(a) The differential equation satisfied by y in terms of a proportionality factor k .

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Answer 1

Question

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

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A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.

Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dt

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Answer 2

Question

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

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Answer 3

Question

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

Expert Solution & Answer

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Answer 4

Question

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

Expert Solution & Answer

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Answer 5

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

Answer 6

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

Answer 7

Chapter 9.4, Problem 8E

To determine

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

Answer 8

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

Answer 9

To determine

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

Answer 10

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

Answer 11

To determine

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 5PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E

(a) The differential equation satisfied by y in terms of a proportionality factor k .

(a) The differential equation satisfied by y in terms of a proportionality factor k.

(b) The value of k in units of day−1 assuming that 10% of the population knows the rumor at t=0 and 40% knows the rumor at t=2 days.

(c) When 75% of the population will know the rumor using the assumptions of part (b).

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Chapter 9 Solutions

(a)

The differential equation satisfied by $y$ in terms of a proportionality factor $k$ .

(b)

The value of $k$ in units of $d a y^{- 1}$ assuming that $10 %$ of the population knows the rumor at $t = 0$ and $40 %$ knows the rumor at $t = 2$ days.

(c)

When $75 %$ of the population will know the rumor using the assumptions of part (b).