless if I have done something horribly wrong

[Mei2016]

But this doesn't align with Rui's answer (which I fully understand) so I'm pretty sure my working out is somehow horribly wrong....
(but I don't know why it doesn't work ...)