Mathematics
Solving Systems by Substitution
Subject:
A good way to solve systems of equations is by substitution. In this method, you solve on equation for one variable, then you substitute that solution in the other equation, and solve. Example:
1. Problem: Solve the following system:
x + y = 11
3x - y = 5
Solution: Solve the first equation for y
(you could solve for x - it
doesn't matter).
y = 11 - x
Now, substitute 11 - x for y
in the second equation. This gives
the equation one variable, which
earlier algebra work has taught
you how to do.
3x - (11 - x) = 5
3x - 11 + x = 5
4x = 16
x = 4
Cross Product
Subject:
Tags:
Vector Algebra ? Vector Addition ? Scalar Multiplication ? How about the product of two vectors? 1. Dot Product ?v ? ?u 2. Cross Product ?v ? ?u Before the geometry, Determinant ? Determinant of a 2? 2 matrix, ? ? ? ? a b c d ? ? ? ? = ad ? bc ? Determinant of a 3? 3 matrix, ? ? ? ? ? ? a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 ? ? ? ? ? ? = a 1 ? ? ? ? b 2 b 3 c 2 c 3 ? ? ? ? ? a 2 ? ? ? ? b 1 b 3 c 1 c 3 ? ? ? ? + a 3 ? ? ? ? b 1 b 2 c 1 c 2 ? ? ? ? =a 1 (b 2 c 3 ? b 3 c 2 )? a 2 (b 1 c 3 ? b 3 c 1 ) + a 3 (b 1 c 2 ? b 2 c 1 ) Example 1 1. ? ? ? ? ?1 2 3 5 ? ? ? ? = ?5? 6 = ?11 2. ? ? ? ? ? ? 2 4 6 ?1 3 5 7 2 6 ? ? ? ? ? ? = 2 ? ? ? ? 3 5 2 6 ? ? ? ? ? 4 ? ?
Cross Product
Subject:
Tags:
Vector Algebra ? Vector Addition ? Scalar Multiplication ? How about the product of two vectors? 1. Dot Product ?v ? ?u 2. Cross Product ?v ? ?u Before the geometry, Determinant ? Determinant of a 2? 2 matrix, ? ? ? ? a b c d ? ? ? ? = ad ? bc ? Determinant of a 3? 3 matrix, ? ? ? ? ? ? a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 ? ? ? ? ? ? = a 1 ? ? ? ? b 2 b 3 c 2 c 3 ? ? ? ? ? a 2 ? ? ? ? b 1 b 3 c 1 c 3 ? ? ? ? + a 3 ? ? ? ? b 1 b 2 c 1 c 2 ? ? ? ? =a 1 (b 2 c 3 ? b 3 c 2 )? a 2 (b 1 c 3 ? b 3 c 1 ) + a 3 (b 1 c 2 ? b 2 c 1 ) Example 1 1. ? ? ? ? ?1 2 3 5 ? ? ? ? = ?5? 6 = ?11 2. ? ? ? ? ? ? 2 4 6 ?1 3 5 7 2 6 ? ? ? ? ? ? = 2 ? ? ? ? 3 5 2 6 ? ? ? ? ? 4 ? ?
Function
Subject:
Y=X is a parent function as well as Y=X squared. However, the second function makes a parabola.
Function
Subject:
Y=X is a parent function as well as Y=X squared. However, the second function makes a parabola.
Pythagorean Theorem
Subject:
(c^2)=(a^2)+(b^2)
Algebra
Subject:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.
Slope Intercept Form
Subject:
y=mx+b is SLOPE INTERCEPT FORM.
Geometry
Geometry ? a Greek term meaning ?measure of the earth? Geometry is concerned with questions of size, shape, and relative positions of figures. The ancient Greek mathematician Euclid applied rigorous logic to the properties of Geometry and created an axiomatic system. Axiom ? self-evident truth that provides a starting point for deductive reasoning; sometimes called a ?postulate? Euclid was so influential that his textbook Elements was taught for over two millennia. What we study is called ?Euclidean Geometry.? There is also non-Euclidean Geometry, which is beyond the scope of this course.
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