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Reply 20
Original post by Chlorophile
Your answer to part a is correct. For part b, think about the cosine function. The period of the cosine function is 2pi. The period of our function is 1.875.


thanks for replying, but could you explain what exactly you meant there? I understand that the period that we have is 1.875, but what am I supposed to do with the cosine part of it? I keep getting stuck when as I have 2 different unknown variables to deal with. i must be forgetting something to do with the cosine as i'm drawing blanks here.
Original post by Rhys808
thanks for replying, but could you explain what exactly you meant there? I understand that the period that we have is 1.875, but what am I supposed to do with the cosine part of it? I keep getting stuck when as I have 2 different unknown variables to deal with. i must be forgetting something to do with the cosine as i'm drawing blanks here.


The cosine function repeats with a period of 2pi, just as our function repeats with a period of 1.875. So we know that when t=1.875, pi*b*t = 2pi. Does that make sense?
Reply 22
Original post by Chlorophile
The cosine function repeats with a period of 2pi, just as our function repeats with a period of 1.875. So we know that when t=1.875, pi*b*t = 2pi. Does that make sense?


so as you said pi*b*t = 2pi, would i just have to divide 2pi by 0.9375 (half of one ocillation) or something like that?

I can sort of work out the cos part, but I'm always left with both a and c, but I can't figure out how to figure either one of them out. I hope this is what you're trying to do, because as you can tell i'm not great at maths.

i hope you don't mind making this as painfully obvious as you can.
Original post by Rhys808
so as you said pi*b*t = 2pi, would i just have to divide 2pi by 0.9375 (half of one ocillation) or something like that?

I can sort of work out the cos part, but I'm always left with both a and c, but I can't figure out how to figure either one of them out. I hope this is what you're trying to do, because as you can tell i'm not great at maths.

i hope you don't mind making this as painfully obvious as you can.


We know that 2pi = pi*b*t. so 2=bt. t=1.875 so b=2/1.875. However, it's also dividing by 180 within the cos function (which I didn't realise before) so you need to multiply this by 180, giving b=192. You can check if this works - entering t=0 and t=1.875 should both give 1. Indeed, it does. For the time being, you can totally ignore the A and the C. The A controls the amplitude and the C controls the offset. The only bit that controls the period, hence the answer to b, is what's inside the cos function.
Reply 24
Original post by Chlorophile
We know that 2pi = pi*b*t. so 2=bt. t=1.875 so b=2/1.875. However, it's also dividing by 180 within the cos function (which I didn't realise before) so you need to multiply this by 180, giving b=192. You can check if this works - entering t=0 and t=1.875 should both give 1. Indeed, it does. For the time being, you can totally ignore the A and the C. The A controls the amplitude and the C controls the offset. The only bit that controls the period, hence the answer to b, is what's inside the cos function.


after reading that i'm not sure that we're going on about the right thing? The question is asking for me to find a and c. I already have the value of b as 192.

what am i supposed now that i know the value of b is 192 to work out a and c?
Original post by Rhys808
after reading that i'm not sure that we're going on about the right thing? The question is asking for me to find a and c. I already have the value of b as 192.

what am i supposed now that i know the value of b is 192 to work out a and c?


You said your problem was part b?

A scales the function vertically. The function is modelling the height. The range of the cosine function is 2 (it goes from -1 to 1). The range of the spring oscillation is 0.5. So by what do you need to multiply 2 by to get 0.5?

Once you have that, you need to use C to adjust the base height of the function. You need to make the maximum function value = 2 and the minimum to be 1.5.
Reply 26
Original post by Chlorophile
You said your problem was part b?

A scales the function vertically. The function is modelling the height. The range of the cosine function is 2 (it goes from -1 to 1). The range of the spring oscillation is 0.5. So by what do you need to multiply 2 by to get 0.5?

Once you have that, you need to use C to adjust the base height of the function. You need to make the maximum function value = 2 and the minimum to be 1.5.


finally! i've done it! thanks for all the help with it! i've got that a=0.25 and c=1.75, and this seems to work!

Thanks so much!
Reply 27
I suffered on a similar issue on my last assignment. Trying to figure out how to take my equations, and turn them into the one I'm given :P

Brain blender XP
Reply 28
I'm on part d now. Any tips on how to work this one out? I have the answer as 0.46875, but I did this through trial and error and I need to show workings out. Is this answer right, and any hints towards the steps that I should have taken?
Reply 29
Actually don't worry about that, apparently I'm an idiot!
Original post by Rhys808
finally! i've done it! thanks for all the help with it! i've got that a=0.25 and c=1.75, and this seems to work!

Thanks so much!


Glad you understand :smile:
Reply 31
you've been so helpful, there is one last question that I have to do, and it looks to be a lot simpler, I just need a few things explained to me about it if you don't mind!

A sweet manufacturer found that the sales figures for a certain item depended on its selling price. The company’s market research department advised that the maximum number of items that could be sold weekly was 20000 and that the number decreased by 100 for every 1p increase in its price. The total production cost consists of a set-up cost of £200 plus 50p for every item manufactured.

If the price increase one week is p pence, find expressions in terms of p for:

(a) the number N of items sold weekly; (1 mark)

(b) the production cost £C; (2 marks)

(c) the revenue £R from the sales. (2 marks)

(d) Show that the profit £P is given by

P = 250p 10200 p2 (2 marks)

(e) What values of p will generate no profit? Give your answers to the nearest penny. (5 marks)

(f) From your knowledge of the behaviour of quadratic functions and using your answers to part (e), what value of p will generate the maximum profit and what is this maximum profit? (No calculus is needed.)
(4 marks)

Where it says "find expressions in terms of p", does that mean that p has to be the main focus? So p=? or just that it has to involve p?

I'm on part b. at the moment but I don't seem to be able to involve p in it. I have C=200+0.5N. Is this right so far, and any tips on how I would go about adding p into it if I need to.
Reply 32
Original post by Rhys808
you've been so helpful, there is one last question that I have to do, and it looks to be a lot simpler, I just need a few things explained to me about it if you don't mind!

A sweet manufacturer found that the sales figures for a certain item depended on its selling price. The company’s market research department advised that the maximum number of items that could be sold weekly was 20000 and that the number decreased by 100 for every 1p increase in its price. The total production cost consists of a set-up cost of £200 plus 50p for every item manufactured.

If the price increase one week is p pence, find expressions in terms of p for:

(a) the number N of items sold weekly; (1 mark)

(b) the production cost £C; (2 marks)

(c) the revenue £R from the sales. (2 marks)

(d) Show that the profit £P is given by

P = 250p 10200 p2 (2 marks)

(e) What values of p will generate no profit? Give your answers to the nearest penny. (5 marks)

(f) From your knowledge of the behaviour of quadratic functions and using your answers to part (e), what value of p will generate the maximum profit and what is this maximum profit? (No calculus is needed.)
(4 marks)

Where it says "find expressions in terms of p", does that mean that p has to be the main focus? So p=? or just that it has to involve p?

I'm on part b. at the moment but I don't seem to be able to involve p in it. I have C=200+0.5N. Is this right so far, and any tips on how I would go about adding p into it if I need to.


Check out this thread which is currently active:

http://www.thestudentroom.co.uk/showthread.php?t=2991745
Reply 33
Original post by Rhys808
I'm on part d now. Any tips on how to work this one out? I have the answer as 0.46875, but I did this through trial and error and I need to show workings out. Is this answer right, and any hints towards the steps that I should have taken?

i've got the same answer in radian. but if i do it degree i got 26.85 which made more sense . i dont know which one to put
How we can get cost and sales ? Can u help me
Reply 35
Original post by Haziqhaikal11
How we can get cost and sales ? Can u help me

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