Answer:
cubic units
Step-by-step explanation:
We are to find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.
f(x)=2x+1, y=0, x=0, x=4.
The picture is given as shaded region.
This is rotated about x axis
Limits for x are already given as 0 and 4
f(x) is a straight line
The solid formed would be a cone
Volume = ![\pi \int\limits^a_b {(2x+1)^2} \, dx \\= \pi \int\limits^4_0 {(4x^2+4x+1)} \, dx \\=\pi [\frac{4x^3}{3} +2x^2+x]^5_0\\\\=\pi[\frac{4*4^3}{3}+2*4^2+4-0]\\=\frac{364\pi}{3}](https://tex.z-dn.net/?f=%5Cpi%20%5Cint%5Climits%5Ea_b%20%7B%282x%2B1%29%5E2%7D%20%5C%2C%20dx%20%5C%5C%3D%20%5Cpi%20%5Cint%5Climits%5E4_0%20%7B%284x%5E2%2B4x%2B1%29%7D%20%5C%2C%20dx%20%5C%5C%3D%5Cpi%20%5B%5Cfrac%7B4x%5E3%7D%7B3%7D%20%2B2x%5E2%2Bx%5D%5E5_0%5C%5C%5C%5C%3D%5Cpi%5B%5Cfrac%7B4%2A4%5E3%7D%7B3%7D%2B2%2A4%5E2%2B4-0%5D%5C%5C%3D%5Cfrac%7B364%5Cpi%7D%7B3%7D)
Answer:
Step-by-step explanation:
The answers is Scenic pathway has no sign up fee and a greater cost per day
Answer:
x > - 8
Step-by-step explanation:
- 4 ( x - 4 ) < - x + 40
- 4x + 16 < - x + 40
+ 16 - 40 < - x + 4x
- 24 < 3x
3x > - 24
x > - 24 / 3
x > - 8
x² - 80 = 0
Add 80
to each side: x² = 80
Square root
each side: x = √80
Look it up: x = + 8.944... (rounded)
and
x = - 8.944... (rounded).
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Here's a cleaner solution:
x² - 80 = 0
Add 80
to each side: x² = 80
Square root
each side: x = √80
But 80 = 16 · 5
So √80 = √16 · √5
√16 = 4, so x = 4 √5
