Problems 51–58 refer to the following slope fields: Figure for 51–58 57. Use a graphing calculator to graph y = 1 – Ce − x for C = −2, −1, 1, and 2, for − 5 ≤ x ≤ 5, −5 ≤ y ≤ 5, all in the same viewing window. Observe how the solution curves go with the flow of the tangent line segments in the corresponding slope field shown in Figure A or Figure B.
Problems 51–58 refer to the following slope fields: Figure for 51–58 57. Use a graphing calculator to graph y = 1 – Ce − x for C = −2, −1, 1, and 2, for − 5 ≤ x ≤ 5, −5 ≤ y ≤ 5, all in the same viewing window. Observe how the solution curves go with the flow of the tangent line segments in the corresponding slope field shown in Figure A or Figure B.
Solution Summary: The author explains how to draw the graph of the general solution of y=1-Ce-x for the differential equation for C=-2,1 and 2
Problems 51–58 refer to the following slope fields:
Figure for 51–58
57. Use a graphing calculator to graph y = 1 – Ce−x for C = −2, −1, 1, and 2, for − 5 ≤ x ≤ 5, −5 ≤ y ≤ 5, all in the same viewing window. Observe how the solution curves go with the flow of the tangent line segments in the corresponding slope field shown in Figure A or Figure B.
In Problems 37–44, find the midpoint of the line segment joining the points P1 and P2 .
. Find the equation of the line passing through the point (7, 2) andperpendicular to the line 5y = 9 – 2x
Use the four-step procedure for solving variation problems given
on page 480 to solve Exercises 1–10.
1. y varies directly as x. y = 65 when x = 5. Find y when
x = 12.
2. y varies directly as x. y = 45 when x = 5. Find y when
x = 13.
3. y varies inversely as x. y = 12 when x = 5. Find y when
x = 2.
4. y varies inversely as x. y = 6 when x = 3. Find y when
x = 9.
5. y varies directly as x and inversely as the square of z. y = 20
when x = 50 and z = 5. Find y when x=3 and z = 6.
6. a varies directly as b and inversely as the square of c. a = 7
when b = 9 and c=6. Find a when b= 4 and c= 8.
7. y varies jointly as x and z. y = 25 when x = 2 and z = 5.
Find y when x = 8 and z = 12.
8. C varies jointly as A and T. C = 175 when A = 2100 and
T = 4. Find C when A = 2400 and T = 6.
9. y varies jointly as a and b, and inversely as the square root
of c. y = 12 when a = 3, b = 2, and c = 25. Find y when
a = 5, b = 3, and c = 9.
10. y varies jointly as m and the square of n, and inversely as p.
y =…
Chapter 5 Solutions
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