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# c2 question Geometric sequences

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1. 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
2. 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
3. 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??
4. 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
5. 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.
6. 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!
7. (Original post by christinajane)

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

Now pull out a factor of :

Looks like you've done something wrong prior to this with regards to the - is it really 1/2 pi x^2 or is it something else...? Think about it. What's the radius?
8. 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??
9. (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??
10. oh wait the diameter is x! which would mean the radius is x/2??
11. (Original post by christinajane)
oh wait the diameter is x! which would mean the radius is x/2??

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