A letter to the editor is presented in response to the issue regarding how to find the exact values for the sine of angles that are multiples of 18° without using double or triple angle formulas.WenjiangOswegoTuOswegoMathematics Teacher
The parametrization of the lines by y = kx + d can be numerically problematic if very large values of the slope k are possible. A more robust parametrization of the line has the form \(x\cos \varphi +y\sin \varphi -c=0\). The curve in the Hough space of φ and c pass...
It is time to get back to what sets our souls on fire. We need to find that thing, the process, the creation, the writing, whatever it is and let that have the lead part in this portion of our lives once again. This may take stripping down and letting go of some things we’ve ...
Answer to: Consider the following function. Without finding the inverse, evaluate the derivative of the inverse at the given point. f(x) = 3x + 4;...
Find the binomial coefficient. (2020)Simplification of Coefficient:When the total number of items and the selected item from this set of items are the same in the binomial expression, then we can compute its exact value using the formula shown below: ...
To get the closest point to endPoint on the Polyline, you should use the other overload and set the 'extend' argument to false (in this case, there's no need to get an angle from the user). Point3d next = line.GetClosestPointTo(endPoint, false); If this is not exactily your goal...
Suppose thatr(t)gives the position of an object at timet. We first recall that the velocity of the object isv(t)=r′(t)and the acceleration isa(t)=v′(t)=r″(t). We are often interested in how much the acceleration points...
We propose a way to obtain the closed-form solutions for such systems. We use the approximate dual Hamiltonian method to construct the first integrals and closed-form solutions of the Van der Pol equation. First the solutions of the initial value VdP equation is obtained using approximate dual ...
Solve the given initial-value problem by finding an appropriate integrating factor. {eq}x \ dx +(x^2y + 4y) dy = 0, \ y(4) = 0 {/eq} Integrating Factor If a given differential equation in the form {eq}\displaystyle M(x,y)\,dx + N(x,y)...
inevitably requires eigenvalue clustering, that is, the Schur decomposition ofneeds to be reordered so that multiple eigenvalues are grouped together. Eigenvalue clustering is a numerically subtle task sensitive to roundoff error. On the other hand, using eigenvectors for (partial) diagonalization does...