Algebra 2 Notes 7-1
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1. A logarithm expresses the power to which a base number must be raised to equal the value of the logarithm. Logarithms allow for easier calculation of multiplication and exponential functions by converting them to addition. 2. Logarithmic rulers allow for multiplication calculations to be performed as additions by taking advantage of the logarithmic property that log(ab) = log(a) + log(b). 3. Common logarithms have a base of 10 and are useful in many scientific and engineering contexts for condensing and working with very large and small numbers.
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The passage discusses the importance of summarization in efficiently conveying key information from lengthy documents. It notes that effective summaries distill the most critical details and events into a brief yet informative recap of the overall topic and narrative. The ability to produce high-quality summaries is a useful skill for professionals across many fields in order to save time and focus on the most pertinent details.
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This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
Lsn 11-12: Kites
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
Lsn 11-10: Applications & Regents Problems
This document contains 3 trigonometry word problems: 1) Find the length of a segment labeled x in a diagram with a 12 foot side. 2) Given a 46 foot sign on a building, find the height of the building using angles of elevation. 3) Given angles of elevation to a lighthouse from a ship and its distance traveled, find how close the ship is to dangerous rocks near the lighthouse.
Lsn 11-6: Law of Cosines
The document provides examples of using the Law of Sines and Law of Cosines to solve for missing sides and angles of triangles. It includes 5 multi-step triangle problems worked out using the two trigonometric laws, with the key points being that Law of Sines is used when an angle is given alone, Law of Cosines is used when a side is given alone or one triangle has a right angle, and letter assignments in the Law of Cosines formula can be changed.
Lsn 11-7: Law of Cosines to find an Angle
The document provides 3 examples of using the Law of Cosines to find the measure of an angle given the lengths of 3 sides of a triangle. The first example finds the measure of an acute angle C in a triangle with sides of lengths 5, 12, and 9. The second finds the right angle C in a triangle with sides of lengths 5, 12, and 13. The third finds the measure of an obtuse angle C in a triangle with sides of lengths 5, 12, and 15.
Lsn 11-5: Law of Sines
Here are the steps to solve these Law of Sines problems:
1. Given: a = 13, b = 20, A = 75°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(75°)/13 = sin(B)/20
sin(75°)*20/13 = sin(B)
B = sin-1(0.8) = 67°
2. Given: a = 25, B = 38°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(38°)/25 = sin(m°)/20
sin(38°)*20/25 = sin
Lsn 11-8: Proving a Rhombus/Rectangle
To prove that a quadrilateral is a rectangle or rhombus, you must first prove that it is a parallelogram by showing that both pairs of opposite sides are parallel and congruent. Then, you need only one additional condition - either that the diagonals are congruent (rectangle) or that one angle is a right angle (rectangle), or that the diagonals are the same length (rhombus) or that one pair of consecutive sides are congruent (rhombus). The document provides an example proof of showing a quadrilateral is a rectangle.
Lsn 11-7 Proofs Given Rhombii
O documento apresenta várias equações matemáticas com símbolos de igualdade e desigualdade relacionando números e medidas de área. As equações definem relações entre diferentes variáveis numéricas e unidades de medida.
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Algebra 2 Notes 7-1
- 1. Lsn 71: Let's start with a SUPER FUN puzzle! Take a guess at what these Now see if you can statements are saying: fill in the blanks: 1
- 2. Def: A logarithm is ___ ______________. Say it: __________________________ What it means: Say it: __________________________ What it means: 2
- 3. 3.786 + 5.419 3.786 x 5.419 BECAUSE MULTIPLICATION IS HARD. but addition is pretty easy akshully. 3
- 4. "I was just trying to help!" blame this guy 4
- 5. 1024 * 64 = 1000 * 1000000 = Observe: 5.27 * 1.076 = x log10(x) x log10(x) x log10(x) x log10(x) x log10(x) x log10(x) x log10(x) x log10(x) x log10(x) x log10 5
- 6. Addition with a normal ruler: Multiplication with a Logarithmic Ruler: 10 10 10 10 10 10 10 10 10 10 16.6 * 42.2 6
- 7. 7
- 8. 8
- 9. Switching Forms: "log form" "exponential form" 9
- 10. Examples of inverse functions... (the inverse of sine is ________________) (the inverse of square is _________________) Exponentiation also has an inverse function: The inverse of is Def: 10
- 11. 11