Answer:
a) 25.15
b)
x = 1
y = t
z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)
c) (x,y) = (1, -2pi)
Step-by-step explanation:
a)
First lets calculate the velocity, that is, the derivative of c(t) with respect to t:
v(t) = (-sin(t), cos(t), 2t)
The velocity at t0=4pi is:
v(4pi) = (0, 1, 8pi)
And the speed will be:
s(4pi) = √(0^2+1^2+ (8pi)^2) = 25.15
b)
The tangent line to c(t) at t0 = 4pi has the parametric form:
(x,y,z) = c(4pi) + t*v(4pi)
Since
c(4pi) = (1, 0, (4pi)^2)
The tangent curve has the following components:
x = 1
y = t
z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)
c)
The intersection with the xy plane will occurr when z = 0
This happens at:
t1 = -2pi
Therefore, the intersection will occur at:
(x,y) = (1, -2pi)
Answer:
the perimeter is the total length of that plane figure
1. 
- Cone
2. 
- Sphere
3. 
- Cylinder
4. 
- Pyramid
5. 
- Prism
Solution:
1.
Lateral surface area of cone = 
where r is the radius of the cone and l is the slant height of the cone.
2.
Volume of sphere = 
where r is the radius of the sphere.
3.
Total surface area of cylinder = 
where r is the radius of the cylinder and h is the height of the cylinder.
4.
Volume of pyramid = 
where B is the base area of the pyramid and h is the height of the pyramid.
5.
Lateral surface area of prism = 
where p is the perimeter of the base and h is the height of the prism.
Answer:
x>=5
Step-by-step explanation:
If x is less than five, then there will be a negative in the square root, which will yield x an imaginary number.
