Cake Tin, open top, is to be made from following rect. piece of tinplate.

[devebr]

Can someone please help/ give explanation on how to start question. Thanks


Part B
Consider the following rectangular piece of tinplate. An open top cake tin is to be made by cutting a square from each corner.

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Develop a conjecture about the relationship between (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume.
The sides of the rectangle are in a ratio . Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios.
Hint: find exact solutions for (i.e. use the quadratic formula).

 

[devebr]

Can someone please explain how to do this question. Thanks

Part B
Consider the following rectangular piece of tinplate. An open top cake tin is to be made by cutting a square from each corner.

​

​

​

Develop a conjecture about the relationship between (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume.
The sides of the rectangle are in a ratio . Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios.
Hint: find exact solutions for (i.e. use the quadratic formula).

 

[stapel]

Can someone please help/ give explanation on how to start question. Thanks

Part B
Consider the following rectangular piece of tinplate. An open top cake tin is to be made by cutting a squarefrom each corner.

http://www.freemathhelp.com/forum/x...agic/41EEB7D3-3D24-425C-A141-F343B24BCF1C.gif

The graphic is not displaying. Kindly please repost, or else provide a description.

Develop a conjecture about the relationship between (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume.

Use what you learned back in algebra about creating an expression from a drawing. You'll be cutting out squares with sides lengths of, let's say, "x" units. How does this affect your drawing? In particular, after you've cut out these squares and folded up the sides (just like you did back in algebra for quadratic-equation word problems), what will be the dimensions of the base? (here)

The sides of the rectangle are in a ratio. Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios. Hint: find exact solutions for (i.e. use the quadratic formula).

Follow the hint. Use what you learned back in early algebra to create an expression, in terms of one of the dimensions, for the other dimension. For instance, if the length L is twice the width w, then L = 2w. And so forth. (here)

Please reply with the missing information from the graphic, along with your work so far (at least what you've been able to do based on the algebra hints above), so we can know what's going on. Thank you!

 

[devebr]

Reply ( not sure if diagrams work)

Consider the following rectangular piece of tinplate. An open top cake tin is to be made by cutting a square from each corner.

Develop a conjecture about the relationship between x (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume.
The sides of the rectangle are in a ratio r:s. Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of x that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios.
Hint: find exact solutions for x (i.e. use the quadratic formula).

rcm

scm
​

So far i have completed ratios of 2:1, 3:1, 4:1 ( ratio of 2:1, and then 2 other ratios)

e.g
2:1

L= 10
W= 5
1. Found equation that would be: x(10-2x) (5-2x)

2. Expanded: 4x³-30x²+50x
3. Take derivative to get quadratic equation: 12x²-60x+50

4. Put through quadratic equation to get values of: x= 3.94 or x= 1.05

*** Have no idea how these values of x relate to the length and to overall give a conjecture.

Thanks for your help

 

[stapel]

Consider the following rectangular piece of tinplate. An open top cake tin is to be made by cutting a square from each corner.

http://www.freemathhelp.com/forum/w...1-22fe-48f9-9ee6-1a9261d95bb7/application.pdf

Develop a conjecture about the relationship between x (the cut to be made for the square) and the length of each side of the rectangle such that the cake tin has a maximum volume.
The sides of the rectangle are in a ratio r:s. Consider a rectangle where one side is twice the length of the other (i.e. 2:1). Find the value of x that gives the maximum volume for the cake tin. Repeat this process for rectangular tinplates with sides in at least two other ratios.
Hint: find exact solutions for x (i.e. use the quadratic formula).

rcm

http://www.freemathhelp.com/forum/w...8-080b-452f-a07e-1d29e6417208/application.pdf

scm

The graphics are still not displaying. Please reply with a description. Also, please explain the meaning of "rcm" and "scm".

So far i have completed ratios of 2:1, 3:1, 4:1 ( ratio of 2:1, and then 2 other ratios)

e.g
2:1

L= 10
W= 5
1. Found equation that would be: x(10-2x) (5-2x)

How? What was the source of the "10" and the "5"? Was this something that the graphics contained?

2. Expanded: 4x³-30x²+50x
3. Take derivative to get quadratic equation: 12x²-60x+50
4. Put through quadratic equation to get values of: x= 3.94 or x= 1.05

*** Have no idea how these values of x relate to the length and to overall give a conjecture.

How was "x" defined? (Re-read my earlier reply, where I defined the variable.) Then for what does "x" stand?

To figure out how x is related to the final length and width of the formed pan, consider how you came up with your cubic equation in part (1) of your solution. :wink:

 

[devebr]

Hopefully diagram is visible now.
'r'cm= length
's'cm= width

* the diagram is a cake tin- where 'x' are the length of the squares above that need to be cut out to allow it to fold up like a cake tin. The aim is to find out the best value for 'x' to maximise the volume of the cake tin.

They are asking for us to develop of conjure about the relationship between x ( the cut out) and the length of each side ( 'r'cm and 's'cm)

Question: The sides of the rectangle are in a ration r:s ( length:width). Consider a rectangle where one side is twice the length of another (i.e.. ratio 2:1).

Find the value of x that gives the maximum volume for the cake tin. Repeat this process for tinplates with sides in at least two other ratios.

*** They didn't supply ration values ( thats why for ration 2:1 i used r=10cm and s=5cm)- although not sure if this is right.

Thanks

* link to whole assignment* file:///private/var/folders/9f/swn6frjd7kv705qjd0hv6g0w0000gn/T/TemporaryItems/Word%20Work%20File%20D_838026548.htm

 

[stapel]

* link to whole assignment* file:///private/var/folders/9f/swn6frjd7kv705qjd0hv6g0w0000gn/T/TemporaryItems/Word%20Work%20File%20D_838026548.htm

We cannot access files on your computer. Sorry.

diagram:

    length: r cm
+--+----------------+--+
|  |x               |  | width:
+--+                +--+
|                      |  s cm
+--+                +--+
|  |                |  |
+--+----------------+--+

* the diagram is a cake tin- where 'x' are the length of the squares above that need to be cut out to allow it to fold up like a cake tin. The aim is to find out the best value for 'x' to maximise the volume of the cake tin.

They are asking for us to develop of conjure about the relationship between x ( the cut out) and the length of each side ( 'r'cm and 's'cm)

Question: The sides of the rectangle are in a ration r:s ( length:width). Consider a rectangle where one side is twice the length of another (i.e.. ratio 2:1).

Find the value of x that gives the maximum volume for the cake tin. Repeat this process for tinplates with sides in at least two other ratios.

*** They didn't supply ration values ( thats why for ration 2:1 i used r=10cm and s=5cm)- although not sure if this is right.

I'm not sure we yet have the full text of the actual exercise, since nothing in the "Question" says anything about "conjuring" ("conjecturing"?) about any relationship. It really would be helpful if you'd provide that information, as it is quite difficult to help find answers when we don't know the questions.

Note: To learn what "ratios" (not "rations") are, try here.

You are given that the length L is "r" centimeters and the width w is "s" centimeters. What then are the dimensions of the length and width of the final pan? Hint: Use what you learned back in algebra, including what was shown to you in the link provided to you earlier. You will end up with expressions in terms of x, r, and s.

Using these expressions, what then will be the "volume" equation for the final pan? (Again, use what you learned back in algebra.)

Noting that r and s are constants (for any particular pan), differentiate. Set the result equal to zero, and solve for x, using the Quadratic Formula, as instructed. Where does this lead?

Please reply showing your working for the above steps. Thank you!