A cross-section is a disc with radius 
![V = \int_0^7 A(x)\, dx = \int_0^7 \pi(x+1)^2dx = \int_0^7 \pi(x^2 + 2x + 1)dx \\ \\ = \pi \left[ \frac{1}{3}x^3 + x^2 + x\right]_0^7 = \pi\left( \frac{1}{3}(7)^3 + 7^2 + 7\right) = \frac{511}{3}\pi](https://tex.z-dn.net/?f=V%20%3D%20%5Cint_0%5E7%20A%28x%29%5C%2C%20dx%20%3D%20%5Cint_0%5E7%20%5Cpi%28x%2B1%29%5E2dx%20%3D%20%5Cint_0%5E7%20%5Cpi%28x%5E2%20%2B%202x%20%2B%201%29dx%20%20%5C%5C%20%5C%5C%0A%3D%20%5Cpi%20%5Cleft%5B%20%5Cfrac%7B1%7D%7B3%7Dx%5E3%20%2B%20x%5E2%20%2B%20x%5Cright%5D_0%5E7%20%3D%20%5Cpi%5Cleft%28%20%5Cfrac%7B1%7D%7B3%7D%287%29%5E3%20%2B%207%5E2%20%2B%207%5Cright%29%20%3D%20%5Cfrac%7B511%7D%7B3%7D%5Cpi)
Which if the following relations represent functions?
1 answer:
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The equation of a line in Slope-Intercept form, is:
Where "m" is the slope of the line and "b" is the y-intercept.
By definition:
- The slopes of parallel lines are equal and the y-intercepts are different.
- The slopes of perpendicular lines are opposite reciprocals.
For this case you need to rewrite the equations given in the exercise in Slope-Intercept form by solving for "y".
- Line #1:
You can identify that:
- Line #2:
You can identify that:
Therefore, since:
You can conclude that: The graphs of the equation are parallel.