Answer:
y= 49/5 or 9 4/5 or 9.8
Step-by-step explanation:
So you have a rod, laid flat in front of you like this:
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The density of this rod varies Linearly from the left end to the right end. That means that the density increases by a constant amount from one end of the rod to the other, and therefore and density along the rod can be found using a linear equation.
On one side of the rod the density is 5 and on the other the density is 17. The rod is ten feet long. So every 10 feet, the density increases by 17-5 which equals 12. We can simplify this and say that every five feet the density increases by six, because ten and twelve are both divisible by two, and this is a linear equation. So y=6/5x+5 where Y is the density of the tube and X is the distance from the left end of the tube. We add the +5 to the "x" side of the equation because at a distance of zero feet from the left end of the rod the density is already 5, and then goes up by 6/5x from there. So if you want to find the density four feet from the left side of the rod, you let x equal four. y=6/5(4)+5 and simplify.
y=6/5(4)+5
=24/5+5
=49/5 or 9 4/5 or 9.8
