## calculusxy one year ago MEDAL!!! Questions attached below.

1. calculusxy

2. calculusxy

@phi

3. geerky42

4. geerky42

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5. geerky42

Based on what we've observed, it seem that for each one bottom rod we add, we add 4 rods.

6. Australopithecus

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

7. Australopithecus

until you get a function that models your system

8. calculusxy

So how can I write a function to represent that?

9. Australopithecus

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

10. Australopithecus

This new equation also has to satisfy the original requirement, x = 1, y = 3

11. calculusxy

I still don't understand how we would satisfy it if we have x = 1 and y = 3.

12. Australopithecus

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.

13. Australopithecus

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)

14. calculusxy

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 ?

15. Australopithecus

plug in an x value and solve for b

16. Australopithecus

the x value would be 3

17. Australopithecus

got to go you got this though looks good to me, I am sure you can solve for b

18. calculusxy

$11 = 4(3) + b$ $11 = 12 + b$ $11 - 12 = 12 - 12 + b$ $-1 = b$

19. calculusxy

$y = 4x -1$ Would that be correct?

20. geerky42

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21. Australopithecus

yes

22. calculusxy

@geerky42 Hilarious!