Sandy has a personal trainer who encourages her to get plenty of cardiovascular exercise. In her first week of training, Sandy walks for 10 min on a treadmill every day. Each week thereafter, she increases the time on the treadmill by 5 min . Write the n th term of a sequence defining the number of minutes that Sandy spends on the treadmill per day for her n th week at the gym.
Sandy has a personal trainer who encourages her to get plenty of cardiovascular exercise. In her first week of training, Sandy walks for 10 min on a treadmill every day. Each week thereafter, she increases the time on the treadmill by 5 min . Write the n th term of a sequence defining the number of minutes that Sandy spends on the treadmill per day for her n th week at the gym.
Solution Summary: The author calculates the nth term of the sequence defining the number of minutes which Sandy spends on treadmill per day.
Sandy has a personal trainer who encourages her to get plenty of cardiovascular exercise. In her first week of training, Sandy walks for
10
min
on a treadmill every day. Each week thereafter, she increases the time on the treadmill by
5
min
.
Write the nth term of a sequence defining the number of minutes that Sandy spends on the treadmill per day for her
n
th
week at the gym.
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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