An integer greater than 1 is prime if its only positive divisor is 1 or itself. For example, 2, 3, 5, and 7 are prime numbers, but 4, 6, 8, and 9 are not. Key idea: To test whether a number is prime, check whether it is divisible by 2, 3, 4, and so on up to number/2. If a divisor is found, the number is not a prime. The algorithm can be described as follows:
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- In c++ A driver needs help finding the shortest path travelling between a number of points. There are 6 Points, and each point has a coordinate.. the points are as follows Point A 11 6 Point B 29 10 Point C 10 4 Point D 45 19 Point E 21 12 Point F 40 1 How will you calculate and find which point has the shortest path between these points Note: the driver should travel through these points once, you can also check every possible solution and measure which is best. The program should also display which Point was the shortest aswell as which one was the second shortest(in ascending order) Like example the shortest Path are as follows: C,B,A,E,F,DProblem You have a fence post located at the point (x,y) where a goat is tethered by a rope. You also have a house, which is a rectangle with diagonally opposite corners at the points bottom-left: (x1,y1) and top-right: (x2,y2). You want to pick a length of rope that guarantees the goat cannot reach the house. Determine the minimum distance from the fence post to the house, so that you can make sure to use a shorter rope. Recall that the distance formula is: (x2−x1)2+(y2−y1)2 The input consists of a single line containing six space-separated integer values: x, y, x1, y1, x2, and y2. You are guaranteed that x1<x2 and y1<y2, and that (x,y) is strictly outside the axis-aligned rectangle with corners at (x1,y1) and (x2,y2). Return the minimum distance from the goat’s post to the house as a floating-point value from main(). Learning Objectives Be able to create a program with a lesser template. Be able to calculate the min/max of integers. Be able to write a mathematical…Solve the problems Solve the quadratic equation 2x^2 + 6x + 4 = 0. Implement a function that takes incoefficients A,B,and C forthequadratic equation Ax2 + Bx + C = 0 and computes the two solutions. Have the function return the number of valid (not NaN) solutions and fill in the return arguments so the smaller of the two solutions is first.
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- For glass box testing of a recursive function, you should test cases where: a) the function returns without a recursive call, ie using a base case b) the function makes exactly one recursive call c) the function makes more than one recursive call d) all of theseProblem 6: Induction and Recursion Consider a postal system for which the minimum postage required for any service (e.g. mailing a postcard) is 18 cents. [a] Prove by strong induction that any postage ≥ 18 can be formed using only 4-cent and 7-cent stamps. (Hint: consider bases cases for 18 thru 21.) [b] Write a Java/Python-like pseudocode for a function that determines the number of each denomination of stamp for a postage amount ≥ 18. (It need not be concerned with lesser cases as they are never used).Imagine a 3D plane P in your 3D scene. An infinite number of lines can lie on that plane. Consider one set of parallel lines on this 3D plane. This set will produce one vanishing point when projected on the image plane. Consider now all possible sets of parallel line on the plane P. What is the locus of all vanishing points produced by all sets of parallel lines? [Note that you do not have to right down a formula in order to solve this. You need to use a geometric argument.]
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