EDGC 671 Theory Review Dean Owen, Ph.D., LPCC Rational Emotive Behavior Therapy.
Rational Review
51
NO HOMEWORK QUIZ • TURN IN WORK!!!!!!
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Rational Review. Asymptotes and Discontinuity. Asymptotes and Discontinuity. Asymptotes and Discontinuity. Asymptotes and Discontinuity. Asymptotes and Discontinuity. Asymptotes and Discontinuity. Variation. Domain and Range. Translation. Inequality. - PowerPoint PPT Presentation
Transcript of Rational Review
NO HOMEWORK QUIZ
• TURN IN WORK!!!!!!
Rational Review
As X approaches infinity
As X approaches infinity
Asymptotes and Discontinuity
Asymptotes and Discontinuity
Asymptotes and Discontinuity
Asymptotes and Discontinuity
Asymptotes and Discontinuity
Asymptotes and Discontinuity
Domain and Range
Translation
Inequality
Most tunnels are drilled using tunnel-boring machines that begin at both ends of the tunnel. Suppose a new underwater tunnel is being built and one tunnel-boring machine alone can finish the tunnel in 4 years. A different type of machine can tunnel to the other side in 3 years. If both machines start at opposite ends and work at the same time, when will the tunnel be finished?
Let x = number of years together
Let x = number of years together
Equation:
1 job 1 job 1 job
4 years 3 years x together
Let x = number of years together
Equation:
1 job 1 job 1 job
4 years 3 years x together
1 1 1
4 3 x
Solve equation: multiply by common denominator (4)(3)(x).
Solve equation: multiply by common denominator (4)(3)(x).
1(3 ) 1(4 ) 1(4)(3)x x
Solve equation: multiply by common denominator (4)(3)(x).
1(3 ) 1(4 ) 1(4)(3)x x
3 4 12x x
Solve equation: multiply by common denominator (4)(3)(x).
7 12x
1(3 ) 1(4 ) 1(4)(3)x x
3 4 12x x
Solve equation: multiply by common denominator (4)(3)(x).
12 5 or 1 years
7 7x
7 12x
1(3 ) 1(4 ) 1(4)(3)x x
3 4 12x x
If both machines work toward each other it will take 1.7 years to finish the tunnel.
If both machines work toward each other it will take 1.7 years to finish the tunnel.
A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/hr more than the speed of the train. Find the speed of the car and the speed of the train.
A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/hr more than the speed of the train. Find the speed of the car and the speed of the train.
Let x = speed of train
Let x + 20 = speed of car
A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/hr more than the speed of the train. Find the speed of the car and the speed of the train.
Let x = speed of train
Let x + 20 = speed of car
Use the formula d = rt. Solve for “t”.
t = d/r
Use the formula d = rt. Solve for “t”.
t = d/r
car traint t
Use the formula d = rt. Solve for “t”.
t = d/r
car traint t
car train
car train
d d
r r
Use the formula d = rt. Solve for “t”.
t = d/r
car traint t
car train
car train
d d
r r
300 200
x 20 x
Use the formula d = rt. Solve for “t”.
Solve: multiply by the common denominator (x + 20)(x).
Solve: multiply by the common denominator (x + 20)(x).
300 200( 20)x x
Solve: multiply by the common denominator (x + 20)(x).
300 200 4000x x
300 200( 20)x x
Solve: multiply by the common denominator (x + 20)(x).
300 200 4000x x
100 4000x
300 200( 20)x x
Solve: multiply by the common denominator (x + 20)(x).
300 200 4000x x
100 4000x
40x
300 200( 20)x x
Speed of train = x = 40 km/hr
Speed of train = x = 40 km/hr
Speed of car = x + 20 = 60 km/hr
Speed of train = x = 40 km/hr
Speed of car = x + 20 = 60 km/hr
A boat travels 20 miles upstream(means against the current) with a current going 4 miles/hour. The boat makes the trip THERE AND BACK in 5 hours. What is the SPEED OF THE BOAT?
A boat travels 20 miles upstream(means against the current) with a current going 4 miles/hour. The boat makes the trip THERE AND BACK in 5 hours. What is the SPEED OF THE BOAT?
