September 18, 2020, 11:00:58 pm

### AuthorTopic: VCE Methods Question Thread!  (Read 2973722 times) Tweet Share

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#### Bri MT

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##### Re: VCE Methods Question Thread!
« Reply #18675 on: August 05, 2020, 11:57:23 am »
+3

I'm not against asking random level questions on AN, but maybe discuss with the mods on a better place to post it so as to not frighten other students 😅

Agreed that asking questions is good but would be best not to potentially scare other students unnecessarily.

Imo - in general if there's no clear place to post it best practice would be to guess for closest fit (or ask if you're really unsure & would like guidance) and let people know in the post that it's outside the scope of the study design

#### Corey King

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##### Re: VCE Methods Question Thread!
« Reply #18676 on: August 08, 2020, 10:02:23 pm »
0
Hey guys,
I am beginning the year 11 textbook for Methods. In it, there are revision questions for previous years at the beginning.
I am stuck on this question: https://www.symbolab.com/solver/solve-for-equation-calculator/solve%20for%20x%2C%20%5Cfrac%7Ba%7D%7Bx%2Ba%7D%2B%5Cfrac%7Bb%7D%7Bx-b%7D%3D%5Cfrac%7Ba%2Bb%7D%7Bx%2Bc%7D.
There must be a simpler way to solve for x in this equation than the method Symbolab is suggesting.
Anybody know how to solve this?
Would be much appreciated,
Corey

#### james.lhr

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##### Re: VCE Methods Question Thread!
« Reply #18677 on: August 08, 2020, 10:22:16 pm »
+6
Hey Corey！

There is indeed a much simpler way. One problem with Symbol Lab is that it "brute forces" its way to the answer. It is much easier if you do a bit of algebraic manipulation. If you have any questions with my solution don't hesitate to ask!

James
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#### thatdumbstudent

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##### Re: VCE Methods Question Thread!
« Reply #18678 on: August 09, 2020, 02:05:24 pm »
0
Can someone please explain this Bernoulli trial question to me?
During the wet season, the probability that it rains on any given day in Cairns in northern Queensland is 0.89. I am going to Cairns tomorrow and it is the wet season. Let X be the chance that it rains on any given day during the wet season.

- Find Pr(μ−2σ≤X≤μ+2σ)

so I had no problem figuring this out and got Pr(0.2642 ≤ X ≤ 1.5158)

however... I don't get why the final answer is this? (photo attached)

I just don't get why it equals to the Pr(X = 1) thingy. this is probably a dumb question but if someone could explain why I'd appreciate it lol
« Last Edit: August 09, 2020, 02:07:12 pm by thatdumbstudent »

#### ArtyDreams

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##### Re: VCE Methods Question Thread!
« Reply #18679 on: August 09, 2020, 04:55:02 pm »
+1
Can someone please explain this Bernoulli trial question to me?
During the wet season, the probability that it rains on any given day in Cairns in northern Queensland is 0.89. I am going to Cairns tomorrow and it is the wet season. Let X be the chance that it rains on any given day during the wet season.

- Find Pr(μ−2σ≤X≤μ+2σ)

so I had no problem figuring this out and got Pr(0.2642 ≤ X ≤ 1.5158)

however... I don't get why the final answer is this? (photo attached)

I just don't get why it equals to the Pr(X = 1) thingy. this is probably a dumb question but if someone could explain why I'd appreciate it lol

Someone correct me if I'm wrong (I've already seriously forgotten my probability from last year lol)

So: we know that Pr(0.2642 ≤ X ≤ 1.5158).
This is a range - since we are talking about days you can't actually have 1.5158 of a day, etc.
So we need to fix that domain that its given. Since X must be less that 1.5158, that gets rounded to 1. You also cannot have less than 0.2642, making that become 1 as well.

Therefore, Pr(X=1).

In simple terms, you just need to fix that domain so you have whole numbers.

Hope this helps somewhat! (I feel like I've forgotten so much so I'm sure theres a better explanation for this, but I hope it helps in the meantime!)
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#### Azila2004

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##### Re: VCE Methods Question Thread!
« Reply #18680 on: August 10, 2020, 06:22:32 pm »
0
Hello! I hope you all are doing well

I have a question on sinusoidal graphs, it's a small part of a larger question.
Find h if d=0 when h=0 for the equation d= 2 +/- 3sin(2pi/15(t-h))

I wrote the 3 as either negative or positive as we only know that the amplitude is 3. I'm unsure whether this is enough information to find h, and I am confused since wouldn't there be an unlimited values of h? The answer states that h = 1.74202.

I would really appreciate some help!  (•◡•) /
Just someone who likes to learn a lot of questions.

Aspiring medical practitioner! ʕ•́ᴥ•̀ʔっ

#### zhouzhennan

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##### Re: VCE Methods Question Thread!
« Reply #18681 on: August 10, 2020, 08:10:53 pm »
0
Can someone pls confirm this: Dom of f(g(x)) = dom of g(x)
And how would i find the range of f(g(x)) with tech free? Would it just be the intersection of the ranges of both functions?

#### The Cat In The Hat

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##### Re: VCE Methods Question Thread!
« Reply #18682 on: August 10, 2020, 09:42:58 pm »
0
Can someone pls confirm this: Dom of f(g(x)) = dom of g(x)
Off the top of a head none too sure about these things, I'd say that isn't right. Off the top of a head wiser than my own, that depends. If you've restricted the domain of f(x), then the domain of g(x) might not exist within that domain (if that makes sense).
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#### eloisegrace

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##### Re: VCE Methods Question Thread!
« Reply #18683 on: August 10, 2020, 09:59:37 pm »
0
Can someone pls confirm this: Dom of f(g(x)) = dom of g(x)
And how would i find the range of f(g(x)) with tech free? Would it just be the intersection of the ranges of both functions?

Yes, this is correct. The domain of f(g(x)) is the domain of g(x). However, you need to check that f(g(x)) exists using a domain and range table and seeing if the range of g(x) is a subset of the domain of f(x).

Re finding the range, I would probably use the endpoints and find turning points to distinguish where the graph is highest and lowest. I haven't seen this asked too much on tech-free but it could come up.
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#### schoolstudent115

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##### Re: VCE Methods Question Thread!
« Reply #18684 on: August 10, 2020, 10:06:04 pm »
+2
Can someone pls confirm this: Dom of f(g(x)) = dom of g(x)
And how would i find the range of f(g(x)) with tech free? Would it just be the intersection of the ranges of both functions?
That is not correct. There are two conditions for the domain:
1. x is in the domain of g(x)
2. g(x) is in the domain of f(x) (Because g(x) is the input of f(x) in f(g(x)), so g(x) must be a valid input).

So in a precise manner,
$dom(f \circ g) = {{x: x\in dom(g) \wedge g(x) \in dom(f)}}$
(2020) Year 11: Physics 3/4

#### schoolstudent115

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##### Re: VCE Methods Question Thread!
« Reply #18685 on: August 10, 2020, 10:34:55 pm »
+2
Can someone pls confirm this: Dom of f(g(x)) = dom of g(x)
And how would i find the range of f(g(x)) with tech free? Would it just be the intersection of the ranges of both functions?
As for the range, just think of it as the range of f(x), where the domain is the domain of f(g(x)). It is really just a restricted domain problem. Generally, your domain will not get any worse than a single set. E.g. [0,inf).

The range of f(g(x)) is a subset of the range of f(x). Reason being, they are in essence the same function, just that the domain of f(g(x)) might be restricted, so f(g(x)) will only pump out a certain portion of the range of f(x).

E.g. f(x)=x^3, g(x)=x^2
dom(f) = R
dom(g) = R
ran(g) = [0,inf)
f(g(x)) = (x^2)^3 = x^6

The range of f(g(x)) is simply the range of f(x), constrained to the fact that the input x is from 0 to infinity (ran g).
Well then the range is just [0,inf)   {x^3 is greater than or equal to 0 for x>=0}
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#### Coolgalbornin03Lo

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##### Re: VCE Methods Question Thread!
« Reply #18686 on: August 11, 2020, 05:17:09 pm »
+1
Why won’t my cas let me find the integral of sin squared x ? It keeps saying “(“ missing as in THERES a bracket missing even tho there isn’t!
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#### Chocolatemilkshake

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##### Re: VCE Methods Question Thread!
« Reply #18687 on: August 11, 2020, 05:27:47 pm »
+3
Why won’t my cas let me find the integral of sin squared x ? It keeps saying “(“ missing as in THERES a bracket missing even tho there isn’t!
You can't put the squared sign right before the sin (like you write it). Instead you need to put the squared on the outside like this...

(sin(x))^2
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#### james.lhr

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##### Re: VCE Methods Question Thread!
« Reply #18688 on: August 11, 2020, 05:29:08 pm »
+3
Hi El

When you want to square or cube a trig function, you have to type the bracket on the outside. For example, ${\mathrm{sin}}^\mathrm{2}{\mathrm{x}}$ would be error, but ${(\mathrm{sin(x))}}^2$ would be fine.

Hope this helps!
~James

Edit: Beaten by chocolatemilkshake
« Last Edit: August 11, 2020, 05:31:07 pm by james.lhr »
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##### Re: VCE Methods Question Thread!
« Reply #18689 on: August 11, 2020, 07:31:24 pm »
0
Hey Corey！

There is indeed a much simpler way. One problem with Symbol Lab is that it "brute forces" its way to the answer. It is much easier if you do a bit of algebraic manipulation. If you have any questions with my solution don't hesitate to ask!

James

God I remember that question. I could never solve it and neither could the teacher.
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