(a) suppose we have n +1 data points (x , yo). (x, y). , (x , yn). the points are equally spaced, with point spacing h , so that hx1 for j0,1,,n-1. we want to fit a cubic spline s(x) through these points; this consists of n separate cubics, between each sets of points, and joined head-to-tail. show that, in the interval x x, xj,], the cubic spline takes the form s(x) %3d 씨 (x-z) m 1 h h mm-2)m) here, m s"(x) are the second derivatives ("moments") of the spline at each of the knot points x x [10 points (b) the moments mi are determined by making the first derivative of s(x) continuous at all the internal knot points x,,n-1. for the "natural" spline, which takes mo 0 and mn = 0, show that this yields the tri- diagonal matrix system of equations m-1 + 4m,+ m6.1-2y + y-1 h2 for j = ,n -1, and write as a matrix equation. [7 points] (c) explain why the matrix equation in part (b) could be solved successfully by an iterative method like the jacobi method.

Ineed extreme for task 2. my student number is 571721. many to whoever solves this correctly, im in debt to you.

How do the measurements of charge at the different locations on the sphere compare to each other? the charge measurements are different at all locations on the sphere. the charge measurements are virtually not the same at all locations on the sphere except for the charge at the very top and at the very bottom that are equal. the charge measurements are virtually the same at all locations on the sphere except for the charge at the very top. at the top, the conductive sphere has a small disk that is made of different material. the charge measurements are the same at all locations on the sphere. what happens to the charge on the conductive sphere when it is connected to a source of charge such as the electrostatic voltage source? nothing will happen because no charge goes around the surface of the sphere. the charge on the conductive sphere spreads out over the surface of the sphere; being greater in some specific locations on the sphere. the charge on the conductive sphere spreads out uniformly over the surface of the sphere. the charge on the conductive sphere spreads out non-uniformly over the surface of the sphere.

You have been consulted by the mobile phone company hookup about a new augmented reality product called “brows”. they want to develop an alternative to google glasses, which, you recall, is a proposed new product which plans to superimpose a whole range of wireless google services over the user’s ordinary vision of the world. these appear in little circles and ovals, and let you phone people, take photographs, navigate across cities and inside buildings, find shops and update your social media. brows would do this too, but not be limited to special google services. the user would wear a small cylinder-shaped device designed to fit on top of their existing eyewear (glasses or sunglasses). it would project a reversed image onto the inside of the lenses, the reflection of which would be in focus for the user. instead of voice control, the user would control the device by eye and neck movements, which the device would track. the device would connect via bluetooth to the user’s phone, which would supply most of the computing power and wireless connectivity. hookup also wants to know what existing services would be most in demand, and which would not work well with brows. using your knowledge of augmented reality, wearable technology and interface design, is the project feasible? if not, why not? if feasible, how could the product need to be modified for a better experience?