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A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
Since this is a scaled and shifted square of a standard normal variable, it is distributed as a scaled and shifted chi-squared variable. The distribution of the variable X {\displaystyle X} restricted to an interval [ a , b ] {\textstyle [a,b]} is called the truncated normal distribution .
A little algebra shows that the distance between P and M (which is the same as the orthogonal distance between P and the line L) (¯) is equal to the standard deviation of the vector (x 1, x 2, x 3), multiplied by the square root of the number of dimensions of the vector (3 in this case).
The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c 2). Because the speed of light is a large number in everyday units (approximately 300 000 km/s or 186 000 mi/s), the formula implies that a small amount of mass corresponds to an enormous amount of energy.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
One way to generate fairly accurate square wave signals with 1/n duty factor, where n is an integer, is to vary the duty cycle until the nth-harmonic is significantly suppressed. For audio-band signals, this can even be done "by ear"; for example, a -40 dB reduction in the 3rd harmonic corresponds to setting the duty factor to 1/3 with a ...
The expression appears in several equations in special relativity, ... The simplest case is a boost in the x-direction ... 0: 1: 1: 0.050 1.001: 0.999 ...
A 1903 Langley bolograph with an erroneous solar constant of 2.54 calories/minute/square centimeter. Between 1902 and 1957, measurements by Charles Greeley Abbot and others at various high-altitude sites found values between 1.322 and 1.465 kW/m 2. Abbot showed that one of Langley's corrections was erroneously applied.