A jet flies in a parabolic arc to simulate partial weightlessness. The curve shown in the figure represents the plane's height y (in 1000 ft ) versus the time t (in sec). a. For each ordered pair, substitute the t and y values into the model y = a t 2 + b t + c to form a linear equation with three unknowns a , b , and c .Together, these form a system of three linear equations with three unknowns. b. Use a graphing utility to solve for a , b , and c . c. Substitute the known values of a , b , and c into the model y = a t 2 + b t + c . d. Determine the vertex of the parabola. e. Determine the focal length of the parabola.
A jet flies in a parabolic arc to simulate partial weightlessness. The curve shown in the figure represents the plane's height y (in 1000 ft ) versus the time t (in sec). a. For each ordered pair, substitute the t and y values into the model y = a t 2 + b t + c to form a linear equation with three unknowns a , b , and c .Together, these form a system of three linear equations with three unknowns. b. Use a graphing utility to solve for a , b , and c . c. Substitute the known values of a , b , and c into the model y = a t 2 + b t + c . d. Determine the vertex of the parabola. e. Determine the focal length of the parabola.
Solution Summary: The author calculates a system of three linear equations with three unknowns by substituting the values of tandy for each ordered pair into the model.
A jet flies in a parabolic arc to simulate partial weightlessness. The curve shown in the figure represents the plane's height
y
(in
1000
ft
) versus the time
t
(in sec).
a. For each ordered pair, substitute the
t
and
y
values into the model
y
=
a
t
2
+
b
t
+
c
to form a linear equation with three unknowns
a
,
b
,
and
c
.Together, these form a system of three linear equations with three unknowns.
b. Use a graphing utility to solve for
a
,
b
,
and
c
.
c. Substitute the known values of
a
,
b
,
and
c
into the model
y
=
a
t
2
+
b
t
+
c
.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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