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Applied Mathematics Exam
(2 Hours)
Question 1:
1) Solve the following equation and inequality:
a) |3x-6| = |x+6| b) -2 ≤ x- 6 ≤ x+1
2) Determine the slope - intercept form of the linear equation which:
a) passes through (-4,-1) and is parallel to 8x - 2y = 0
b) passes through (3, 10) and is perpendicular to 4x- 2y = - 12
3) Determine the solution set for each of the following systems of equations, for any system having infinitely many solutions specify a generalized form of the solution (use the Gaussian elimination method):
a) - 4x1 + 6x2 + 2x3 = 8 b) 2x1 + 4x2 = -16
2x1 - 3x2 - x3 = -14 x1 - 2x2 = 16
Question 2:
1) find the sum of the following:
a) Σ i (i² -1) ( where the summation sign is from i = 5 to 15)
b) Σ 2i (i² - 5i + 4) ( where the summation sign is from i = 1 to 20)
2) A firm sells a product for $ 80 per unit, raw material costs are $ 12.5 per unit, labor costs are $27.5 per unit, and annual fixed costs are $ 360,000.
a ) How many units must be sold to break even?
b) How many units would have to be sold to earn an annual profit of $ 250,000?
3) Sketch the following function:
-x x < 0
a) f (x) = 2 0 ≤ x <3
x x ≥ 3
b) A machine is purchased for $ 300,000 Accountants have decided to use "a straight line depreciation method". it is assumed that the machine can be resold after 8 years for $ 28,000. Determine the function V = f (t), where V : is the book value of the machine, and t is the age of the machine. Also determine the Constant rate of depreciation.
Question 3:
1) Find the distance separating the following points:
a) (4,6) and (0,0) b) (-1,-3) and (4,3)
2) Determine the domain of the following function:
a) f (x) = 25 - x² b) f (t) = Square Root of ( 9 - t²)
3) Solve the following system of equations using cramer's Rule:
3x1 + 2x2 - 7 = 0
- x2 + 5x1 - 3 = 0
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