Mr.Burn's class is taking aa field trip to the planetatium. The trip will $27 for each student. There are 18 students in his cla
2 answers:
You might be interested in
Answer:
(x,y,z)=(ucos(v), usin(v), )
where and
Step-by-step explanation:
Equation of a cone is
Equation of a paraboloid is
I have parametrised cone here. Please note that equation for cone in the question, is actually a paraboloid.
Imagine a sphere of radius 4, centered at origin and intersecting a cone also centered at origin and height along positive z-axis, given by the equations
where
Solving for these two equations, and substituting for z in the equation of sphere, we get a circle of radius units.
The equation of intersecting circle is:
Now, according to question, parametrizing this region of circle using parameters u and v.
Consider cylindrical co-ordinates: (r,θ,z)
In cylindrical co-ordinates
(x, y, z)= (r cos(θ), r sin(θ), z)
Eliminating z, and changing (r, θ)=(u,v)
For cone: x=ucos(v)
y= usin(v)
z=
or (x,y,z)=(ucos(v), usin(v), )
where and
The radius of the circle is 2.86 cm.
Step-by-step explanation:
Given,
The circumference of the circle = 18 cm
To find the radius of the circle.
Formula
The circumference of a circle of radius r is 2πr
According to the problem,
2πr = 18
or, r = = 2.86 (approx)
Hence,
The radius of the circle is 2.86 cm.