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    Can anyone give me any tips on how to rearrange formula - its something I am severely lacking!

    I am dong the following question :

    A wire is bent into the plane shape ABCDEA. Shape ABDE is a rectangle and BCD is a semicircle with diameter BD. The area of the region enclosed by the wire is Rm2, AE= x metres, AB=ED= y metres. The total length of thee wire is 2m.
    a) find an expression for y in terms of x.
    b) prove that R =x/8(8-4x-nx)
    Given that x can vary, using calculus and showing your working,
    c) find the maximum value of R. (you do not have to prove that the value you obtain is a maximum.)

    I know how to do it but its just rearranging the formulas that I form!!

    For part a - I have:

    2y+x+pi x /2 = 2

    What should I do to make y the subject - it never looks like the answer in the book! Its frustrating coz I know how to do the question but I am having trouble ALL THE TIME rearranging formulas so they ca be incorporated into another formula....

    Any step by step instructions and things I need to look out for for future questions of this nature would be greatly appreaciated. This is really holding me back
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    two things, 1. this isn't geometric sequences, it's differentiation.
    2. im guessing you just want the re-arranging correct, so firstly (im guessing all of the left side is /2) you want to multiply the left and right side by 2 to get 2y+x+pi=4.
    now you subtract x and pi on both sides to get 2y=4-x-pi
    now divide everything by 2 to get y=(4-x-pi)/2. you can write it as y= 4/2 - x/2 - pi/2 (where 4/2 =2) the question sometimes does that to trick people
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    Yeah - clicked the wrong thing in my drop down menu of previous topics.

    Differentiation indeed.

    Sorry - It is just the pi x part this is divided by two - the perimeter of the semi circle.

    If it is just that one term divided by the 2 and I want to get rid of the fraction - do I multiply every term in the equation by 2??
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    oh yeh i didnt read the bottom part of your post, sorry:
    things to look out for:
    (lets pretend for every example you want y=...)
    if it's y+anything you must minus both sides of the equal sign by that "anything"
    if you have 2y=.... you must divide EVERYTHING by 2. that means if it's 2y=4x+6 it means you do 2y/2= 4x/2 + 6/2. the same goes with multiplying and square rooting, exponentials and logarithms if i think of any other help ill post it here but i think those are the main ones
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    If you have a + b + c/2 = d
    Then you can do 2a + 2b + c = 2d by multiply everything by 2.

    Caveat: I haven't looked at your attempt and whether what you've done is right or now.
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    Thanks guys - Im slowly getting there...

    I should probably go for a walk because I get to the next step and then I hit another brick wall..

    So now I have:

    2y + x + pi x /2 = 2

    Making y the subject I get:

    y = 1 - x/2 - pi x/4

    Is this correct?

    So now I need to plug this equation into the equation for the area and make it look like...

    R = x/8( 8 - 4x - pi x)

    So the area of the shap equals

    R = XY +1/2 pi x^2

    Substituting my equation for Y into this one, I get...

    R = x(1 - x/2 - pi x/4) + 1/2 pix^2

    Now this is where I am going around in circles becaue I am not sure how to make the above equation look like this one:

    R = x/8( 8 - 4x - pi x)


    I need a break!
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    (Original post by christinajane)

    R = x(1 - x/2 - pi x/4) + 1/2 pix^2
    Pull out a common factor of x, so:

    \displaystyle R = x\left(1 - \frac{x}{2} - \frac{\pi x}{4} + \frac{\pi x}{2}\right) = x\left(1 - \frac{x}{2} + \frac{\pi x}{4}\right)

    Now pull out a factor of \frac{1}{8}: \frac{x}{8}\left(8 - 4x + 2\pi x\right)

    Looks like you've done something wrong prior to this with regards to the \frac{1}{2} \pi x^2 - is it really 1/2 pi x^2 or is it something else...? Think about it. What's the radius?
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    The I thought was the area of a semi circle..

    Area of circle is = pi r^2

    So I thought the area of a semi circle is half this hence

    Is there a better way to write this? pi r^2 / 2??
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    (Original post by christinajane)
    The I thought was the area of a semi circle..

    Area of circle is = pi r^2

    So I thought the area of a semi circle is half this hence

    Is there a better way to write this? pi r^2 / 2??
    Why do you think your radius is x?
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    oh wait the diameter is x! which would mean the radius is x/2??
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    (Original post by christinajane)
    oh wait the diameter is x! which would mean the radius is x/2??
 
 
 
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