Function problem. Watch

Barry Chuckle
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Hi,

An architect decides that the smallest room in the house needs a window with the area 4000 cm2. The window will be in two parts : a square part at the bottom , and a rectangular part above it hinged at the top and with a height of 25 cm.

(a) Write down a function for the area of the window in correct notation, specifying domain and co-domain. Use, x for the width of the square window as the input of the function.
(b) Use graphical method to find x if the total window area of 4000 cm2.
(c) Find a solution for the problem in (b) with algebraic methods.
(d) Write down the inverse function for that in part (a).
(e) Plot the graph of the-inverse function in part (d) and use it to find the solution for the problem in part (b).

-----------------------------------------------------

Got the function worked out to :

f(x) = X^2+25X-4000

solved for f (x) = 0 and got the domain which is (0,51.97)
obviously the range is (0,4000)

and then the stupid graph such a rule produces.....?!

So any help appreciated, also what the hell is a 'co-domain'?!
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Mr M
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To understand codomain:

http://www.mathsisfun.com/sets/domai...-codomain.html
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Barry Chuckle
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can anybody help?
I cant understand how the graph can be a negative y value, but it can't be anything else (assuming it is correct so far?)
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Barry Chuckle
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bump.
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Mr M
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(Original post by Barry Chuckle)
Hi,

An architect decides that the smallest room in the house needs a window with the area 4000 cm2. The window will be in two parts : a square part at the bottom , and a rectangular part above it hinged at the top and with a height of 25 cm.

(a) Write down a function for the area of the window in correct notation, specifying domain and co-domain. Use, x for the width of the square window as the input of the function.
(b) Use graphical method to find x if the total window area of 4000 cm2.
(c) Find a solution for the problem in (b) with algebraic methods.
(d) Write down the inverse function for that in part (a).
(e) Plot the graph of the-inverse function in part (d) and use it to find the solution for the problem in part (b).

-----------------------------------------------------

Got the function worked out to :

f(x) = X^2+25X-4000

solved for f (x) = 0 and got the domain which is (0,51.97)
obviously the range is (0,4000)

and then the stupid graph such a rule produces.....?!

So any help appreciated, also what the hell is a 'co-domain'?!
As no-one else has helped you, your f(x) in part (a) should just be an expression for the area of the window i.e. you didn't need to get the 4000 involved at this stage.

Part b) draw the graph of y=x^2+25x (make a table of values if you like) and draw a straight line where y=4000 and see where they intersect. It should give you a U shaped parabola. There is one positive solution and one negative solution (ignore the negative solution).

Part c) Solve the quadratic equation x^2+25x-4000=0 by completing the square or using the quadratic formula.

Part d) You will need to complete the square on the expression in part a) and rearrange.

Part e) Hopefully all will have become clear by this point.
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Barry Chuckle
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(Original post by Mr M)
As no-one else has helped you, your f(x) in part (a) should just be an expression for the area of the window i.e. you didn't need to get the 4000 involved at this stage.

Part b) draw the graph of y=x^2+25x (make a table of values if you like) and draw a straight line where y=4000 and see where they intersect. It should give you a U shaped parabola. There is one positive solution and one negative solution (ignore the negative solution).

Part c) Solve the quadratic equation x^2+25x-4000=0 by completing the square or using the quadratic formula.

Part d) You will need to complete the square on the expression in part a) and rearrange.

Part e) Hopefully all will have become clear by this point.
Thanks for your response. Can I just ask, how is it possible to find the domain to part A if you don't include the area (4000)?
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Mr M
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(Original post by Barry Chuckle)
Thanks for your response. Can I just ask, how is it possible to find the domain to part A if you don't include the area (4000)?
Yes -I suggest you think about it in the context of the question.

If you have an expression for the area of a window where x is the width of the window then it would make no sense to allow x to be zero or negative. So x is a member of the set of real numbers and x is greater than zero.
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Barry Chuckle
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(Original post by Mr M)
Yes -I suggest you think about it in the context of the question.

If you have an expression for the area of a window where x is the width of the window then it would make no sense to allow x to be zero or negative. So x is a member of the set of real numbers and x is greater than zero.
So the answer to the domain in part A would simply be - X is greater than or equal to zero?

OK, I think I have it if that is the correct answer.

My tutor went through a question with a garden lawn with a uniform border and the range was set from zero, to half of the length of the whole garden, meaning that the range was set between a value of zero to an actual number instead of to infinity, so that's why I got confused.
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Mr M
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(Original post by Barry Chuckle)
So the answer to the domain in part A would simply be - X is greater than or equal to zero?

OK, I think I have it if that is the correct answer.

My tutor went through a question with a garden lawn with a uniform border and the range was set from zero, to half of the length of the whole garden, meaning that the range was set between a value of zero to an actual number instead of to infinity, so that's why I got confused.
No I think we could have an infinitely wide window here! I would probably go for x>0 rather than x>=0 though.
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Barry Chuckle
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OK thanks, I need to get my head around this.
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