<u>Given</u>:
Let x represents the radius of the cylinder.
Given that the height of the cylinder is twice the radius of its base.
The height of the cylinder is 2x.
We need to determine the volume of the cylinder.
<u>Volume of the cylinder:</u>
The volume of the cylinder can be determined using the formula,
Substituting r = x and h = 2x, we get;
Simplifying, we get;
Thus, the expression that represents the volume of the cylinder is 2πx³ cubic units.
Hence, Option b is the correct answer.
First check for the critical points of <em>f</em> by checking where the first-order derivatives vanish.
Notice how the point (1, 2) lies on the line <em>y</em> = 2<em>x</em> ; at this point, we get a value of <em>f</em>(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find <em>f</em>(0, 0) = 1 (MAX) and <em>f</em>(0, 2) = -3.
Now check on the boundary lines themselves. If <em>x</em> = 0, then
which has a maximum value of -3 when <em>y</em> = 2 (so we get the same critical point as before).
If <em>y</em> = 2, then
with a maximum of -5 when <em>x</em> = 1.
If <em>y</em> = 2<em>x</em>, then
with the same maximum of -5 when <em>x</em> = 1.
Answer:
Option d.
Step-by-step explanation:
Total employment for sheet metal workers in 2016 is projected to be = 201,000
This is a 6.3% increase from 2006.
Let the number of workers in 2006 be n
n + (6.3% of n) = 201,000
n + ( 0.063n) = 201,000
1.063n = 201,000
n =
n = 189,087. 4882 ≈ 189,000
the total employment in 2006 was approximately 189,000
Option d is the answer.