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
Answer:
The region between a chord and either of its arcs is called a segment the circle.
Angles in the same segment of a circle are equal.
Step-by-step explanation:
Let bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F .
Now from figure,
∠D = ∠EDF
∠D = ∠EDA + ∠ADF
Since ∠EDA and ∠EBA are the angles in the same segment of the circle.
So ∠EDA = ∠EBA
Hence ∠D = ∠EBA + ∠FCA
Again ∠ADF and ∠FCA are the angles in the same segment of the circle.
hence ∠ADF = ∠FCA
Again since BE is the internal bisector of ∠B and CF is the internal bisector of ∠C
So ∠D = ∠B/2 + ∠C/2
Similarly
∠E = ∠C/2 + ∠A/2
and
∠F = ∠A/2 + ∠B/2
Now ∠D = ∠B/2 + ∠C/2
=∠D = (180 - ∠A)/2
(∠A + ∠B + ∠C = 180)
∠D = 90 - ∠A/2
∠E = (180 - ∠B)/2
∠E = 90 - ∠B/2
and ∠F = (180 - ∠C)/2
∠F = 90 - ∠C/2
Answer:
a. -16/3
b. 16/3
c. -6
d. -6
e. 6
If x coordinate passes through the 0 it’s called origin
Answer:
Step-by-step explanation:
General form of circle: (x - h)² + (y- k)² = r²
r - > radius and h ,k are the coordinates of the center.
5) (x - 5)² + (y- 1)² = 64 = 8²
radius: 8 ; Center (5 , 1)
6) (x + 7)² + (y- 2k)² = 324 = 18²
Center = ( -7 , 2) ; radius = 18 ; diameter = 18 *2 = 36
7) (x )² + (y + 10)² = 42.25 = 6.5²
Center = (0 , - 10); radius = 6.5 ; diameter = 6.5*2 = 13
8) (x - 6)² + (y + 1)² = 80 = (4√5)²
Center =(6, -1) ; radius = 4√5
