Saudi Oil Revenues The price of crude oil during the period 2000-2010 can be approximated by P ( t ) = 6 t + 18 dolloars per barrel ( 0 ≤ t ≤ 10 ) In year t , where t = 0 represents 2000. Saudi Arabia’s crude oil production over the same period can be approximated by P ( t ) = − 0.036 t 2 + 0.62 + 8 million barrels per day ( 0 ≤ t ≤ 10 ) . Use these models to estimate Saudi Arabia’s daily oil revenue and also its rate of change in 2008. (Round your answer to the nearest $1 million.)
Saudi Oil Revenues The price of crude oil during the period 2000-2010 can be approximated by P ( t ) = 6 t + 18 dolloars per barrel ( 0 ≤ t ≤ 10 ) In year t , where t = 0 represents 2000. Saudi Arabia’s crude oil production over the same period can be approximated by P ( t ) = − 0.036 t 2 + 0.62 + 8 million barrels per day ( 0 ≤ t ≤ 10 ) . Use these models to estimate Saudi Arabia’s daily oil revenue and also its rate of change in 2008. (Round your answer to the nearest $1 million.)
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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