Past paper help please (1 Viewer)

[Boonyak]

Hey guys im doing 2006 past paper i have the success one but dont get the answer:

Questions:
6) b(iii)
7) a(ii) b(ii), c(ii)
8) (iii)(iv)

I know you can tell me all of them but at least one thanks

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_06.pdf (paper).

Would you deem this paper difficult or easy thanks for help

 

[S1MZ8]

limiting value 1? well when t tends to infinity, e^-0.05t tends to 0, thus, P=150

 

[bobmcbob365]

6. b iii.

Basically, what the question is asking, what P will be, if t reaches infinity.
So as t reaches infinity, -0.05t reaches minus infinity.
So as t reaches infinity, e^0.05t reaches 0, because 1 divided by infinity is a really small number.

So you basically treat it as 0. So the answer is just 150.

7. a ii.

What you got in part (i) was ab = 1, so b = 1/a

So you substitute that into part (ii), to get a + b. And you can use sum of roots formula.

b. ii.
solve the two lines simultaneously. i.e. 2x^2 +kx + 9 = 2x+1
then let the discriminant be less than 0.


8. a. iii.



8.a. iv.
The equation x=1- 7/(t+4) as you can see, is the equation for a hyperbola. Now to find the vertical asymptote, make the denominator equal to 0. and for the horizontal asymptote, take make t=infinity. i.e. x=1

 

[S1MZ8]

7aii)For this, use results from (i), i got product of roots=1 and sum of roots=3, substitute from product of roots, beta=1/alpha into sum of roots, you get alpha + 1/alpha=3

 

[J2good4u]

6) b(iii) so it's like finding an asymptote you have to see what it approaches as e^-0.05t approaches infinity
so if you start sticking big numbers, 100, 1000, 1000000 etc you'll see it = 0 therefore p = 150 + 300(0) = 150

7) a(ii) need to do sum of the roots so alpha + beta and from part (i) we know that alpha x beta = 1 so beta = 1/alpha sub this into part (ii) therefore you get:
alpha + 1/alpha = 3

b(ii) don't know how to draw on pc lol

c(ii) solve y=2x^2+kx+9 and y=2x+1 simultaneously and if they don't intersect the line the discriminant must be < 0 so whatever you get from solving simultaneously make that < 0 and solve like a normal inequality

 

[S1MZ8]

6. b iii.

Basically, what the question is asking, what P will be, if t reaches infinity.
So as t reaches infinity, -0.05t reaches minus infinity.
So as t reaches infinity, e^0.05t reaches 0, because 1 divided by infinity is a really small number.

So you basically treat it as 0. So the answer is just 150.

7. a ii.

What you got in part (i) was ab = 1, so b = 1/a

So you substitute that into part (ii), to get a + b. And you can use sum of roots formula.

b. ii.
solve the two lines simultaneously. i.e. 2x^2 +kx + 9 = 2x+1
then let the discriminant be less than 0.

i guess u can tell him the rest

 

[J2good4u]

8 (iii) use the velocity found in part (ii) i.e. v = 7/(t+4)^2 and stick that in v for dv/dt. so you get d/dt [7/(t+4)^2] and do the derivative of that equation.