Let x represent the number of hours that Gordon spends tutoring math, and let y represent the number of hours that he spends tutoring English. For parts (a)-(d), write an inequality to represent the given statement. a. Gordon has at most 12 hr to tutor per week. b. The amount of time that Gordon spends tutoring English is at least twice the amount of time he spends tutoring math. c. The number of hours spent tutoring math cannot be negative. d. The number of hours spent tutoring English cannot be negative. e. Graph the solution set to the system of inequalities from parts (a)-(d).
Let x represent the number of hours that Gordon spends tutoring math, and let y represent the number of hours that he spends tutoring English. For parts (a)-(d), write an inequality to represent the given statement. a. Gordon has at most 12 hr to tutor per week. b. The amount of time that Gordon spends tutoring English is at least twice the amount of time he spends tutoring math. c. The number of hours spent tutoring math cannot be negative. d. The number of hours spent tutoring English cannot be negative. e. Graph the solution set to the system of inequalities from parts (a)-(d).
Solution Summary: The author explains that Gordon has at most 12 hours to tutor per week and the required inequality is x+yle 12.
Let
x
represent the number of hours that Gordon spends tutoring math, and let
y
represent the number of hours that he spends tutoring English. For parts (a)-(d), write an inequality to represent the given statement.
a. Gordon has at most
12
hr
to tutor per week.
b. The amount of time that Gordon spends tutoring English is at least twice the amount of time he spends tutoring math.
c. The number of hours spent tutoring math cannot be negative.
d. The number of hours spent tutoring English cannot be negative.
e. Graph the solution set to the system of inequalities from parts (a)-(d).
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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