Standard Math Q+A Thread

[jamonwindeyer]

Sorry this is more of an administration question, but why doesnt any general maths questions come up on my unread topics board page thingy or sidebar?

Seeing as im a mod i want to try to contribute as much as possible!

It wouldn't appear in the sidebar because it isn't recent (well this one is now), but as for 'Unread Posts,' did this show up?

[studybuddy7777]

It wouldn't appear in the sidebar because it isn't recent (well this one is now), but as for 'Unread Posts,' did this show up?

Yes it showed up now thanks

[aimbotted]

For this question the possibilities are

3,3
5,1
5,1
4,2
4,2
3,3

so it would be 1/36 + 1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 1/6

but the answer is 5/36 could anyone tell me what exactly i'm doing wrong?

question from 2013 hsc past paper

[jamonwindeyer]

For this question the possibilities are

3,3
5,1
5,1
4,2
4,2
3,3

so it would be 1/36 + 1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 1/6

but the answer is 5/36 could anyone tell me what exactly i'm doing wrong?

question from 2013 hsc past paper

Hey! So you've actually counted the same outcome (3, 3) twice. (5, 1) and (1,5) are different, (2,4) and (4,2) are different, but (3,3) and (3,3) are the same, you can't count it twice!

If you draw a table of all the possible options, you might be able to visualise this better!

[aimbotted]

wooops what a silly mistake

thanks haha

[jamonwindeyer]

wooops what a silly mistake

thanks haha

No worries!!

[RuiAce]

For this question the possibilities are

3,3
5,1
5,1
4,2
4,2
3,3

so it would be 1/36 + 1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 1/6

but the answer is 5/36 could anyone tell me what exactly i'm doing wrong?

question from 2013 hsc past paper

As a tip, try to write out your numbers such that the ordering matters. That way, your first number corresponds to die 1, \your second to die 2, and you open up opportunity for comparison.

1 5
2 4
3 3
4 2
5 1

That'll make it more obvious that 3 3 cannot be repeated.

[kmorritt]

Hi,
could I please have some help with chapter 10 Exercise 10.07 questions.
Thank you

[jakesilove]

Hi,
could I please have some help with chapter 10 Exercise 10.07 questions.
Thank you

Hey! The difficult part of this question is setting up the equation. We know that the strength will increase with relation to the square of the thickness. This means that



(In English, weight is proportional to thickness squared). To turn this into a real equation, we need to introduce a constant, k.



Great, so now we have a complete formula! We know that if W=1440kg, t=1.2cm. So,






For a) we let t = 0.7



For b) we let W = 3000kg

[jamonwindeyer]

Hi,
could I please have some help with chapter 10 Exercise 10.07 questions.
Thank you

Edit: Jake beat me but I'll post anyway because our answers end up different, mistake in finding your constant Jake? I'm doing mentally so not sure

Hi there! My working might differ slightly from the typical method you use in General Math, but it should be close! There is also an error in the wording of the question, it should read, of the cable is varied.

So, what we have here is a proportional relationship, because \(M\) grows in proportion to \(t^2\).

We can write this in two ways:



Here, \(k\) is our constant of proportionality. We can use either of these relationships to proceed (they are, in effect, the same thing) but I'll use the second one.

So we know that when \(t=1.2\), \(M=1440\). This lets us find \(k\):



What this proves is that the weight that the cable can carry is always one thousand times greater than the square of the thickness of the cable. We can use this to solve both our questions. For Question A, if we have a thickness of 0.7 centimetres:



Try your luck at Question B by substituting into the equation, the only difference being you'll have to rearrange, because you are looking for t!

You don't have to use the equation btw, you can just figure out the relationship between \(M\) and \(t^2\) and then apply it, but the equation formalises the matter

[jakesilove]

Edit: Jake beat me but I'll post anyway because our answers end up different, mistake in finding your constant Jake? I'm doing mentally so not sure

Hi there! My working might differ slightly from the typical method you use in General Math, but it should be close! There is also an error in the wording of the question, it should read, of the cable is varied.

So, what we have here is a proportional relationship, because \(M\) grows in proportion to \(t^2\).

We can write this in two ways:



Here, \(k\) is our constant of proportionality. We can use either of these relationships to proceed (they are, in effect, the same thing) but I'll use the second one.

So we know that when \(t=1.2\), \(M=1440\). This lets us find \(k\):



What this proves is that the weight that the cable can carry is always one thousand times greater than the square of the thickness of the cable. We can use this to solve both our questions. For Question A, if we have a thickness of 0.7 centimetres:



Try your luck at Question B by substituting into the equation, the only difference being you'll have to rearrange, because you are looking for t!

You don't have to use the equation btw, you can just figure out the relationship between \(M\) and \(t^2\) and then apply it, but the equation formalises the matter

I think I must have made a calculation error somewhere, thanks for correcting!

[kmorritt]

Thank you Jake and Jamon,
This has helped alot. Great to be able to see how to set out working.
I wasnt sure which formula to use.
Thanks again,
Katie

Edit: Jake beat me but I'll post anyway because our answers end up different, mistake in finding your constant Jake? I'm doing mentally so not sure

Hi there! My working might differ slightly from the typical method you use in General Math, but it should be close! There is also an error in the wording of the question, it should read, of the cable is varied.

So, what we have here is a proportional relationship, because \(M\) grows in proportion to \(t^2\).

We can write this in two ways:



Here, \(k\) is our constant of proportionality. We can use either of these relationships to proceed (they are, in effect, the same thing) but I'll use the second one.

So we know that when \(t=1.2\), \(M=1440\). This lets us find \(k\):



What this proves is that the weight that the cable can carry is always one thousand times greater than the square of the thickness of the cable. We can use this to solve both our questions. For Question A, if we have a thickness of 0.7 centimetres:



Try your luck at Question B by substituting into the equation, the only difference being you'll have to rearrange, because you are looking for t!

You don't have to use the equation btw, you can just figure out the relationship between \(M\) and \(t^2\) and then apply it, but the equation formalises the matter

[Dani_98]

Hi all!

Is anyone able to explain how to work out simultaneous equations? Both the substitution and elimination method.
Thank you all

[RuiAce]

Hi all!

Is anyone able to explain how to work out simultaneous equations? Both the substitution and elimination method.
Thank you all

How they work is just a matter of words.

Elimination works by using the operations of addition and subtraction (or possibly multiplication/division but perhaps not in general) to combine multiple equations. The way they are combined is rigged so that one of the variables disappears.

Substitution works by setting one variable equal to a giant thing first. Then, for the other equation(s), where that variable used to be, the giant thing replaces it.


If you want a demo of how to use them, that requires an example question.

[jamonwindeyer]

Hi all!

Is anyone able to explain how to work out simultaneous equations? Both the substitution and elimination method.
Thank you all

Hey Dani! Steph is going to stop in and give you an explanation tomorrow, I know you couldn't stay to hear her explain it today, so hang tight and Steph will stop in welcome to the forums!!