MEDAL!!! Questions attached below.

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MEDAL!!! Questions attached below.

Mathematics
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Let's start with something simple; |dw:1436914236068:dw|

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|dw:1436914308206:dw|
Based on what we've observed, it seem that for each one bottom rod we add, we add 4 rods.
essentially what geerky42 is doing he is simply modeling this problem by starting at the simplest form of the problem, then you work up to include complexities
until you get a function that models your system
So how can I write a function to represent that?
so for the first equation, we will denote, y = the total number of rods x = the total number of bottom rods we have from just a triangle made of rods: 3x = y because we know that one triangle uses 3 rods: 3(1) = 3 Now lets think about when we have 3 rods We sub 3 into our original equation we developed: 3(3) = 9 9 does not equal 11 Now think how can we change this equation: 3x = y to equal 11, when x = 3
This new equation also has to satisfy the original requirement, x = 1, y = 3
I still don't understand how we would satisfy it if we have x = 1 and y = 3.
you are simply modifying your original expression: 3x = y to give you an expression that satisfies when x = 1, y = 3 when x = 3, y = 11 Just play with the numbers in the original equation so it satisfies these conditions. Or you could just realize this is a linear function, and just use y=mx+b formula to solve it.
right now it satisfies the first condition x = 1 and y = 3 you need it to also satisfy when you have 3 (x=3) bottom rods you need 11 rods total (y=11)
so if we are using y = mx + b we know that y = 3 and x = 1 so 3 = mx + b Then we need to find out the slope: \[\frac{ y_2 - y_1 }{x_2 - x_1 } \] \[\frac{ 11 - 3 }{ 3 -1 } = \frac{ 8 }{ 2 } = 4 \] Our slope would then be 4. Now we have: \[11 = 4x + b \] So do we just plug in 3 for x ?
plug in an x value and solve for b
the x value would be 3
got to go you got this though looks good to me, I am sure you can solve for b
\[11 = 4(3) + b \] \[11 = 12 + b\] \[11 - 12 = 12 - 12 + b\] \[-1 = b\]
\[y = 4x -1 \] Would that be correct?
|dw:1436915563228:dw|
yes
@geerky42 Hilarious!

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