Factorise the following: x^(3)-2x^(2)-5x+6 02:38 Factorise (Using factor theorem ) : a^(3)-7a^(2)+7a+15 03:16 Factorise (Using factor theorem ) : 2a^(3)-5a^(2)b+6ab^(2)+3b^(3) 02:26 Factorise (Using factor theorem ) : x^(4)+4x^(3)-7x^(2)-34x-24 05:47 ...
Using factor theorem, show that (x-5) is a factor of the polynomial 2x^(3) - 5x^(2) - 28x + 15
Create the symbolic variable T and the following symbolic functions: r(t) is a continuous function representing a spot interest rate. This rate determines the discount factor for the final payoff at the time T. u(t,x) is the expected value of the discounted future price calculated as X(T...
Rational Zero Theorem The rational zero theorem is a very useful theorem for finding rational roots. It states that if any rational root of a polynomial is expressed as a fraction pq in the lowest terms, then p will be a factor of the constant term and q will be a factor of the...
where \(C=\begin{bmatrix}c&\,&0\end{bmatrix}\); c is the calibration factor related to the experimental time-series which can be set to unity if the data is already in desired units. Using the AR structure (Eq. 8) and the partial observation of the process, the Kalman filter algo...
b Middle image of the sharp sequence a used as ground truth. c The convolution of b with the blur function. d The deconvolution of c with the blur function. Scale bar 25 µm Full size image Using the central-ordinate theorem:41 $$\underline I (x,y) = \left. {\Im _t\left\...
The critical failure plane is the one that corresponds to the lowest Factor of Safety (FoS), from examining a large number of different failure planes. LAM includes the upper bound theorem of plasticity in the analysis, and is a more rigorous approach (Michalowski, 1995; Chen et al., 2001...
However, we should consider another important factor that was explained before. We cannot wait to collect uncorrelated RSS samples in the online phase. Other algorithms need to collect uncorrelated RSS samples to achieve an acceptable accuracy. We defined another column, named same accuracy time (...
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However, partial slope factor of complex surface is often beyond the capacity of spatial sample, which produces the sampling information loss in the region of steep surface. Take the involute gear for example, which is widely used in mechanical engineering. To ensure the stability of gear drive ...