The radius of the cylinder's base is 8, so the volume of the cylinder is
(using the approximation of
).
The sphere has radius 6, so the volume of the sphere is
.
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.
Answer:
Step-by-step explanation:
0.04
9514 1404 393
Answer:
- vertical scale ×2; translate (-1, -5); (-1, -5), (0, -3), (-2, -3)
- vertical scale ×1/2; translate (3, 1); (3, 1), (1, 3), (5, 3)
- reflect over x; vertical scale ×2; translate (-3, -4); (-3, -4), (-2, -6), (1, -8)
Step-by-step explanation:
Transformation of parent function f(x) into g(x) = c·f(x-h)+k is a vertical scaling by a factor of c, and translation by (h, k) units to the right and up. If c is negative, then a reflection over the x-axis is also part of the transformation. Once you identify the parent function (here: x² or √x), it is a relatively simple matter to read the values of c, h, k from the equation and list the transformations those values represent.
For most functions, points differing from the vertex by 1 or 2 units are usually easily found. Of course, the vertex is one of the points on the function.
<h3>1.</h3>
(c, h, k) = (2, -1, -5)
- vertical scaling by a factor of 2
- translation 1 left and down 5
Points: (-1, -5), (-2, -3), (0, -3)
__
<h3>2.</h3>
(c, h, k) = (1/2, 3, 1)
- vertical scaling by a factor of 1/2
- translation 3 right and 1 up
Points: (3, 1), (1, 3), (5, 3)
__
<h3>3.</h3>
(c, h, k) = (-2, -3, -4)
- reflection over the x-axis
- vertical scaling by a factor of 2
- translation 3 left and 4 down
Points: (-3, -4), (-2, -6), (1, -8)
_____
<em>Additional comment</em>
For finding points on the parabolas, we use our knowledge of squares and roots:
1² = 1, 2² = 4
√1 = 1, √4 = 2
