Download Algebra with Career Applicaons

Unit8Vol1.notebook
February 04, 2013
Algebra with Career Applicaons
Unit 8: Ewen 12.1
Angles and Polygons
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Unit8Vol1.notebook
February 04, 2013
Angles
Angles are formed by two rays that have a common endpoint. The point is called the vertex and the rays are called sides. Angles are names with just the vertex or with three leers, pung the vertex in the middle. 2
Unit8Vol1.notebook
February 04, 2013
Measuring Angles
We use a protractor to measure angles. Make sure the vertex is at the center mark. Place one side of the angle in line with the 0o mark. Read the measurement on the other side of the angle. Decide if it is less than 90o or greater than 90o . Virtual Protractor
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Unit8Vol1.notebook
February 04, 2013
Coplanar Lines
Intersecng lines will intersect at one point. If the intersecng lines form a right angle, then the lines are perpendicular If the lines never intersect, then they are parallel
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Unit8Vol1.notebook
February 04, 2013
Angle Relaonships
Adjacent angles are two angles that share an endpoint and a side. Complementary angles are two angles that add up to 90o Supplementary angles are two angles than add up to 180o . 5
Unit8Vol1.notebook
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Find each of the following 1. Find the complement of 32o 2. Find the supplement of 112o 3. Find the supplement of 15o 4. Find the complement of 132o 5. Find the complement of 49o 6. Find the supplement of 67o 7. Find the complement of the supplement of 120o 6
Unit8Vol1.notebook
February 04, 2013
Transversals
If a transversal intersects two lines, two regions are created: the interior region and the exterior region. 7
Unit8Vol1.notebook
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Parallel Lines Cut by a Transversal
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Examples
Find the measure of all of the angles pictured at the le
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Polygons
Polygons are 2‐D closed figures with straight sides.
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Polygons
Polygons are 2‐D closed figures with straight sides.
Not Polygons 11
Unit8Vol1.notebook
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Categorizing Polygons
Polygons are named by the number of sides they have. Number of Sides Name of Polygon
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Triangle
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Quadrilateral
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Pentagon
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Hexagon
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Heptagon
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Octagon
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Nonagon
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Decagon
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Dodecagon
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Pentadecagon
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23­gon
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n­gon
Assignment: EWEN p. 373 # 1 ­ 36 all
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Unit8Vol1.notebook
February 04, 2013
Assignment: EWEN p. 373 # 1 ­ 36 all
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Unit8Vol1.notebook
February 04, 2013
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Unit8Vol1.notebook
February 04, 2013
Algebra with Career Applicaons
Unit 8: Ewen 4.1
Approximate Numbers and Accuracy
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Unit8Vol1.notebook
February 04, 2013
Tachometer
A tachometer is used to measure the number of revoluons an object makes with respect to some unit of me (usually minutes). The measurement is usually given in integral units, such as 25 rpm. Uses for a tachometer: Industrial: to test motors to see if they turn at a specified rate
Producon: Wood and metal lathes have specific rpm rates
Automove: Sports cars have tachometers to help drivers determine when to shi gears
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Unit8Vol1.notebook
February 04, 2013
Reading a Tachometer
Oen a tachometer is labeled with what the integral numbers represent. The one below is in hundreds. This one reads 10 hundred rpm or 1000 rpm. 18
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Read the tachometer.
Answer: 36 thousand rpm or 36,000 rpm
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Approximate Measures
Tachometer reading are approximate. They are calibrated in tens, hundreds, thousands…It is impossible to read an exact number of rpm.
All measurement is based on observaon. They give us approximate results. Consider measuring the block on the next slide. 20
Unit8Vol1.notebook
February 04, 2013
Measurement is approximate
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Exact versus Approximate
Exact numbers: • a result of counng such as 16 students
• Given by definion such as 1 in = 2.54 cm
• Operaons on exact numbers yield exact numbers
Approximate numbers: • Nearly all technical data, such as measurements
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Accuracy and Significant Digits
The accuracy of a measurement is the number of significant digits it contains. This means the number of units that we reasonably measured. The greater the number of significant digits, the more accurate
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Significant Digit Rules
1. All nonzero digits are significant.
2638 has 4 significant digits
2. All zeros between significant digits are significant
24,030 has 4 significant digits
3. A zero that is specifically tagged, such as by a bar is significant has 2 significant digits
4. All zeros to the right of a significant digit and a decimal point
3.140 has 4 significant digits
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Significant Rules Connued
• Zeros to the right in a whole number that are not tagged are not significant
4600 has 2 significant digits
6. Zeros to the le in a decimal measurement less than 1 are not significant
0. 000321 has 3 significant digits
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Examples
Determine the level of accuracy for each number (in other words, how many significant digits does each number have?) •
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109.006 m
0.000589 kg
75 V
239,000 mi
mi mi
0.03200 mg
1.20 cm
• 9.020 mA
• 100.050 km
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3
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Significant Digit Rules Summarized
The following are significant: • All nonzero digits • All zeros between significant digits
• A zero that is specifically tagged • All zeros to the right of a significant digit and a decimal point
The following are NOT significant:
• Zeros to the right in a whole number that are not tagged
• Zeros to the le in a decimal measurement less than 1
Assignment: EWEN p. 151 # 1 ­ 36 all
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Assignment: EWEN p. 151 # 1 ­ 36 all
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February 04, 2013
Algebra with Career Applicaons
Unit 8: Ewen 4.2
Precision and Greatest Possible Error
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February 04, 2013
Even Answers p. 151 # 1‐ 36 all
34. 3
36. 4
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Unit8Vol1.notebook
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Significant Digit Rules Summarized
The following are significant: • All nonzero digits • All zeros between significant digits
• A zero that is specifically tagged • All zeros to the right of a significant digit and a decimal point
The following are NOT significant:
• Zeros to the right in a whole number that are not tagged
• Zeros to the le in a decimal measurement less than 1
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Precision
The precision of a measurement means the smallest unit with which the measurement is made. In other words, it is the posion of the last significant digit. 32
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Examples
The precision of the measurement 3.20 m is 0.01 m because the last sig dig is in the hundredths spot. The precision of the measurement 521,000 mi is 1000 mi because the last sig dig is in the thousands spot. The precision of the measurement 23, 500 kg is 100 kg because the last sig dig is in the hundreds spot. 33
Unit8Vol1.notebook
February 04, 2013
Examples
Determine the precision of each of the following measurements. Measurement
• 109.006 m
• 0.000589 kg
• 75 V
• 239,000 mi
• mi • mi
• 0.03200 mg
• 1.20 cm
• 9.020 mA
• 100.050 km
Significant Digits
• 6
• 3
• 2
• 3
• 6
• 5
• 4
• 3
• 4
• 6
Precision
• 0.001 m
• 0.000001 kg
• 1 V
• 1000 mi
• 1 mi
• 10 mi
• 0.00001 mg
• 0.01 cm
• 0.001 mA
• 0.001 km
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Measuring Precision
The precision of a measuring instrument is determined by the smallest marked unit (called calibraon). The precision of the tachometers are below. Precision: 100 rpm
Precision: 1000 rpm
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Precision on a Ruler
The precision of a ruler graduated in eights is 1/8 in. The precision of a ruler graduated in quarters is ¼ in. If a measurement is given as 51/8 in it could have been measure with a ruler that is precise to sixteenths, thirty‐seconds, etc. We can never assume more precision, so we would say the smallest unit recorded. In this example, it would be 1/8 in.
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Reading Tachometers
Noce below that the enlargement of all of the tachometers give the same reading: 4100 rpm.
Any measure between 4050 rpm and 4150 rpm is registered at 4100 rpm. 37
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Greatest Possible Error
The greatest possible error is one‐half of the smallest unit on the scale on which a measurement is read. If a tachometer reads 5300 rpm, the precision is 100 rpm. The greatest possible error is ½ (100) = 50 rpm. This means that the actual measurement falls between 5250 rpm and 5350 rpm. 38
Unit8Vol1.notebook
February 04, 2013
Examples
• Find the precision and greatest possible error of the measurement 0.0460 mg. Precision: .0001 mg
Greatest Possible Error: .00005 mg
Range of actual: 0.04595 mg – 0.045605 mg
• Find the precision and greatest possible error of the measurement in. Precision: in Greatest Possible Error: in.
Range of Assignment: EWEN p. 155 # 1­ 30 all
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Assignment: EWEN p. 155 # 1 ­ 30 all
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