VCE Methods Question Thread!

[pi]

The standard of maths in this thread really has declined since my last post here :O

[datfatcat]

The standard of maths in this thread really has declined since my last post here :O

[Jakelee]

The sum of two non negative numbers is 16, find:
a) the minimum value for the sum of their squares
b) the maximum value for the sum of their squares

I'm not so bright so I don't have the slightest clue on how to start this. Can anyone please help me?

[Conic]

The sum of two non negative numbers is 16, find:
a) the minimum value for the sum of their squares
b) the maximum value for the sum of their squares

I'm not so bright so I don't have the slightest clue on how to start this. Can anyone please help me?

Let the 2 numbers be a and b. We know that a+b=16, so b=16-a.
The sum of the squares is which can be written as

[Sanguinne]

my answer keeps coming out wrong..i  think im missing something
so il just post this here

find the area between the pairs of curves below, over the given interval
b) y=sin(x) and y=cos(x) [0,pi]

[Phy124]

my answer keeps coming out wrong..i  think im missing something
so il just post this here

find the area between the pairs of curves below, over the given interval
b) y=sin(x) and y=cos(x) [0,pi]

The area between to curves and , over the interval , is given by:



Where is the upper curve and is the lower curve.

In this case over the interval of integration the upper and lower curves interchange at , as can be seen by graphing the two functions, so we must split it up into two integrals. ( is above over the interval and is above over the interval )



Alternatively, if you have your calculator you can do it in one integral:



edit: I accidentally a word

[Sanguinne]

thanks :DDDDDDDDDDDDD

[shadows]

Hi guys,

being doing some final revision for my SAC tmr.. and I have a question.

This is a equation modelling of population of insects
if where      (t represents time in days, N represents no of insects)

Calculate the population after 15 days/

N= 164.31 (assuming t= 15)

Since the population is decreasing, shouldn't the population be 165 ? (as it hasn't reached 164 yet)

The answer says 164. I am confused.

[brightsky]

as a general rule of thumb, just round up or down as you usually would. don't attempt to get too tricky. they really should word questions better, but unfortunately similarly worded questions have popped up in the real exam (and in sacs). one of the tasmania jones questions from the actual exam a few years ago caused a little controversy, but they ended up paying both solutions (in your case, both 164 and 165).

[shadows]

Wow thanks for the quick response!

That sucks. This was a question from last years SACS. And the solutions stated 164. (didn't mention 165 o.o)

[shadows]

can someone please show how


how does f(g(x)) have range of (0,1)

omg I haven't done composite functions in ages D:

[BubbleWrapMan]

The range of g is (0,∞) (it starts off at 0 and keeps increasing because it's a log)

If you change the domain of f to (0,∞) (which is effectively what you do when you compose it with g) then you get the portion of f to the right of the y-axis, which has a range of (0,1) (i.e. it starts off at 1 and keeps getting smaller, approaching 0)

[Smiley_]

I always get stuck on these kinds of questions
could i have some help please
solve for x

loge y = (loge x) + 2
and
 log10 y = log10 x + 1

[Phy124]

I always get stuck on these kinds of questions
could i have some help please
solve for x

loge y = (loge x) + 2
and
 log10 y = log10 x + 1

Take the exponential of both sides:



Use the exponential identity







Try and have a go at the second one yourself using the same methods as above

Spoiler

*Note: Complex solutions were ignored because they aren't on the course

[zvezda]

Vcaa 2011 exam 2 q4 part f,
Would anyone be able to explain why k> or equal to the number (too hard to type on iPad lol).