VCE Methods Question Thread!

[zvezda]

Hey,
Im having an immensely difficult time trying to figure out q4b in the extended response of the chapter 17 review in essentials. Ive tried a few things but have gotten nowhere.
Help appreciated
Thanks

[JieSun92]

I think that's a typo.
h=0???
Now I think the real problem is the value of h 
From the answer at the back of essential, I got the value of h as approximately 10 cm.

Yeah I had a look at the solutions supplement and h=10. Thanks anyways

[09Ti08]

Hey,
Im having an immensely difficult time trying to figure out q4b in the extended response of the chapter 17 review in essentials. Ive tried a few things but have gotten nowhere.
Help appreciated
Thanks

For X: 8*0.6*1
For Y:
I don't have a calculator here, but adding those two should give you the answer

[zvezda]

For X: 8*0.6*1
For Y:
I don't have a calculator here, but adding those two should give you the answer

Why must they be added?

[b^3]

We don't want to know the amount of money taken in for packets and loose nails separately, rather we want to know the total amount of money taken in from both, hence (as 09Ti08 has said above) we add the two values above, as they represent the money taken in for X packets, and the money taken in for Y kilograms of loose nails.

[Zealous]

Could someone quickly run through how in the photo (maybe just break it down a bit), the working that went from line 2 to line 3.. too much happened I couldn't follow =o



Also, are there any good methods of sketching graphs to a fractional power, without a calculator?
For example:



I had troubles doing this accurately when I did a MAV Exam 1... (did pretty bad overall =[ )

Thanks guys!
sushi./ovazealous

[SocialRhubarb]

From step 2 to step 3, they multiplied top and bottom by .

Fractional powers look like sideways integer powers, but obviously even powered functions are kind of cut in half.

[lzxnl]

Could someone quickly run through how in the photo (maybe just break it down a bit), the working that went from line 2 to line 3.. too much happened I couldn't follow =o

(Image removed from quote.)

Also, are there any good methods of sketching graphs to a fractional power, without a calculator?
For example:



I had troubles doing this accurately when I did a MAV Exam 1... (did pretty bad overall =[ )

Thanks guys!
sushi./ovazealous

The easiest way of sketching those graphs?
Let where n does not have to be an integer



What's the point of this? We defined n>1, so the second derivative, or the rate of change of the first derivative, is negative. This means that the first derivative, or the slope, is always decreasing. When sketching , always have your slope dropping.
However, as x becomes large, so does y, so make sure that you never actually draw in an asymptote.
Also, the first derivative is always positive, so make your graph always increasing.
Essentially, you just want to have it so that your function is always increasing, but its increase is slowing down and never flattens out despite looking like it should.
This is for x>0.
If your exponent is odd, then y will be defined for negative x as well, so just make a mirror image. At the origin, as 1-n<0, is undefined, so make it vertical. Do this if n is even as well; for y = x^1/2, make the part of the curve at the origin appear vertical.

Of course, diagrams speak better than words so look at graphs on your calculator as a guide as well.

[Alwin]

Also, are there any good methods of sketching graphs to a fractional power, without a calculator?
For example:



I had troubles doing this accurately when I did a MAV Exam 1... (did pretty bad overall =[ )

Thanks guys!
sushi./ovazealous

Im kinda lazy, so here's a screenshot rather than me type it all up again:


nliu's method is pretty good, but only covers x^1/n using calculus.

Hope it helps

[Alwin]

A game consists of rolling three dice. If the three numbers uppermost are the same, you win $10. If only two are the same, you win $2. If all three are different you lose $2. If the random variable X represents the amount won or lost in a game, find the probability distribution for wr
The only way I know how to do questions like this is to list out every single possibility in a tree then multiply/add the values together which is ridiculous for questions like these (in my opinion).
I'm really interested in seeing how you guys would approach this question.

I have the answer if you need.

Pr(3 same) = 1* 1/6 * 1/6 = 1/36
Pr(2 same) = 1* 1/6 * 5/6 *3 = 15/36
Pr(3 different) = 1 * 5/6 * 4/6 * = 20/36

E(X) = 10 *1/36 + 2*15/36 + (-2) * 20/36 = 0    ...I think iirc probability correctly

[Alwin]

Well you're correct but I'm still unsure how the probabilities of 2 same and 3 different were obtained.

Could you please go through your thinking process to get those values?

You made that seem so easy haha :S

sorry!! I skipped.. quite a few steps haha.

for Pr(2 same), suppose they are two 1's.  Pr(two 1s) = Pr(1, 1, other) + Pr(1, other, 1) + Pr (other, 1, 1)
So, the probability is Pr(two 1s) = 1/6 * 1/6 * 5/6 + 1/6 * 5/6 * 1/6 + 5/6 * 1/6 * 1/6 = 1/6 * 1/6 * 5/6 * 3
But, there are six option, two 1's two 2's two 3's ... two 6's,
So, Pr(2 same) = 6*Pr(two 1s) = 6 * 1/6 * 1/6 * 5/6 * 3 = 1/6 * 5/6 * 3 = 1/36

for Pr(3 different), there are two ways.
1.  Pr(3 same) + Pr(2 same) + Pr(3 different) = 1,   so 1/36 + 15/36 + Pr(3 different) = 1  -->  Pr(3 different) = 20/36
2.  Pr(3 different) = Pr(chose any number, say a) * Pr(chose any number not a, say b) * Pr(chose any number not a and not b)
     Pr(3 different) = 1 * 5/6 * 4/6 = 20/36

Hope it makes more sense!

[shaiga95]

How are you meant to find the median on cas ti-nspire I have been trying
menu>3>1 menu>4>1 typing function with unknown terminal as m = 0.25 and keep getting answers with n13 in them

[b^3]

0.25 will give you the first quartile, while solving that integral =0.5 will give you the median. What function are you trying to integrate? It may need a domain restriction (e.g. if it's a trig function, that's why you'd be getting a general solution), by adding '' where and are the lower and upper bounds respectively.

[Zealous]

Hi!
If an exam question defines a function with a restricted domain such as:



Do transformations (i.e. dilations) always affect a restricted domain?

eg.

Spoiler

If
What is the amplitude and domain of this new function?

[Eugenet17]

, d= depth of water in metres at a port entrance, t is in hours.

A certain ship needs the depth at the port entrance to be more than 5m. The ship can be loaded and unloaded, and in and out of the port in 9 hours. Assumng that the ship enters the port just as the depth at the entrance passes 5 metres, will the ship be able to exit 9 hours later? How long will it have to spare, or by how many minutes will it miss out?

I've managed to find whether it will be able to exit 9 hours later, but I'm not sure how to figure out the amount of time to spare it has.

Thanks :>