First let's move change the coordinate system so that the rotation axis becomes y
then f(x)=`16x becomes f(x)=16(x-2)=16x-32, y=0 stays as it is but x=1 becomes x=3
then we apply the formula for cyl shells method:
V=integral 2 to 3 (2pi*x*f(x))dx = int 2-3 (2pi*x*16x-2pi*x*32)dx=
int 2-3 32pi*x^2 dx - int 2-3 64pi*x dx = 2-3| 32pi*x^3/3 - 32pi*x^2 =
32pi*27/3 - 32pi*9 - 32pi*8/3+ 32pi*4 = 32pi*(9-9-8/3+4) = 32pi*4/3 = 128pi/3
6×ax+6×by =6ax+6by =3a+2b,6×bx-6×ay=3b-2a=6bx-3a+2b
Step-by-step explanation:
practical range = 8
vertical line test = 5
range = 3
domain = 2
relation = 1
function = 4
function Notation =6
practical domain=7
Answer:
The correct way to interpret the difference of a number divided by 6 and 5 equals 8 is
n/6 - 5 = 8. I believe that another tutor has misled you; there should be only one division, applying to n only.
Answer:
<h3>The answer is 15 units</h3>
Step-by-step explanation:
The distance between two points can be found by using the formula
![d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%20%28%7Bx1%20-%20x2%7D%29%5E%7B2%7D%20%2B%20%20%28%7By1%20-%20y2%7D%29%5E%7B2%7D%20%20%7D%20%5C%5C)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-1,-6) and (8,6)
The distance between them is
![d = \sqrt{( { - 1 - 8})^{2} + ({ - 6 - 6})^{2} } \\ = \sqrt{ ({ - 9})^{2} + ( { - 12})^{2} } \\ = \sqrt{81 + 144} \\ = \sqrt{225} \: \: \: \: \: \: \: \: \: \: \\ = 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%28%20%7B%20-%201%20-%208%7D%29%5E%7B2%7D%20%2B%20%20%28%7B%20-%206%20-%206%7D%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%28%7B%20-%209%7D%29%5E%7B2%7D%20%2B%20%28%20%7B%20-%2012%7D%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B81%20%2B%20144%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B225%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%5C%20%20%3D%2015%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20)
We have the final answer as
<h3>15 units</h3>
Hope this helps you