There are two types of special right triangles: 45-45-90 and 30-60-90. The legs on a 45-45-90 triangle are 1 and 1 and the hypotenuse is the square root of 2. The legs on a 30-60-90 triangle are 1 and the square root of 3 and the hypotenuse is 2. If you were to take the three trigonometric functions of either 45 degree angle, you would get the (square root of 2)/2 for both cosine (x) and sine (y) and 1 for tangent (y/x). If you were to take the three trigonometric functions of the 30 degree angle, you would get the (square root of 3)/2 for cosine, ½ for sine and the (square root of 3)/3 for tangent.
You can find the volume of a rectangular prism using the same formula given above (V= l × w × h.) Another way to say it is to multiply the area of the base times the height. 1. 2. 3. Find the area of the base for the rectangular prism pictured above.
Set up the matrix equation to solve this system. 2. Given the inequality y < x2 + 2x – 3, is the point (0, -3) part of the solution? Name a point that is part of the solution and one that is not. 3.
Identify if the order triple (1, 2,3) is a solution of the given system of equations. 3x 5 y z 16 7 x y 3z 4 x 5 y 7 z 10 4. Identify if the system of equations given below has unique solution, infinitely many solutions, or no solution. 2 x 5 y 16 3x 7.5 y 24 5. Given is the augmented matrix of a system of equations: 1 5 6 2 7 1 3 5 1 5 7 13 Write the new form of the augmented matrix after the following row operations.
The naval battle won by the Greeks happened at the Straits of Salamis, while the 500 Spartans previously made a valiant last stand against the Persians at the Pass of Thermopylae in northern Greece. Intro: The Classical Chinese Dynasties of the Qin and Han established the basic components of the longest-lived civilization in world
The letters tell you about the number of dimensions of the representation (dimensions are the characters under E on the character table). A means 1D (E = 1) and symmetric (positive value) when rotating along the principal axis. B means 1D (E = 1) and asymmetric (negative value) when rotating along the principal axis. E means 2D (E = 2) T means 3D (E = 3) 1 The subscripts and superscripts tell you about the symmetry of the reps with
e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x. f) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for x. A) x² - 2x – 13 = 0 x² - 2x = 13 4x² - 8x = 52 4x² - 8x + 4 = 56 (2x – 2) ± 56 2x – 2 = 56 2x – 2 = 56 2x = 56+2 2x = 56+2 x = 56+2/2 x = 56+2/2 Project 2 C) x² + 12x – 64 = 0 -x² + 12x = 64 4x² + 48x = 256 4x² + 48 + 144 = 400 2x + 12 = ±20 2x +12 = 20 2x + 12 = -20 2x = 8 2x = -32 x = 4 x = -16 The method selected was the method shown in our text. I do not think I will ever have a chance to use this knowledge in a real-world situation. Algebra and Geometry are the hardest subjects for me, and I do not retain the teaching very well, so I am sure I will never use this formula. References Bluman, A.
n mathematics, the Pythagorean theorem—or Pythagoras' theorem—is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of thehypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1] where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. The Pythagorean theorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca.
The History of the Calculus The Calculus, being a difficult subject requires much more than the intuition and genius of one man. It took the work and ideas of many great men to establish the advanced concepts now known as calculus. The history of the Calculus can be traced back to c. 1820 BC to the Egyptian Moscow papyrus, in which an Egyptian successfully calculated the volume of a pyramidal frustum. [1][2] Calculating volumes and areas, the basic function of integral calculus, can be traced back from the school of Greek mathematics, Eudoxus (c. 408−355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes while Archimedes (c. 287−212 BC) developed this idea further, inventing heuristics which resemble integral calculus. [3] The method of exhaustion was later used in China by Liu Hui in the 3rd century AD in order to find the area of a circle.
The Golden Mean is the moderate position between two extremes. This is known as the ideal position because it is the “most appealing rectangle to the human eye.” The Golden Mean was said to be first used by the Ancient Egyptians and Greeks when building the Great Pyramids and Parthenon’s. Around 1200 AD, the Fibonacci sequence was discovered by a man named Leonardo Fibonacci, an Italian man born in 1175 AD. Although he discovered this, it is still not certain if he related it to the Golden Mean and Phi. The Golden Mean being “most appealing to the human eye” started being used in art.