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The graph in the question is missing.
Answer:
y =
Step-by-step explanation:
The function is cubic
It has roots as -4, -4 , 6
this means the value of x = -4, -4 , 6 which makes the entire equation zero
so we have solutions as
x+4 = 0
x+4 = 0
x- 6 = 0
on forming a cubic equation using these
(x+4)(x+4)(x-6)
the equation passes through (2,36)
put x = 2
(2+4)(2+4)(2-6) = (6)*(6)*(-4)
which exceeds 36 so we product the equation with -1/4 to get 36
Final equation
y =
y =
Given:
A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.
To find:
The volume of the figure.
Solution:
Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.
Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.
If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.
Volume of a cone is
where, r is radius of the base and h is vertical height of the cone.
Putting r=6 and h=9, we get
Therefore, the volume of the figure is sq. units.