VCE Methods Question Thread!

[chantelle.salisbury]

hello..
i was wondering whether someone could help with this q.? 
i have a function h(x) = x^4 and want to find the integral of (h(x))^2?
does it mean that it is integral of x^16? because my calculator doesn't seem to think so? any ideas of the reasoning behind this?

thanks  

[Syndicate]

hello..
i was wondering whether someone could help with this q.? 
i have a function h(x) = x^4 and want to find the integral of (h(x))^2?
does it mean that it is integral of x^16? because my calculator doesn't seem to think so? any ideas of the reasoning behind this?

thanks  

(h(x))^2 = x^(4x2) = x^8

It would only be x^16, if it is something like x^4^2 (so x to the power of 4, then 4 to the power of 2).

Integrating that gives (x^9)/9 + c

[chantelle.salisbury]

s

(h(x))^2 = x^(4x2) = x^8

It would only be x^16, if it is something like x^4^2 (so x to the power of 4, then 4 to the power of 2).

Integrating that gives (x^9)/9 + c

sweet,.. u come to my rescue once again i just wanted to confirm my suspicions. thankyou

[school2017]

hello..
could you please help me with what a question means by express in the terms of p(i)??
also how do you find the exact values of a geometric centre of a integrated area, in terms of a limit?

thanks....any help will be great...

[Shadowxo]

hello..
could you please help me with what a question means by express in the terms of p(i)??
also how do you find the exact values of a geometric centre of a integrated area, in terms of a limit?

thanks....any help will be great...

If they say to express in terms of Pi, then you leave it in terms of Pi (the exact value) and don't approximate it
Eg the circumference of a circle with radius 2m expressed in terms of Pi is 4pi. This is also approximately 12.566 but this isn't in terms of Pi
I'm not quite sure what you mean by your second question, could you post an example?

Ps if you meant p(i) as a function then you'd do a similar thing, express the answer as a multiple of that function

[school2017]

If they say to express in terms of Pi, then you leave it in terms of Pi (the exact value) and don't approximate it
Eg the circumference of a circle with radius 2m expressed in terms of Pi is 4pi. This is also approximately 12.566 but this isn't in terms of Pi
I'm not quite sure what you mean by your second question, could you post an example?

Ps if you meant p(i) as a function then you'd do a similar thing, express the answer as a multiple of that function

Hello...thanks for the first question!.....its referring to a function so must be that...

with the second question....
we r given a graph of h(x) with an area bound by the line x=c
we have to find the exact value of the x-coordinate of the geometric centre of this area...as in find the rule...
where should I start??

thanks

[TheCommando]

How do i do d
http://imgur.com/a/Er9ke
Also why cant i upload theese pics on here

[TheCommando]

How do u do a and b i have no idea
http://imgur.com/a/eZfOr

[MisterNeo]

How do i do d
http://imgur.com/a/Er9ke
Also why cant i upload theese pics on here

You need to find the equation of one of the lines, find the area under the line, then double it because an isosceles triangle is made of two equal parts.
(The equation of AB is y=3x-4 and BC is y=-3x+26)
The area of the isosceles triangle is:

There's more than one answer as you could also do:

And also:

[gnaf]

Hello

I'm stuck on a probability question (in pictures 1 and 2). Specifically, I don't understand how to find Pr(p hat=1/3)/ how the solutions (in picture 3) finds it!

Thanks

[gnaf]

Another probability question (Sorry, I've tried editing my last post to make 1 post rather than two, but I can't attach all the photos)

In the worked solution (picture 2), how did they come up with this: "a<2... in order to be a probability density function"?

And in the 2nd last line when cos((pi*a)/2)=0, do I need to specify the domain or that I'm choosing the smallest positive value closest to 0, etc.?

Thanks

[Eric11267]

Hello

I'm stuck on a probability question (in pictures 1 and 2). Specifically, I don't understand how to find Pr(p hat=1/3)/ how the solutions (in picture 3) finds it!

Thanks

So Pr(p hat=1/3) is basically asking for the probability of picking only one red fish in the sample of eight, which just uses combinatorics. In the answers the numerator is the number of combinations with one red and two gold fish and the denominator is the total number of possible combinations.
And to get Pr(p hat> 1/4) there needs to be at least 1 red fish since there are only three fish. Then the Pr(p hat>1/4) = 1-Pr(p hat=0) = 1-(8/16)*(7/15)*(6/14)

Sorry if my explanation is ambiguous, I'm not really sure how to do the formatting for maths questions on atarnotes yet

[Eric11267]

Another probability question (Sorry, I've tried editing my last post to make 1 post rather than two, but I can't attach all the photos)

In the worked solution (picture 2), how did they come up with this: "a<2... in order to be a probability density function"?

And in the 2nd last line when cos((pi*a)/2)=0, do I need to specify the domain or that I'm choosing the smallest positive value closest to 0, etc.?

Thanks

a<2 since any value larger than 2 would go under the x axis, and you can't have negative probabilities. And in the second last line you would mention that a=1 since a<2.

[VanillaRice]

Sorry if my explanation is ambiguous, I'm not really sure how to do the formatting for maths questions on atarnotes yet

Be sure to check out this guide

[Shadowxo]

Hello...thanks for the first question!.....its referring to a function so must be that...

with the second question....
we r given a graph of h(x) with an area bound by the line x=c
we have to find the exact value of the x-coordinate of the geometric centre of this area...as in find the rule...
where should I start??

thanks

I don't believe they'd test you on that, but I think to find the x value of the centre of that area, they want to find the x value which leads to the area to the left (ie the integral between the start and the x value) being equal to the area of the right. If this doesn't work and you're still stuck, feel free to post the question (preferably with the solution) and I can solve it for you although I doubt it would be on the course if they're doing an alternate method.

How do u do a and b i have no idea
http://imgur.com/a/eZfOr

a) I'm guessing you just missed a bit of information
It says w=1.5L = 3L/2
Sub this into the equation for the area and you get the answer
b) it's just using the chain rule, you may want to go over this. No major tricks here

Hope this helps