PPT
... eqi = cos q + i sin q a is a nth root of unity if an = 1 Square roots of unity: +1, -1 Fourth roots of unity: +1, -1, i, -i Eighth roots of unity: +1, -1, i, -i, b + ib, ...
... eqi = cos q + i sin q a is a nth root of unity if an = 1 Square roots of unity: +1, -1 Fourth roots of unity: +1, -1, i, -i Eighth roots of unity: +1, -1, i, -i, b + ib, ...
12-10-14_solving_eq_w-variables_on_both_sides
... 7x + 19 = - 2x + 55 Let’s analyze this equation first… Deciding where to start….I see that on the left side is 7x and on the right side is – 2x. In this instance I will use the general rule and collect the x’s to the left side of the equation…I do that by working on the right side of the equation an ...
... 7x + 19 = - 2x + 55 Let’s analyze this equation first… Deciding where to start….I see that on the left side is 7x and on the right side is – 2x. In this instance I will use the general rule and collect the x’s to the left side of the equation…I do that by working on the right side of the equation an ...
Algebra1 - Tramore maths circle
... Substitute this into the other equation so there is now only one variable and the equation can be solved. (y + 4)2 + y2 = 10 y2 + 8y + 16 + y2 = 10 2y2 + 8y + 16 - 10 = 0 2y2 + 8y + 6 = 0 y2 + 4y + 3 = 0 (y + 3)(y + 1) = 0 y = -1 or y = -3 Now for each solution we have to go back and solve for the o ...
... Substitute this into the other equation so there is now only one variable and the equation can be solved. (y + 4)2 + y2 = 10 y2 + 8y + 16 + y2 = 10 2y2 + 8y + 16 - 10 = 0 2y2 + 8y + 6 = 0 y2 + 4y + 3 = 0 (y + 3)(y + 1) = 0 y = -1 or y = -3 Now for each solution we have to go back and solve for the o ...
Core A-level mathematics - User Web Areas at the University of York
... (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers. (b) The laws of indices for positive integer exponents. (c) Solution of problems involving ratio and proportion (including similar triangles, and links between length, area and volume of similar figures). (d ...
... (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers. (b) The laws of indices for positive integer exponents. (c) Solution of problems involving ratio and proportion (including similar triangles, and links between length, area and volume of similar figures). (d ...
C1 Scheme of Work Outline
... The form y = mx + c should be known, as should the meanings of m and c, but what are x and y? Does the point (3, 7) lie on the line y = 2x + 3, or above it, or below it? Justify the form by joining the points (0, c) and (x, y) by a line of gradient m. The one exception is a line parallel to the y-ax ...
... The form y = mx + c should be known, as should the meanings of m and c, but what are x and y? Does the point (3, 7) lie on the line y = 2x + 3, or above it, or below it? Justify the form by joining the points (0, c) and (x, y) by a line of gradient m. The one exception is a line parallel to the y-ax ...
All of Math in Three Pages
... Here is an overview of “high school mathematics.” Most of the non-Calculus topics that you have studied and a lot that you haven’t will appear somewhere in the following outline. In a some cases a formula or example is given, but many of these important results are just named, which leaves the inter ...
... Here is an overview of “high school mathematics.” Most of the non-Calculus topics that you have studied and a lot that you haven’t will appear somewhere in the following outline. In a some cases a formula or example is given, but many of these important results are just named, which leaves the inter ...
roots
... multiple roots, 0 and –3. For example, the root 0 is a factor three times because 3x3 = 0. The multiplicity of root r is the number of times that x – r is a factor of P(x). When a real root has even multiplicity, the graph of y = P(x) touches the x-axis but does not cross it. When a real root has od ...
... multiple roots, 0 and –3. For example, the root 0 is a factor three times because 3x3 = 0. The multiplicity of root r is the number of times that x – r is a factor of P(x). When a real root has even multiplicity, the graph of y = P(x) touches the x-axis but does not cross it. When a real root has od ...
