如何求两条平行线之间的距离？圆周角的公式是什么？如何求求根公式？what's Absolute value & piecewise functions? how do get the equation of exponential growth & decay?

视频信息

答案文本 复制

视频字幕 复制

To find the distance between two parallel lines, we use a specific formula. For lines in the form Ax plus By plus C₁ equals zero and Ax plus By plus C₂ equals zero, the distance is the absolute value of C₁ minus C₂, divided by the square root of A squared plus B squared. This formula gives us the perpendicular distance between the parallel lines. The inscribed angle formula states that an inscribed angle is half the measure of its intercepted arc. In this diagram, angle ABC is inscribed in the circle, and it intercepts arc AC. The measure of angle ABC equals half the measure of arc AC. This relationship is fundamental in circle geometry and applies to any inscribed angle. The quadratic formula is used to find the roots of any quadratic equation in the form ax squared plus bx plus c equals zero, where a is not equal to zero. The formula is x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a. The discriminant, b squared minus 4ac, determines the nature of the roots. When positive, there are two real roots, as shown in this parabola crossing the x-axis at two points. The absolute value of a number x, denoted as |x|, represents its distance from zero on the number line. It's defined as x when x is greater than or equal to zero, and negative x when x is less than zero. This creates a V-shaped graph. Piecewise functions are functions defined by different expressions on different intervals of their domain, like the absolute value function shown here. Exponential functions model growth and decay processes. The general forms are y equals a times b to the x, or y equals a times e to the kx. Here, a is the initial value when x equals zero. For growth, b is greater than 1 or k is positive, creating an upward curve. For decay, b is between 0 and 1 or k is negative, creating a downward curve. These functions appear in population growth, radioactive decay, and compound interest.