4 and 5
This is because when you multiply 6 by 4 you get 24. Then you divide it by 5 which is 4.8, the answer lies between 4 & 5.
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

Answer: (3, -1)
Step-by-step explanation:
y = |x-3|-1
When y=|x|, vertex is (0, 0).
Now, let's translate the graph so it becomes y = |x-3|-1.
|x| ==> |x-3| Translate the graph 3 units to the right
Vertex: (0+3, 0) ==> (3, 0)
|x-3| ==> |x-3|-1 Translate the graph 1 unit down
Vertex: (3, 0-1) ==> (3, -1)
Vertex: (3, -1)
Answer:
x = ±
- 2
Step-by-step explanation:
x² + 4x = 4
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 4 + 4
(x + 2)² = 8 ( take square root of both sides )
x + 2 = ±
( subtract 2 from both sides )
x = ±
- 2