Answer:
x = all real numbers.
Step-by-step explanation:
3 x minus 8 = negative x + 4 (x minus 2)
3x - 8 = -x + 4(x - 2)
3x - 8 = -x + 4x - 8
3x - 8 = 3x - 8
3x - 3x = -8 + 8
0 = 0
Since the result is a true statement, but 0 = 0, x is equivalent to all real numbers.
Hope this helps!
It is hard to comprehend your question. As far as I understand:
f(x,y) = e^(-x)
Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.
That is all I understood. It would be easier to understand with a picture or some kind of visual aid.
Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.

Now evaluate,

which evaluates to, 5/6 if I did the math correct. Correct me if I am wrong.
Now integrate this w.r.t. y:

So,

Both fractions have the same denominator so it's going to be easy. First set up your equation:

Add the whole numbers:

Now add the fractions:

add both together:

is an improper fraction so change it:

Since 6 is one more than 5, add 1 to the whole number and subtract the numerator and denominator(6 - 5 = 1) and make the remaining the new numerator. That leaves you with 
Your answer is 
All you need to do is multiply 18*60 = 1080 feet per minute, which is really fast.
It's the slope-point formula:

We have:

Therefore, the slope 