Mathematics Question Thread

[angelahchan]

Hi, could someone please help with Q16 b(iii) of 2013? I don't get how we're meant to work out it's shape - is it by plotting points?
https://www.boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf

[EEEEEEP]

Hi, could someone please help with Q16 b(iii) of 2013? I don't get how we're meant to work out it's shape - is it by plotting points?
https://www.boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf

Hint hint: It's an exponential. ALso consider the previous answers.

(i) How many trout were in the lake when the carp were introduced? This tells you the value of N when T is 0.
(ii)    When will the population of trout be zero? This tells you the value of T (when N = 0).

Given these 2, you can graph it.

YOu only need 2 or 3 points and you know the general shape of the graph =)

[sidzeman]

Halp pls

[adelaidecruz]

Halp pls

Q7:
ln (6-x) = 2lnx
loge (6-x) = 2logex
loge (6-x) = loge (x^2)
6-x = x^2 ..... x^2 + x - 6 =0 .... (x+3) (x-2)
x = -3, 2

[EEEEEEP]

Halp pls

q7
The 2 rules that are applicable here are...
ln(x ^ y) = y ∙ ln(x)              AND    e^ ln(x) = x

1. 2 ln x = X^2
ln (6-x) = ln (X^2)

2. Make both sides the superscipt for e
(6-x) = (X^2)

Take the LHS to the RHS and you get...
X^2 + x - 6

Solve for x.

[RuiAce]

How often do we have to use the product of roots in questions? Like is it something we should keep in mind when dealing with intersection points?

The product and sum of roots are useful when you aren't interested in intersection points themselves, but any relationships between the intersection points. They're a bit less likely to appear than the discriminant, but probably the next thing as obscure to it.

[asahyoun3]

Halp pls

Hi I have attached the solution to Q10, If you have any problems understanding just let me know

[RuiAce]

Halp pls

[asahyoun3]

Q7:
ln (6-x) = 2lnx
loge (6-x) = 2logex
loge (6-x) = loge (x^2)
6-x = x^2 ..... x^2 + x - 6 =0 .... (x+3) (x-2)
x = -3, 2

Solution is only x=2 as x>0 for logs

[RuiAce]

Halp pls

You can plug this into the calculator

[RuiAce]

Hi, could someone please help with Q16 b(iii) of 2013? I don't get how we're meant to work out it's shape - is it by plotting points?
https://www.boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf

The procedure is to build it up.

1. Sketch \(e^{0.04t}\), because you know how to sketch the ordinary exponential.
2. Sketch \(-e^{0.04t}\) by reflecting about the \(t\)-axis.
3. Sketch \(375-e^{0.04t}\) by translating the graph up by 375

You were taught all of these techniques; the hardest bit is about doing them in the correct order.

[RuiAce]

Part 1/2 List of SOS 2010 2U HSC Asks – 5(b)(iii), 8(d), 9(b)

...help.

[RuiAce]

Part 1/2 List of SOS 2010 2U HSC Asks – 5(b)(iii), 8(d), 9(b)

...help.

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[RuiAce]

Part 1/2 List of SOS 2010 2U HSC Asks – 5(b)(iii), 8(d), 9(b)

...help.

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Note: You can actually check that in fact, \(f(4) = 0\) as well.

The graph should look something like a sine curve between 0 and 4, and then a straight line with gradient m=-3, from 4 to 6.

[sidzeman]

Thanks so much for all your help guys!
Sorry for the spam but, for part iv of this question, I found P and so found the rate of increase of carp. When I go to find the rate of decrease of trout so as to equate the two and find t, I get -0.04e^0.04t - leaving me unable to solve for t as you cannot log a negative. The answers has it as postive 0.04... - Am i differentiating wrong or what I'm not sure what I'm missing