I'll probably post alot of math, that's what I need to get 80% in today and I have like 50%
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Let be the line given by the vector equation
.
First, we use the director vectors of the lines L1 and L2 to get the
vector equation of the plane containing them, which we denote by . This is,
We observe that . Therefore, the vector equation of
defines a plane and
is a normal vector to
Finally, the vector equation for the wanted plane, which we denote by , is
Thus, if , then
and since
is parallel to
, then it is perpendicular to
.
Alright, so the rate of change is the same thing as the slope, so we can find this by using the slope formula (which I took a picture of because it's super messy to type it out like this)
Now that we know the slope formula, we need to find the x values and the y values to plug into the equation. We'll say that the years are our x values and the money spent (in billions) are our y values. Now that we've set up an axis, we can create points! Our points would be (2000, 1243) and (2005, 1838)
Now we can plug our points into our equations! On the top of our equation, we'll put (1838-1243), and on the bottom we'll put (2005-2000). When we simplify that, we end up with 595/5, which simplifies to 119. Now we know that the rate of change for the credit cards was 119 billion!
Now that we know the slope formula, we need to find the x values and the y values to plug into the equation. We'll say that the years are our x values and the money spent (in billions) are our y values. Now that we've set up an axis, we can create points! Our points would be (2000, 1243) and (2005, 1838)
Now we can plug our points into our equations! On the top of our equation, we'll put (1838-1243), and on the bottom we'll put (2005-2000). When we simplify that, we end up with 595/5, which simplifies to 119. Now we know that the rate of change for the credit cards was 119 billion!