# C3 questionWatch

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#1

Q) Calculate the maximum value of H predicted by this model and the value of t, to 2 decimal places, when this maximum occurs. [3]

I don't really have much clue where to start on this, it's quite tragic lol... I was thinking about when sin and cos are maximum but a train hit me through the light at the end of the tunnel. Any help will be much appreciated, thank you.
0
8 years ago
#2
If you were to plot a graph of H against t, then I guess you'd get some sort of curve between 0 <= t < 12. What would you do to find the value of the maximum point of this curve?
0
#3
(Original post by Goldfishy)
If you were to plot a graph of H against t, then I guess you'd get some sort of curve between 0 <= t < 12. What would you do to find the value of the maximum point of this curve?
differentiate and make it equal to 0?
wait no, there's no coordinates to play around with
hmm
0
8 years ago
#4
(Original post by tripodd)
differentiate and make it equal to 0?
wait no, there's no coordinates to play around with
hmm
Differentiate wrt t. Co-ordinates don't have to take (x,y) values.
1
8 years ago
#5
Differentiate to find dH/dt
make that equal to zero
you'll get an equation with sin and cos equal to zero
you can make sin of blah equal to cos of blah
divide to get tan of blah equal to something and solve for t.
put that back into H to find the maximum
1
8 years ago
#6
the blah is 4pit/25 by the way
0
#7
From the earlier question I got

2 sin theta - 1.5 cos theta = 2.5 sin (theta - 0.6435)

Can this be used in any way? Question is a 3 marker, surely it's too much work for 3 marks? But I've started following your methods :]
thanks
0
8 years ago
#8
yeah it can
I just did it

H = 6 + 2sinA - 1.5cos A where A is 4pit/25
so we can use what you've got from the earlier question to find what dH/dt is when equal to zero
so H = 6 + 2.5sin(A - 0.6435)
dH/dt = 10pi/25. cos(A-0.6435)
when dH/dt = 0
cos(A-0.6435) = 0
you can solve for t now
0
#9
Got 8.5 and 4.41 respectively, just checked and they're both correct
Thanks for the help both of you... the second I get my daily rep allowance I'll make sure you come back and thumbsup your posts.
Much appreciated.
1
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