Design a function that utilizes Newton's method for calculating the cube root of a given number....

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Design a function that utilizes Newton's method for calculating the cube root of a given number. ; contract: calcCubeRoot: number(x) → number 2. (25 points) Design a function that applies binary addition for given two binary numbers. For example, z = 0010 (= 2 in 10-base system) and y = 1010 (= 10), then x + y = 1100 (= 12). ; contract: addBinaryNumbers: string(x) string(y)→ string 3. (25 points) Design a function that finds the smallest root of a quadratic equation. For example, for the given function x²-3x - 4, the smallest root is -1. ; contract: calcSmallest Root: number(coef1) number(coef2) number(coef3)→ num ; coef (coefficient) parameters are given in order such that coef1 corresponds to the coefficient of ², coef2 corresponds to x and coef3 is for xº 4. (25 points) Design a function that finds the first occurrence index of the given pattern in the given sentence. For example, assume that the query is "world" and the sentence is "Hello world", then the function returns 6. If any occurrence of the pattern is not found, then the function returns -1 indicating that the pattern does not exist in the given sentence. ; contract: findPatternIndex: string(sentence) string(query) → number Design a function that utilizes Newton's method for calculating the cube root of a given number. ; contract: calcCubeRoot: number(x) → number 2. (25 points) Design a function that applies binary addition for given two binary numbers. For example, z = 0010 (= 2 in 10-base system) and y = 1010 (= 10), then x + y = 1100 (= 12). ; contract: addBinaryNumbers: string(x) string(y)→ string 3. (25 points) Design a function that finds the smallest root of a quadratic equation. For example, for the given function x²-3x - 4, the smallest root is -1. ; contract: calcSmallest Root: number(coef1) number(coef2) number(coef3)→ num ; coef (coefficient) parameters are given in order such that coef1 corresponds to the coefficient of ², coef2 corresponds to x and coef3 is for xº 4. (25 points) Design a function that finds the first occurrence index of the given pattern in the given sentence. For example, assume that the query is "world" and the sentence is "Hello world", then the function returns 6. If any occurrence of the pattern is not found, then the function returns -1 indicating that the pattern does not exist in the given sentence. ; contract: findPatternIndex: string(sentence) string(query) → number