The input to an exponential function is the initial value of the variable.
Step-by-step explanation:
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For the equation of the line expressed as Ax + By + C = 0, the value of the slope (m) is calculated by -A / B. For perpendicular lines, the slope of one should be the negative reciprocal of the other. From the choices given, the lines that are perpendicular is Option A.
Answer:
or
Step-by-step explanation:
Given
![[a,b] = [0,2]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%20%3D%20%5B0%2C2%5D)
Required
The volume of the solid formed
Rotating about the x-axis.
Using the washer method to calculate the volume, we have:
Integrate
Substitute values for a, b, f(x) and g(x)
Evaluate the exponents
Simplify like terms
Factor out 8
Integrate
![v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2x%5E%7B2%2B1%7D%7D%7B2%2B1%7D%20-%20%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%20%5D%7C%5Climit%5E2_0)
![v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2x%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%20%5D%7C%5Climit%5E2_0)
Substitute 2 and 0 for x, respectively
![v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%28%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D%20-%20%5B%20%5Cfrac%7B2%2A0%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B0%5E%7B4%7D%7D%7B4%7D%20%5D%29)
![v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%28%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D%20-%20%5B%200%20-%200%5D%29)
![v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D)
![v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B16%7D%7B3%7D%20-%20%5Cfrac%7B16%7D%7B4%7D%20%5D)
Take LCM
![v = 8\pi [ \frac{16*4- 16 * 3}{12}]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B16%2A4-%2016%20%2A%203%7D%7B12%7D%5D)
![v = 8\pi [ \frac{64- 48}{12}]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B64-%2048%7D%7B12%7D%5D)
Simplify
or
