VCE Methods Question Thread!

[Guideme]

Question 4 g pls. I don't understand how to determine the domain and range for this composite function because it needs to be restricted I think.

[zhen]

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Question 4 g pls. I don't understand how to determine the domain and range for this composite function because it needs to be restricted I think.

After restricting it so it exists. I think that domain of the inside function is the domain of the entire function. For range you insert the range of the inside into the outside function. For example if f(x)=x² and g(x)=sin(x). f(g(x))=(sin(x))². The range of the inside is [-1,1]. Inserting that into y=x², you get the range as [0,1], as f(0)=0, f(-1)=1 and f(1)=1. Also, the domain is just the domain of the inside function which in this case is R. Hope that helps 

[codebreaker1_91]

Can someone please show me step by step solutions for these two questions?
Thankyou

[zhen]

Can someone please show me step by step solutions for these two questions?
Thankyou

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Can you show us your working out so far, since just giving the solutions won't really help you learn.

[codebreaker1_91]

My working out for qn 8

[zhen]

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My working out for qn 8

The attached image is the graph you want to find the area of. So you find the integral of the function from -2 to -1. I don't know why there's a negative sign in front of everything. Also, note that when you take the integral of the fraction part, it becomes log_eIx-1I, where when x-1 is negative, you take the positive value. Hopefully that fixes the problem you've been having. 
Edit: Realised that you're really close the the answer. If you drop that negative in the front, then you get the answer. Also you can combine the logs to make log_e2/3. Tell me if you don't get it.

I'm going to show my working for the start of the other question since I'm not going to be online for a while. I don't know if it's right, but the method should be legit I hope.
Let y=(log_ex)²

[codebreaker1_91]

The attached image is the graph you want to find the area of. So you find the integral of the function from -2 to -1. I don't know why there's a negative sign in front of everything. Also, note that when you take the integral of the fraction part, it becomes log_eIx-1I, where when x-1 is negative, you take the positive value. Hopefully that fixes the problem you've been having. 
Edit: Realised that you're really close the the answer. If you drop that negative in the front, then you get the answer. Also you can combine the logs to make log_e2/3. Tell me if you don't get it.

I'm going to show my working for the start of the other question since I'm not going to be online for a while. I don't know if it's right, but the method should be legit I hope.
Let y=(log_ex)²

Thankyou very much!! I completely understand now

[ringring]

Hey everyone!
For the following question I know how to find A (amplitude) and n but I need help with b

Function with rule y=Asin(nt)+b has range [2,8] and period 2π/3. Find the values of A, n and b.

[RuiAce]

Hey everyone!
For the following question I know how to find A (amplitude) and n but I need help with b

Function with rule y=Asin(nt)+b has range [2,8] and period 2π/3. Find the values of A, n and b.

Hint: b is just the equilibrium point of the sine curve. It's halfway between the two extremities, which you know are 2 and 8.

[clarke54321]

Hey everyone!
For the following question I know how to find A (amplitude) and n but I need help with b

Function with rule y=Asin(nt)+b has range [2,8] and period 2π/3. Find the values of A, n and b.

Hey!

So you are given the range [2,8]. The difference between 8 and 2 is 6. When you halve 6 you have your amplitude, which is 3.

Therefore your b will be at 5 (2+3). Your graph will keep oscillating 3 up and 3 down from the point 5.

[Lavar Big BBB Balls]

Hi, could I have some help with these questions http://imgur.com/a/rMAIp

For 18c)i) what's stop us from using the point (9,0) in this part, is it because the strat is not the normal so we don't know if the normal passes through this point?
Also when finding the normal line, why can we use (x,y) as our second point?

For Q19) Is this question broken? The equation we are given doesn't resemble their graph in the question at all. So I'm getting all different answers apart from part a)i).

Thanks all! 

[Syndicate]

Hi, could I have some help with these questions http://imgur.com/a/rMAIp

For 18c)i) what's stop us from using the point (9,0) in this part, is it because the strat is not the normal so we don't know if the normal passes through this point?
Also when finding the normal line, why can we use (x,y) as our second point?

For Q19) Is this question broken? The equation we are given doesn't resemble their graph in the question at all. So I'm getting all different answers apart from part a)i).

Thanks all! 

For 8ci, the question is asking for you to find the equation of the line in terms of a, x and y. Instead of using (x,y) use (a,f(a)).

1) Calculate dy/dx, and substitute in x = a
2) Find the gradient of the normal by using the formula m1 x m2 = -1
3) Substitute in your values in the equation y - f(a) = -dx/dy(x-a)

19ai) Just substitute in t = 0 into the equation dV/dt to get the rate of water.

Tell us how it goes

[Lavar Big BBB Balls]

For 8ci, the question is asking for you to find the equation of the line in terms of a, x and y. Instead of using (x,y) use (a,f(a)).

1) Calculate dy/dx, and substitute in x = a
2) Find the gradient of the normal by using the formula m1 x m2 = -1
3) Substitute in your values in the equation y - f(a) = -dx/dy(x-a)

19ai) Just substitute in t = 0 into the equation dV/dt to get the rate of water.

Tell us how it goes

Thanks man!

For Q19 I meant that I only got part ai) correct. I did subbed the value stated in parts ii and iii in to the same function but I ended up with different values to what the answer had.

Could someone do ii, iii? I got 3 and 9 respectively.

[Syndicate]

Thanks man!

For Q19 I meant that I only got part ai) correct. I did subbed the value stated in parts ii and iii in to the same function but I ended up with different values to what the answer had.

Could someone do ii, iii? I got 3 and 9 respectively.

Yep you are correct

[Cyka]

With the probability notation for normal distribution, is it  X ~ N(u, o^2) or X ~ N(u,o) ?? With u = mean, o = s.d and o^2 = variance