Program Description: Purpose of problem is to write the system of differential equations in the form x ′ = P ( t ) x + f ( t ) . Summary introduction: Problem will use the non-homogeneous solution for the differential equation x ′ = 2 x + 4 y + 3 e t , y ′ = 5 x − y − t 2 .

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Answer 1

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Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

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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

An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ No

Answer 2

Question

Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Answer 6

Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Answer 7

Chapter 5.1, Problem 13P

Program Plan Intro

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Answer 8

Expert Solution & Answer

Answer 9

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Answer 10

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Answer 11

Ch. 5.1 - Let A=[2347] and B=[3451]. Find (a) 2A+3B; (b)...Ch. 5.1 - Prob. 2P Ch. 5.1 - Find AB and BA given A=[203415] and B=[137032].Ch. 5.1 - Prob. 4P Ch. 5.1 - Prob. 5P Ch. 5.1 - Prob. 6P Ch. 5.1 - Prob. 7P Ch. 5.1 - Prob. 8P Ch. 5.1 - Prob. 9P Ch. 5.1 - Prob. 10P

Program Description: Purpose of problem is to write the system of differential equations in the form x ′ = P ( t ) x + f ( t ) . Summary introduction: Problem will use the non-homogeneous solution for the differential equation x ′ = 2 x + 4 y + 3 e t , y ′ = 5 x − y − t 2 .

Solution Summary: The author explains that the problem will use the non-homogeneous solution for the differential equation xprime.

Concept explainers

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Want to see the full answer?

Chapter 5 Solutions

Program Description: Purpose of problem is to write the system of differential equations in the form x ′ = P ( t ) x + f ( t ) . Summary introduction: Problem will use the non-homogeneous solution for the differential equation x ′ = 2 x + 4 y + 3 e t , y ′ = 5 x − y − t 2 .

Solution Summary: The author explains that the problem will use the non-homogeneous solution for the differential equation xprime.

Concept explainers

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) . Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .

Want to see the full answer?

Chapter 5 Solutions

Program Description: Purpose of problem is to write the system of differential equations in the form x′=P(t)x+f(t) .

Summary introduction: Problem will use the non-homogeneous solution for the differential equation x′=2x+4y+3et,y′=5x−y−t2 .