Consider the initial value problem for the function y given by y' = 3y (1 -...

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Consider the initial value problem for the function y given by y' = 3y (1 - ²/), y(0) = 3. (a) Find an implicit expression of all solutions y of the differential equation above, in the form (t, y) = c, where c collects all constant terms. (So, do not include any c in your answer.) (t, y) = Σ K 1 1 = + y (K-y) Y (K Y) (b) Find the explicit expression of the solution y of the initial value problem above. y(t) = Σ Hint: Recall the partial fraction decomposition where K is any constant. 180 5. The equations y = -x + 4 and y-x-8 form a system of linear equations. The table below shows the (x, y) values for these equations at six different values of x. X y=-x+4 y= A. 0, 1, 2, 3 8.-2,-1.2.7 MIN 0 4 2 2 -8 -7 What can you conclude from the table? F. The system has one solution, when x = 0. G. The system has one solution, when x = 4. H. The system has one solution, when x = 8. 1. The system has no solution. 5 114 Chapter 4 Functions 75-4-3-2 7 6. The temperature fell from 54 degrees Fahrenheit to 36 degrees Fahrenheit over a six-hour period. The temperature fell by the same number of degrees each hour. How many degrees Fahrenheit did the temperature fall each hour? (8.EE.5) 4 3 7. What is the domain of the function graphed in the coordinate plane below? (&EI) 47 4 4 3 1 0 -6 0 -24 6 -2 -5 (8.EE.8a) 8 8. What value of w makes the equation below true? (8.EE.7b) -3(w-1)-1 10 -6 -3 H. C. -3, -2,-1,0, 1.2.3 D. -2,-1,0, 1, 2.3.7 Explain Consider the initial value problem for the function y given by y' = 3y (1 - ²/), y(0) = 3. (a) Find an implicit expression of all solutions y of the differential equation above, in the form (t, y) = c, where c collects all constant terms. (So, do not include any c in your answer.) (t, y) = Σ K 1 1 = + y (K-y) Y (K Y) (b) Find the explicit expression of the solution y of the initial value problem above. y(t) = Σ Hint: Recall the partial fraction decomposition where K is any constant. 180 5. The equations y = -x + 4 and y-x-8 form a system of linear equations. The table below shows the (x, y) values for these equations at six different values of x. X y=-x+4 y= A. 0, 1, 2, 3 8.-2,-1.2.7 MIN 0 4 2 2 -8 -7 What can you conclude from the table? F. The system has one solution, when x = 0. G. The system has one solution, when x = 4. H. The system has one solution, when x = 8. 1. The system has no solution. 5 114 Chapter 4 Functions 75-4-3-2 7 6. The temperature fell from 54 degrees Fahrenheit to 36 degrees Fahrenheit over a six-hour period. The temperature fell by the same number of degrees each hour. How many degrees Fahrenheit did the temperature fall each hour? (8.EE.5) 4 3 7. What is the domain of the function graphed in the coordinate plane below? (&EI) 47 4 4 3 1 0 -6 0 -24 6 -2 -5 (8.EE.8a) 8 8. What value of w makes the equation below true? (8.EE.7b) -3(w-1)-1 10 -6 -3 H. C. -3, -2,-1,0, 1.2.3 D. -2,-1,0, 1, 2.3.7 Explain

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