Consider the helix
r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t).
Compute, at t=π/6
A. The unit tangent vector T=T= ( , , )
B. The unit normal vector N=N= ( , , )
C. The unit binormal vector B=B= ( , , )
D. The curvature κ=κ=
IN EXCEL: 5.2.1 At time t = 0, a yeast culture weighs 0.5 g. Two
hours later, it weighs 2 g. The maximum weight of the culture is 8
g.
1. Create a spreadsheet to model the population using a logistic
equation. Use a scroll bar to vary the value of k.
2. Use the scroll bar to find a value of k so that the condition
y(2) = 2 is satisfied.
3. At what time is the weight increasing...
Temperature and Observations for Heating Curve.
Time (Min)
Temperature (°C)
Observations
0
0
Solid state
1
0
Solid with a little liquid
2
1
Solid and liquid
3
4
Liquid and bits of solid
4
8
Liquid and a tiny solid
5
25
liquid
6
35
liquid
7
54
Liquid
8
68
Liquid
9
78
Liquid
10
92
Liquid
11
101
Liquid
12
104
Liquid& gas
13
104
Liquid& gas
14
104
Liquid& gas
15
104
Liquid& gas
Questions
C....
Consider the equation t^2 -y"-t(t+2)y'+(t+2)y=2t^3,
(t>0). Given that y1(t)=t3, y2(t)=te^t are the two fundamental
solutions of the corresponding homogeneous equation, find the
general solution of the nonhomogeneous equation.
Table 1: Temperature of Frozen Water Over
Time
Time (min.)
Temperature (°C)
Observation
0
-12
Water is frozen
5
0
Water is frozen
10
1
Ice is attached to thermometer but unstuck from test tube
15
14
There is a pool of water in the bottom of the test tube
20
2
The pool of water is flightly bigger, ice chunk is getting
smaller
25
4
The ice chunk is over halfway melted
30
5
The Ice chunk is over...
Let r(t) = 2t ,4t2 ,2t be a position function for some
object.
(a) (2 pts) Find the position of the object at t = 1. (b) (6
pts) Find the velocity of the object at t = 1.
(c) (6 pts) Find the acceleration of the object at t = 1. (d) (6
pts) Find the speed of the object at t = 1.
(e) (15 pts) Find the curvature K of the graph C determined by
r(t) when...