1a. Eliminate the parameter t to rewrite the parametric
equation as a Cartesian equation.
x(t)
=
cos(t) + 1
y(t)
=
7 sin2(t)
1b. A dart is thrown upward with an initial velocity of 68 ft/s
at an angle of elevation of 52°. Consider the position of the dart
at any time t. Neglect air resistance. (Assume t
is in seconds.)
Find parametric equations that model the problem situation.
x(t)
=
y(t)
=
1c.
A dart is thrown upward with...
1. Find a Cartesian equation for the curve.
r cos(θ) = 2
Identify the curve.
2. Find a Cartesian equation for the curve.
r = 4 sin(θ)
Identify the curve.
Write the heat conduction equation (without flow in and out) in
cartesian coordinates for the following case:
1. Steady-state, 1-D, without heat generation (2 points)
2.Transient, 1-D, without heat generation (2 points)
3.Transient, 3-D, with heat generation (3 points)
3. Write the three types of boundary conditions. (3 points)
Write the equation of the line.
What is r?
What is r squared?
Using the equation of the line if x is 25 what is y?
Using the equation of the line if y is 20 what is x.
x
25
32
27
24
26
18
20
23
20
16
19
15
20
27
27
y
28
34
36
28
31
22
24
26
24
23
22
13
23
35
29
The Cartesian coordinates of a point are given.
(a) (2, −5)
(i) Find polar coordinates (r, θ) of the point, where r > 0
and 0 ≤ θ < 2π. (r, θ) =
(ii) Find polar coordinates (r, θ) of the point, where r < 0
and 0 ≤ θ < 2π. (r, θ) =
(b) (-2, −2)
(i) Find polar coordinates (r, θ) of the point, where r > 0
and 0 ≤ θ < 2π. (r, θ) =...