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PAST EXAM QUESTION

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Guys...grateful if you could solve this
 

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PlanetMaster

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For part (i),

For the curve \(y=3 cos (2x) \), we get \(y=3 \) for \(x=0 \) and \(x=2\pi \).
And since we know that the graph of \(cos (x) \) looks like,
g8y9ergt9et5y.png

We can deduce that minima and maxima are \(y=-3,3 \)
Remember its a 3 mark question so you just need an idea of how the graph would look like and don't need an actual sketch/plot.

For the line \(2y+\frac{3x}{\pi}=5 \),
we can see this is a straight line as it can be manipulated in the form \(y=mx+c \) and therefore only has one minima and one maxima.
So we just substitute \(x=0 \) and \(x=2\pi \) and we get \(y=\frac{1}{2},\frac{5}{2} \).

For part (ii), we just need to sketch based on answers from (i).

The sketches would look like
gp7uw84ytfw.png
and
giuyert5b0e956.png

For part (iii),
As the new equation is just a combination of the two equations above, we can see from the two sketches that the line will intersect with graph at 4 points so we have 4 solutions.

If anything is unclear, please let me know and I'll be happy to explain it further.

P.S. To get an answer faster in the future,
either post in a similar thread instead of making a new one,
or put your full subject (and code) in title i.e. Mathematics (9709) if you have to make a new thread.
 
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