The above equation can be decoded as “y varies directly with x” or “y varies directly as x.” The equation can be used to derive different formulas according to the requirements of a solution. Different forms of the direct variation formula are as follows: ...
To find the direct variation equation for this point, find the constant of variation. The constant of variation is the ratio of the y-value to the x-value of the given point so it is: k=6416=4. So, the formula for the direct variation about this point would be y=4x. Finally, ...
A direct variation equation will produce a straight line through the origin (0,0). If k (or the slope) is positive, then the line will rise from left to right, passing through the origin. If k (or the slope) is negative, then the line will fall from left to right, passing throug...
The Neumann Problem for the Poisson Equation We consider the problem (n is the unit outer normal on Γ) [17]−Δu=finΩ∂u∂n=honΓ Setting E(Δ) = {v∈ H1 (Ω); Δv∈ L2(Ω)}, the space sD(Ω―) is a dense subspace, and we have the following Green formula for all...
The variation of constant formula In this section, we establish a result on the existence and uniqueness of mild solutions for the Caputo fractional stochastic differential equation with jump–diffusion, and then present the variation of constant formula for the equation. Example Example 4.1 Consider ...
SNRwas calculated as the ratio between the X-ray average photocurrent measured at each dose rate value and the standard deviation of the dark current, as reported in the following equation: $${\it{SNR}}=\frac{\frac{1}{n}\sum_{i}^{n}{I}_{{ph}_{i}}}{\sqrt{\frac{1}{n}\sum_...
Owing to its unique penetrating power and high-resolution capability, X-ray imaging has been an irreplaceable tool since its discovery. Despite the significance, the resolution of X-ray imaging has largely been limited by the technical difficulties on X-
The half-life of93Mo was calculated based on the measured number of93Mo (N93Mo) atoms in the master solution and its measured specific activity (A93Mo) using the formula: T1/2=ln(2)⋅N93MoA93Mo whereN93Mois the number of93Mo atoms per gram of the master solution 4.415(23)∙10...
Using this equation, values for the final decomposition temperatures have been calculated and compared with data found in the literature for the decomposition of calcium carbonate and for the dehydration of potassium chrome alum and orthoboric acid. The equation also has been applied to the ...
Wave equationVariable coefficientThis article presents a new analytical formula for the Cauchy problem of the wave equation with variable coefficients, which is a much simpler solution than that given by the Poisson formula. The derivation is based on the variation-of-constants formula and the ...