Year 13 Maths Help Thread

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    (Original post by physicsmaths)
    What is it to u, so racist


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    Aliens, I tell you.
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    (Original post by Tau)
    I agree it's unnecessary, it was to highlight that it was an example of the general case of  \int f'(x)e^{f(x)}\ dx = e^{f(x)} +c .
    Yeah, u = x^2 or u =x^2/2 does the best job to highlight that, not u = -x^2/2.
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    (Original post by Zacken)
    Yeah, u = x^2 or u =x^2/2 does the best job to highlight that, not u = -x^2/2.
    Sorry Zacken I would have actually used  u = x^2/2 if I was doing it.
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    (Original post by Tau)
    Sorry Zacken I would have actually used  u = x^2/2 if I was doing it.
    DNt say sorry to him hes just being salty cause he cant deal with - signs
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    http://www.ukmt-resources.org.uk/SMC12.html

    Q17 on the link. The question references 'four quarter circles' but I can't spot any in the diagram! Am I missing something?
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    (Original post by Palette)
    http://www.ukmt-resources.org.uk/SMC12.html

    Q17 on the link. The question references 'four quarter circles' but I can't spot any in the diagram! Am I missing something?
    Says they are of radius 1, so I assume if you split the diagram into 4 equal parts, you will have your 4 quarter-circles. One such way is to draw 2 diagonals across the circle and you will have split it into 4 quarter circles of radius 1.
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    Name:  image.jpeg
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    I get that time to get to the meeting point will be the same for both cars but I honestly can't get any further than that. Please help
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    How do I sketch the graph  y=sin(5x) +\frac{3}{10}xsin(5x) between 0 and pi? I know I could get the points where the graph crosses the x axis, but how would I know that the amplitude of the graph increases as x increases?
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    (Original post by NotNotBatman)
    How do I sketch the graph  y=sin(5x) +\frac{3}{10}xsin(5x) between 0 and pi? I know I could get the points where the graph crosses the x axis, but how would I know that the amplitude of the graph increases as x increases?

    Factor out the sin(5x) and since 1+0.3x>0 for x>0 then sin(5x) +\frac{3}{10}xsin(5x)> sin(5x) for x>0 so the amplitude is increasing.
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    (Original post by solC)
    Factor out the sin(5x) and since 1+0.3x>0 for x>0 then sin(5x) +\frac{3}{10}xsin(5x)> sin(5x) for x>0 so the amplitude is increasing.
    I don't understand on the second line how LHS>RHS means the amplitude is increasing.
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    (Original post by NotNotBatman)
    I don't understand on the second line how LHS>RHS means the amplitude is increasing.
    Well if sin(5x)=1 then sin(5x) +\frac{3}{10}xsin(5x) = 1+\frac{3}{10}x so as x gets larger, the peak also gets larger whenever sin(5x)=1 since 1+\frac{3}{10}x is always increasing
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    (Original post by solC)
    Well if sin(5x)=1 then sin(5x) +\frac{3}{10}xsin(5x) = 1+\frac{3}{10}x so as x gets larger, the peak also gets larger whenever sin(5x)=1 since 1+\frac{3}{10} is always increasing
    Okay, thanks.
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    Can someone explain this fp2 question 15 ex 3hName:  Screenshot_20161015-204550.jpg
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    Can someone also explain why for part b when x=4 the equation =2Attachment 587012587014
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    (Original post by youreanutter)
    Can someone explain this fp2 question 15 ex 3hName:  Screenshot_20161015-204550.jpg
Views: 31
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    For this one I think it's easiest if you let z=2(cos(\theta)+isin(\theta)), as it makes it easier to see what k is.
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    (Original post by youreanutter)
    Can someone explain this fp2 question 15 ex 3hName:  Screenshot_20161015-204550.jpg
Views: 31
Size:  198.0 KB
    Let z=2e^ix
    Falls right out


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    (Original post by solC)
    For this one I think it's easiest if you let z=2(cos(\theta)+isin(\theta)), as it makes it easier to see what k is.
    Howcomes u are allowed to jist let z be what u want and how did u no to do that and what wud i do next still confused sorry
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    (Original post by medhelp)
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    I get that time to get to the meeting point will be the same for both cars but I honestly can't get any further than that. Please help
    Please post the image the right way round I know iT looks right when you upload it though
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    (Original post by youreanutter)
    Howcomes u are allowed to jist let z be what u want and how did u no to do that and what wud i do next still confused sorry
    Well since we know the points are on the circle |z|=2 the general point on that circle is z=2(cos(\theta)+isin(\theta)). Using the exponential form works too as Physicsmaths said

    Let z=2(cos(\theta)+isin(\theta))
    \Rightarrow w=2(cos\theta+isin\theta) +\frac{4}{2(cos(\theta)+isin(\th  eta))}
    \Rightarrow  w=2(cos\theta+isin\theta) +\frac{2(cos\theta-isin\theta)}{\cos^2\ + \sin^2\theta}
    \Rightarrow  w=4cos\theta
    And the range of this is -4 \leq \theta \leq 4 so K is 4
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    (Original post by youreanutter)
    Can someone explain this fp2 question 15 ex 3hName:  Screenshot_20161015-204550.jpg
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    It can be done with a little rearranging, using  |z|^2 = zz^*
 
 
 
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