Given an unlimited supply of coins of denominationsx1,x2,...,xn, we wish to make change for a valuev; that is, we wish to find a set of coins whose total value isv. This might not be possible: for instance, if the denominations are 5 and 10 then we can make change for 15 but not for 12. Give a dynamicprogramming algorithm for the following problem: You are givenx1,...,xn;v. Required:
Is it possible to make change forvusing coins of denominationsx1,...,xn

Establish which of the following statements are true. (a) a sequence is convergent if and only if all of its subsequences are convergent. (b) a sequence is bounded if and only if all of its subsequences are bounded. (c) a sequence is monotonic if and only if all of its subsequences are monotonic.

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Write a method that takes in an array of point2d objects, and then analyzes the dataset to find points that are close together. be sure to review the point2d api. in your method, if the distance between any pair of points is less than 10, display the distance and the (x,y)s of each point. for example, "the distance between (3,5) and (8,9) is 6.40312." the complete api for the point2d adt may be viewed at ~pf/sedgewick-wayne/algs4/documentation/point2d.html (links to an external site.)links to an external site.. try to write your program directly from the api - do not review the adt's source code.