Mathematics Question Thread

[RuiAce]

Part 2/2 2010 2U HSC Asks – 10(a)(iv), 10(b)(ii)

First one was answered here

[RuiAce]

Part 2/2 2010 2U HSC Asks – 10(a)(iv), 10(b)(ii)

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You can now just plug π/3 in to find how much volume is left, and thus the required fraction.

[Thebarman]

Hey, I'm constantly getting confused when it comes to Simpson's rule and the trapezoidal rule in regards to the number of subintervals. When working out h = (b - a)/n, how many subintervals are there? Because for some questions, it will be one more than the number provided (say there are 5 function values provided, then the number of sub intervals will be 6), while other times it will be one less. Sorry if that's a bit confusing, but I;m a bit confused myself.

Thanks

[RuiAce]

Hey, I'm constantly getting confused when it comes to Simpson's rule and the trapezoidal rule in regards to the number of subintervals. When working out h = (b - a)/n, how many subintervals are there? Because for some questions, it will be one more than the number provided (say there are 5 function values provided, then the number of sub intervals will be 6), while other times it will be one less. Sorry if that's a bit confusing, but I;m a bit confused myself.

Thanks

n is the number of intervals but n+1 is the number of function values.

For Simpson's rule, there will always be an even number of subintervals, and an odd number of function values.

It never goes the other way. If somehow you ended up with n-1 function values it means you have made a mistake somewhere.
Sometimes, that mistake happens because you forget that one of the function values can actually be 0.

[_____]

How do I find the required angle here? I know to use two segments but apart from that I'm stuck. Solution says to use equilateral triangles but I don't understand how that would work.



Thanks

[MisterNeo]

How do I find the required angle here? I know to use two segments but apart from that I'm stuck. Solution says to use equilateral triangles but I don't understand how that would work.

(Image removed from quote.)

Thanks

There are 2 equiliateral triangles that make up the segments, so the angle would be 120^o because each angle is 60^o.

[RuiAce]

How do I find the required angle here? I know to use two segments but apart from that I'm stuck. Solution says to use equilateral triangles but I don't understand how that would work.

(Image removed from quote.)

Thanks

[cxmplete]

How do you do part i

[jamonwindeyer]

How do you do part i

Hey! This is actually a 3U question (purely because of that factorial notation at the bottom), did you still want us to tackle it for you? We can move it to the MX1 section and help you out if it is something you need help with, but if it is just 2U you can definitely ignore

[cxmplete]

Hey! This is actually a 3U question (purely because of that factorial notation at the bottom), did you still want us to tackle it for you? We can move it to the MX1 section and help you out if it is something you need help with, but if it is just 2U you can definitely ignore

Hi. Yah, I'll move it to the MX1 section

[georgiia]

What am I doing wrong with this probability question?
Thx !

[jamonwindeyer]

What am I doing wrong with this probability question? (Image removed from quote.)(Image removed from quote.)
Thx !

Hey! For your tree diagram, instead of a branch for each person, do a stage for each person. So three stages, each with two branches of support (70%) and not support (30%)

[georgiia]

Hey! For your tree diagram, instead of a branch for each person, do a stage for each person. So three stages, each with two branches of support (70%) and not support (30%)

cool thanks I’ll try that, but how come this method doesn’t work?

Thank you

[jamonwindeyer]

cool thanks I’ll try that, but how come this method doesn’t work?

Thank you

Basically, it is because you are assigning a probability to which person you pick, when really that isn't something that matters - Because all of their opinions are counted.

The best way to think of it is to think, well, if all three are for it, then

Person A is for it
AND
Person B is for it
AND
Person C is for it

So you can turn that into an equation (which a tree diagram helps you visualise) -



Remember, the word AND means you multiply, the word OR means you add the respective probabilities

[RuiAce]

What am I doing wrong with this probability question? (Image removed from quote.)(Image removed from quote.)
Thx !

You can label the F's and A's as appropriate.

The idea is that your probability tree diagram assumed that you had to pick one out of three, then ask for only THAT person's opinion, when in reality you're interested in all three of their opinions.