VCE Methods Question Thread!

[lzxnl]

Well it DOES fit the domain, the function is just zero there.

That means the flowers are guaranteed to survive past 1.5 days; integrating your function from 1.5 to infinity would yield 1.
So ok, you're really just finding the probability the flowers survive at least 4.5 days in total. That's easy.

[Sanguinne]

Well it DOES fit the domain, the function is just zero there.

That means the flowers are guaranteed to survive past 1.5 days; integrating your function from 1.5 to infinity would yield 1.
So ok, you're really just finding the probability the flowers survive at least 4.5 days in total. That's easy.

Thanks, got the right answer now 

[jono88]

Can someone explain how to obtain the period of 60sin{(5t-1)pi/ 2}

[Lasercookie]

Can someone explain how to obtain the period of 60sin{(5t-1)pi/ 2}

So expand it out into the form you recognise,

So hence

[clıppy]

I'm having some trouble with part a) of this question. I'm not really sure how to begin solving it.

Also, when the question has variables and says that these are constants are these important details? Do they affect how you derive the equation?

[b^3]

When you differentiate an expression that has constants in it, you can think of it as differentiating it as if the constants were some number, for example . It just means that for any expression we get, that value (the constant) isn't going to change as (well our independent variable) changes.
e.g. . For any value of , this holds.

For part a, Hint: Expand the expression out first.

Spoiler

Now we need to know what values can take. To find the largest value of this fraction we need to minimise the denominator. So first we look at . The smallest this can be is when , we have . Which means , and so . So our upper bound is (non inclusive).

Now to minimise the fraction we need to maximise the denominator, which in turn means we need to maximise . As , . . Now dividing by a really large number will give us a really small number, that is approaching zero. . So our lower bound is (non inclusive).

That is we have .
 .

[clıppy]

For part a, Hint: Expand the expression out first.

You lost me in the middle, how did you get from the first step to the second step, where did the come from?

[b^3]

It's a little trick to expanding it out, you could also long divide.

In the above, we want to form the expression we have in the denominator on the top, so that we can cancel part of it down to get a constant. So to do this what do we need to add to to get ? right? But we need the expression to be equal to the line before it, so to do this if we add we need to also minus as well. Which is how we get to , as this is the same as .

EDIT: I guess this is how you would do it if you were to long divide.

[clıppy]

Ohh okay, the long division helped explain what you were trying to achieve
Thanks b^3!

[Sanguinne]

The volume of milk in a 1-litre carton is normally distributed  with a mean of 1.000 litres and a standard deviation of 0.006 litres. A randomly selected carton is known to have more than 1.004 litres. Find the probability, correct to 4 decimal places that it has less than 1.011 litres.

Answer apparently is 0.8676

[darklight]

The volume of milk in a 1-litre carton is normally distributed  with a mean of 1.000 litres and a standard deviation of 0.006 litres. A randomly selected carton is known to have more than 1.004 litres. Find the probability, correct to 4 decimal places that it has less than 1.011 litres.

Answer apparently is 0.8676

This is conditional probability. So find the prob of carton having less than 1.011 litres given that it is more than 1.004 litres. So, therefore, it will be the prob between 1.004 and 1.011 litres divided by probability greater than 1.004 litres.

[Homer]

i get 0.8678

[clıppy]

I'm having trouble understanding what the question is asking or what it's asking me to find.
The answer is apparently A but I don't know why.

[lzxnl]

For angle between two curves, tan theta =
So
And at x = 0
Plugging into formula, tan theta = (2-1)/(1+1*2)=1/3 or A

Where does this formula come from? The angle between two curves
from the tangent subtraction formula.
As and , the result follows.

[fleet street]

I think that angle between two curves isn't on the study design. From the Essentials textbook, "This topic is not listed in the study design, but can be included for the understanding of other topics that are included."But yeah, it's good to know anyway. Also, if your teacher does decide to put it on SACs, then I guess you'd have to know it.