The ENM 503 Pretest An exercise in frustration Let’s see now. I remember that a log is associated with the lumber industry and a radical favors extreme change?

The ENM 503 Pre-Test Results Statistics: Mean and median – 60 percent Average number missed: 16 out of 40 Median number missed: 16 Minimum number missed: 9 Maximum number missed: 24 Standard deviation: 12.5% I really enjoyed that pretest. Me too! This is going to be one of my favorite classes. Engineering management students enjoy reminiscing about today’s class.

Problem 2 If an automobile averaged 40 miles per (mph) for 45 minutes and 50 mph for 1.5 hours, how far did it travel? 40 x 45/ x 1.5 = = 105 miles

Problem 3 Subtract (-2a + 7x – 5c 2 ) from (-2x + 8a + c 2 ) (-2x + 8a + c 2 ) - (-2a + 7x – 5c 2 ) - = -2x + 8a + c 2 +2a - 7x + 5c 2 = -9x + 10a +6c 2

Problem 5 log 2 8 = ? Log a x = y a y = x 2 y = 8; y = 3 working with logs

Problem 6 Multiply: (-3st 2 ) (2s 2 t 3 ) (-2s 2 t 2 ) = ? (-3st 2 ) (2s 2 t 3 ) (-2s 2 t 2 ) =12s 5 t 7 We know how to multiply.

Problem 7 Find the values for x for which -3x + 2 < 0. -3x < -2 X > 2/3 Read me the story again about changing the direction of an inequality when dividing by a negative number.

Problem 8 Express in simplest terms:

Problem 9 Factor into two binomial expressions: x 2 – xy – 2y 2 x 2 – xy – 2y 2 =(x+y)(x-2y)

Problem 11 Solve for y: y – (1/3) y + 1 = 3 – (2/3) y (2/3)y + 1 = 3 – (2/3)y (4/3)y = 2 Y = 2(3/4) = 6/4 = 1.5

Problem 12 Solve for w and z : w – 2z – 3 = 0 2w + 2z + 6 = 0 3W + 3 = 0 W = -1, Z = -2 You nailed this one Chuck.

Problem 13 An equilateral triangle is one whose sides are all the same length. If the perimeter of an equilateral triangle is 36 inches, what is its height? Side (hypotenuse) = 12; 144 – 36 = 108

Problem 14 Add:

Problem 15 Simplify:

Problem 17 Solve for x: 2x 2 – 13 = x x 2 = 25 x =  5 I forgot the minus sign.

Problem 18 A man has a rope 180 feet long that he wishes to cut into three parts in the ratio of 2:3:4. How long in feet will each piece of the rope be? 2x + 3x + 4x = 180 9x = 180 x = 20 therefore ratio is 40:60:80

Problem 19 If y varies directly with x (i.e. y is directly proportional to x), and y = 8 when x = 4, what is the value of y when x = 6? y = kx 8 = k4 k = 2 y = 2x = 2(6) =12

Problem 22 A man has a car with a 6 gallon radiator filled with a solution containing 10 percent coolant. He drains off a certain amount and replaces it with a solution that contains 70 percent coolant. How much was drained off if the solution then contained 20 percent coolant? Let x = gallons drained.70x +.10(6-x) =.20(6).7x -.1x = =.6 x = 1 gallon

Problem 25 (reduce to simplest terms) I like things in simplest terms.

Problem /3 = ?

Problem 27 Two airfields A and B are 400 miles apart and B is due east of A. A plane flew from A to B in 2 hours and then returned to A in 2.5 hours. The wind blew with a constant velocity from the west during the entire trip, find the speed of the plane in still air and the speed of the wind. Let x = speed of the airplane and y = speed of the wind recall that distance/ rate = time

Problem 28 Expand: (x – 2y) 3 = ? (x-2y)(x-2y)(x-2y) = (x-2y)[x 2 – 4xy + 4y 2 ] = x 3 – 4x 2 y + 4xy 2 -2x 2 y + 8xy 2 – 8y 3 = x 3 - 6x 2 y + 12xy 2 – 8y 3 Press the button

Problem 29 The amount of money available at simple interest is equal to the principle plus the product of the principle, the rate, and the time. Find the time required for a principle of $300 to accumulate to $336 at 4 percent per year. t = amount of time (years) required (.04) t = t = 36 t = 3 years

Problem 31 The perimeter of a rectangle is 20 inches and one side is 4 inches. What is its area? Perimeter = 2 length + 2 width = 20 2 length + 2(4) = 20 length = 6 Area = length x width = 6 x 4 = 24 sq. in.

Problem 32 Perform the indicated operation and simplify:

Problem 33 Rationalize the denominator (eliminate the radical from the denominator): It always bothers me to see a radical in the denominator.

Problem 34 Factor completely: 2x 4 y – 32y = ? 2y (x 4 – 16) = 2y (x 2 + 4) (x 2 - 4) 2y (x 2 + 4) (x - 2) (x+2) I just ran out of time.

Problem 35 Remove parentheses and simplify

Problem 36 Solve for x: log 10 x 3 – 2 log 10 x = 2 3 log 10 x – 2 log 10 x = 2 log 10 x = 2 x = 10 2 = 100 My head hurts.

Problem 38 The following system of equations has how many solutions? 2x + 3y = 10 4x + 6y = 7 Why, I can’t find any solution to these equations.

Tune in again next week, same place, same time… The Block 1 Exam This ought to be good. Come-on…