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It's difficult to explain without the visuals so yeah.
1. The function would be linear? Or cubic?
you were right. it's cubic
I'm not sure why some are positive while some are negative.
How is it cubic? Because linear just go's straight up and expo starts stable then swoops up.
because volume increases between some values and decreases between others. positive rate of change means the function is increasing, negative rates of change means it's decreasing
the rate of changes are just the volume of the cubes right?
okay that's cleared up.
no, the rates of change are the CHANGES in volume over the interval. So going from 1 cut to 2 increases volume by 28 cubic units. Going from 3 to 4 decreases volume by 44 units
oh oh okay right.
Okay confusion cleared.
you know it's cubic because volume is in cubic units for one. tbh, this question is incredibly misleading. This is like the one we did where the equation turned out to be 2^x. You're building your data from a specific function, so you don't really need to do regression. That's what @mathmate was saying. When you do regression you're going to get the function you used to build the data
When you calculate volume, you're using \[V=x(12-2x)(12-2x)\] That's exactly what you'll get when you do regression
***12 - 2x***
so should I tell you the height of all of my cubes? Maybe that will also help me understand this better.
ok. If you use the spreadsheet to do regression, make sure you're using the right degree on the polynomial. It's cubic so it should be degree 3
The heights are 1, 2, 3, 4, and 5, right?
thats what YOUR equation looks like sorry thats what I meant
mine looks like y= 4x^3 - 48x^2 + 144x - 1.123E-12
So the equation is 4x³ - 48x² + 144x because 1.123E-12 is very close to 0 and it can be dropped. The r^2 = 1 means that that equation is an exact fit for the data, which makes sense b/c we used the equation to create the data. In general the closer r^2 is to 1, the better the fit. Also 4x³ - 48x² + 144x is what you get if you multiply out x(12-2x)²
plug in 2.5 for x
into the equation we just got?
because x is the change of volumes right?
x is the size of the cut y is the volume the rate of change is the change in volume
okay got it. so it's 122.5
not sure if if I round up.
Well thank you again so much. I won't bother you again -ever lol. You're the best x100
haha its no bother. you're welcome