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MAT-2240 Final: MATH 2240 App State Fall2012 Final Exam answer key

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turquoisegnu128
15 Feb 2019
School
App State
Department
Mathematics
Course
MAT-2240
Professor
All

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Document Summary

Use the variables t, s, r, . for free variables. X1 + x2 + x3 x4 = This translates back into the system of equations: x1 + x2 2x4 = 1, x3 + x4 = 3, 0 = 0 and 0 = 0. We have that x4 and x2 are free variables the other variables are basic. Let x4 = t. then x3 + t = 3 so x3 = 3 t. let x2 = s. then x1 + s 2t = 1 so x1 = 1 s + 2t. The general solution is. x1 = 1 + s 2t x2 = s x3 = 3 t x4 = t or in vector form . x1 x2 x3 x4: (10 points) A, b, and c are invertible square matrices of the same size. Let y = (abc) 1 and z = (ab)t .

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Related Questions

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f -1(x) = (x - 20)/2
b. f -1(x) = x - 20
c. f -1(x) = (x/2) - 20
d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log 4 12, 12)
b. (log 4 12, 4)
c. (log 4 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2.
a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2
b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2
c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2
d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

Show transcribed image text

I need help with these as soon as possible Please. Thank You!!

Q15. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million.
a. approximately the year 2093
b. approximately the year 2041
c. approximately the year 2088
d. approximately the year 2016

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f -1(x) = (x - 20)/2
b. f -1(x) = x - 20
c. f -1(x) = (x/2) - 20
d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log 4 12, 12)
b. (log 4 12, 4)
c. (log 4 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2.
a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2
b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2
c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2
d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

Show transcribed image text