VCE Methods Question Thread!

[IndefatigableLover]

3. How do I overcome "resource exhaustion" on CAS?
-- whenever I try to work this out on my CAS, it says 'resource exhaustion' so is there another method to solve this?

Yeah my school SACs tend to have a few questions where your CAS tends to screw up, freeze or get the 'Resource Exhaustion' sign.. basically means it's taking up too much memory to perform the calculation I believe (this has mainly been from Calculus Questions).

I'm not sure how legit it is but whenever I got that problem I tried using a graphical approach to attain my answer (like subbing in values) or maybe you need to define restrictions on your equation so that it doesn't take so long to compute/solve for the variable in which you're looking for..

Hope that helps-ish :|

[Reus]

Could someone please show me how to do this question? Thanks.

[Phy124]

[Rishi97]

The probability of Vanessa's car starting on a cold morning is 0.6, while on a normal morning the chance of it starting is 0.9. The probability of any morning being a cold one is 0.3. If Vanessa's car starts tomorrow morning, find the probability that the morning is cold

I am not even sure how to approach this one
Any help is much appreciated

edit: haha wrote the ending for another question. LOL...moral: get enough sleep
Thanks AN

[keltingmeith]

You have either given us not enough information, or the wrong ending for the question. Instead of trying to assume what you're trying to ask, I'll just try starting you off.

Let C be the event that Vanessa's car starts, and M be the event that the morning is cold. Then, we have the following probabilities:



Then, by the total probability theorem, we have:

[Rishi97]

You have either given us not enough information, or the wrong ending for the question. Instead of trying to assume what you're trying to ask, I'll just try starting you off.

Let C be the event that Vanessa's car starts, and M be the event that the morning is cold. Then, we have the following probabilities:



Then, by the total probability theorem, we have:

soo sorry for asking the wrong question. Thanks for all your help

[Reus]

I don't see how
even on CAS it gives otherwise. :/

[keltingmeith]

I don't see how
even on CAS it gives otherwise. :/

Because f(x) is a probability density function. The definition of a probability density function is such that

The reason we go from 0 to 6 in this instance is because that's the domain for which that part of the piecewise function is defined - everywhere else, it's zero, and

[keltingmeith]

The probability of Vanessa's car starting on a cold morning is 0.6, while on a normal morning the chance of it starting is 0.9. The probability of any morning being a cold one is 0.3. If Vanessa's car starts tomorrow morning, find the probability that the morning is cold

I am not even sure how to approach this one
Any help is much appreciated

edit: haha wrote the ending for another question. LOL...moral: get enough sleep
Thanks AN

Okay, here's the full solution now that I know what you're being asked.

You want to find . Now, we know that this is equal to , and we can turn that top part into . From this, we have the following formula:



This is actually a famous formula called Baye's rule - feel free to look it up. It's not explicitly mentioned in the study design (neither is the total probability theorem to memory, but I think there's an informal treatment of it in there [or the new study design, at least]), however it could certainly come up if the question leads you into it.

[Reus]

Because f(x) is a probability density function. The definition of a probability density function is such that

The reason we go from 0 to 6 in this instance is because that's the domain for which that part of the piecewise function is defined - everywhere else, it's zero, and

Ah thanks for that! Teacher who don't explain everything when giving you theory kill me haha 

[Blondie21]

What does x: mean?

[achre]

What does x: mean?

Context? I'm assuming it's being used in a way where you're supposed to read the colon as meaning "such that", i.e. "x such that x is less than 0". Though I guess it could also be for a ratio, or even as a function mapping.

[nhmn0301]

Can someone check my solution to this question? Not entirely sure if this is right.
In order, state the transformations that would be required to transform the graph of y = cos (pi/2 - x) into y = 3sin (2x-4) +2.
My solution: a translation of 5pi/4 units to the negative direction of the x-axis (to get y=sin(x) ), then a dilation of factor 3 from the x-axis, a dilation of factor 1/2 from the y-axis, a translation of 2 units in the positive direction of the x-axis, a translation of 2 units in the positive direction of the y-axis.
Thanks!

[lzxnl]

Can someone check my solution to this question? Not entirely sure if this is right.
In order, state the transformations that would be required to transform the graph of y = cos (pi/2 - x) into y = 3sin (2x-4) +2.
My solution: a translation of 5pi/4 units to the negative direction of the x-axis (to get y=sin(x) ), then a dilation of factor 3 from the x-axis, a dilation of factor 1/2 from the y-axis, a translation of 2 units in the positive direction of the x-axis, a translation of 2 units in the positive direction of the y-axis.
Thanks!

I don't understand the 5pi/4. y = cos(pi/2 - x) is already y = sin x
Omit that step and the rest looks fine

[Alwin]

What does x: mean?

It's just some more maths jargon Usually for set notation it's Domain = {x:x>0}  or equivalently Domain = {x|x>0}
It's read as: x such that x is bigger than zero

If you're not confident with it, you can stick to interval notion (eg Domain = (0, infinity) ) so long as you know how to read set notation for the exam

I don't think I ever came across an exam that stipulated set notation not interval notation for your answer (or vice versa)