Acubic polynomial v = p(u) can be written x0 + x1 u + x2 u 2 + x3 u 3 . this question has to do with the least squares optimization to determine the unknown coefficients, xi, j=0,1,2,3. assume that you are given n data points {(uj, vj), j=1,2, …, n with n> 4. write the four linear equations produced by least squares and whose solution would give the values of the xi.

create an interactive presentation of ms powerpoint or any other presentation software in which define the product's characteristics, benefits, why people consider it, etc.

a  social news website  is an  internet  website  that features  user-posted stories. such stories are ranked based on popularity, as voted on by other users of the site or by website administrators. users typically comment online on the news posts and these comments may also be ranked in popularity. since their emergence with the birth of  web 2.0, social news sites have been used to link many types of information, including news, humor, support, and discussion. all such websites allow the users to submit content and each site differs in how the content is moderated. on the  slashdot  and  fark  websites,  administrators  decide which articles are selected for the front page. on  reddit  and  digg, the articles that get the most votes from the community of users will make it to the front page. many social news websites also feature an online comment system, where users discuss the issues raised in an article. some of these sites have also applied their voting system to the comments, so that the most popular comments are displayed first. some social news websites also have a  social networking  function, in that users can set up a user profile and follow other users' online activity on the website.