Answer:
Answer is 5x+2
Step-by-step explanation:
![Given \: f(x) = 4x - 1 \: \: and \: \\ g(x) = x + 3 \\ f(x) + g(x) = 4x -1 + x + 3 \\ = 5x + 2](https://tex.z-dn.net/?f=Given%20%5C%3A%20f%28x%29%20%3D%204x%20-%201%20%5C%3A%20%20%5C%3A%20and%20%5C%3A%20%20%5C%5C%20g%28x%29%20%3D%20x%20%2B%203%20%5C%5C%20f%28x%29%20%2B%20g%28x%29%20%3D%204x%20-1%20%20%20%20%2B%20x%20%2B%203%20%5C%5C%20%20%3D%205x%20%2B%202)
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The radius of the cylinder's base is 8, so the volume of the cylinder is
![\pi8^218\approx3617.28](https://tex.z-dn.net/?f=%5Cpi8%5E218%5Capprox3617.28)
(using the approximation of
![\pi\approx3.14](https://tex.z-dn.net/?f=%5Cpi%5Capprox3.14)
).
The sphere has radius 6, so the volume of the sphere is
![\dfrac43\pi6^3\approx904.32](https://tex.z-dn.net/?f=%5Cdfrac43%5Cpi6%5E3%5Capprox904.32)
.
The volume of the shaded region is the difference between the two: 3617.28 - 904.32 = 2712.96. Rounded to the nearest integer gives an answer of 2713.
4.07 * 100 = 407%
407 / 100 = 4.07
Answer:
The value at x =3 is undefined for the given expression
Step-by-step explanation:
Given expression is ![\frac{2x^2+8x}{(x+4)(x^2-9)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2%2B8x%7D%7B%28x%2B4%29%28x%5E2-9%29%7D)
To find for what value of x is undefined in the given expression :
![\frac{2x^2+8x}{(x+4)(x^2-9)}=\frac{2x(x+4)}{(x+4)(x^2-9)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2%2B8x%7D%7B%28x%2B4%29%28x%5E2-9%29%7D%3D%5Cfrac%7B2x%28x%2B4%29%7D%7B%28x%2B4%29%28x%5E2-9%29%7D)
![=\frac{2x}{x^2-9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2x%7D%7Bx%5E2-9%7D)
![\frac{2x^2+8x}{(x+4)(x^2-9)}=\frac{2x}{x^2-9}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2%2B8x%7D%7B%28x%2B4%29%28x%5E2-9%29%7D%3D%5Cfrac%7B2x%7D%7Bx%5E2-9%7D)
If we put x=3 in the above expression we get
![\frac{2x}{x^2-9)}=\frac{2(3)}{3^2-9}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7Bx%5E2-9%29%7D%3D%5Cfrac%7B2%283%29%7D%7B3%5E2-9%7D)
![=\frac{6}{9-9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6%7D%7B9-9%7D)
![=\frac{6}{0}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6%7D%7B0%7D)
Therefore ![\frac{2x^2+8x}{(x+4)(x^2-9)}=\frac{6}{0}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2%2B8x%7D%7B%28x%2B4%29%28x%5E2-9%29%7D%3D%5Cfrac%7B6%7D%7B0%7D)
The value at x =3 is undefined for the given expression