2. Write a program that implements the first order (linear) interpolations.
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2. Write a program that implements the first order (linear) interpolations..
3. Use the program to apply first order (linear) interpolation to the function
f(x)=sin(x²)
initially calculated in 10 uniform points in the interval [0.0, 5.0].
(1)
4. Write a program that implements n-point Lagrange interpolation. Treat n as an
input parameter.
5. Use third and fifth order polynomial interpolation to interpolate the function f(x)
Equation (1) above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72de7928-1ec0-4629-8ffd-ec2773b0f8fd%2Ff3ec39bb-1926-4290-a0b2-8965053fb725%2Fu5p7ht_processed.png&w=3840&q=75)
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- 2. Write a program that implements the first order (linear) interpolations. 3. Use the program to apply first order (linear) interpolation to the function f(x)=sin(x²) initially calculated in 10 uniform points in the interval [0.0, 5.0]. GWrite a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, the pattern generated is as follows: **** *** ** * * ** *** **** Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the preceding pattern.Going missing Some calculations involving blank values may give different results to what you might expect. For example, when you pass a blank value into the AND() function, it is treated as TRUE. This is often unhelpful. To make blanks behave in a sensible way in calculations, you must first convert them to be "not available" using NA(). This function takes no inputs, and returns a missing value. To convert a blank value to a missing value, use this pattern. =IF(ISBLANK(cell), NA(), cell) Instruction In column H, use AND() to find women who have kids and get benefits. In column I, convert the blanks in column G to missing values. In column J, again find women who have kids and get benefits, this time using column I rather than G. please show the formula used to "has kids and gets benefits" , "gets benefits with missing values", has kids and gets benefits". Thank you Is non-white Has over 12 years of school? Is married? Has kids? Has young kids? Is head of household? Gets…
- // Description: Write a program that outputs a root of a given function f(x) by using a bi-section method. // f(x) = x3 + 5x2 +7x +2Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is:********************Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern.Write a python function that takes one integer (n) parameter and prints the first n digits from the Fibonacci series using recursion.Sample input: 5Sample output: 0, 1, 1, 2, 3 Write a function that takes one integer parameter, makes sure it is an integer, prints sum of every two digits and return the sum of digits from the number entered by the user up to 1, using recursion.Sample input: 4 Sample output: 4+3 = 77+2 = 99+1 = 10
- In loop functions.py, define a function named permutations that takes two paramters, n and r, in that order. This function returns the number of different permutations of length r from set of size n. Essentially to calculate these permutations, the function should compute the product (n - r+1)*(n-r+2)*(n-r+3)*...*(n-2)*(n-1) or n!/(n-r)!. No if statements or built in math functions should be used. For or while loops are best reccomended.Write a function which returns “odd” or “even” for odd or even inputs, respectively. HINT: evenOrOdd(2) returns “even” and evenOrOdd (7) returns “odd”2. Write a Python program that uses a function to find and return the factorial of a positive integer n. The function the receives a value and returns its factorial. If the passed parameter is negative, the function return the string "ERROR". Factorial of zero is one. Test your function. If n is a positive integer, n factorial denoted by nl is a product of all positive integers less than or equal to n. It is defined by =n(n-1)(n-2)..(2)(1) As a special case: 0! 1 3. In a new program, use the function you wrote in question 2 to print the factorials of values from 1 to 10. Use for loop.
- In python, Problem Description:Sheldon and Leonard are physicists who are fixated on the BIG BANG theory. In order to exchange secret insights they have devised a code that encodes UPPERCASE words by shifting their letters forward. Shifting a letter by S positions means to go forward S letters in the alphabet. For example, shifting B by S = 3 positions gives E. However, sometimes this makes us go past Z, the last letter of the alphabet. Whenever this happens we wrap around, treating A as the letter that follows Z. For example, shifting Z by S = 2 positions gives B. Sheldon and Leonard’s code depends on a parameter K and also varies depending on the position of each letter in the word. For the letter at position P, they use the shift value of S = 3P + K. For example, here is how ZOOM is encoded when K = 3. The first letter Z has a shift valueof S = 3 × 1 + 3 = 6; it wraps around and becomes the letter F. The second letter, O, hasS = 3 × 2 + 3 = 9 and becomes X. The last two letters…Use Sage to program Exercise 5.In 1202 AD, Leonardo Pisano asked the following famous problem:A certain man had a pair of rabbits together in a certain enclosedplace, and one wishes to know how many are created from the pair inone year when it is the nature for of them in a single month to bearanother pair, and in the second month those born bear also. Becausethe abovewritten pair in the first month bore, you will double it. therewill be two pairs in one month. One of these, namely the first, bears inthe second month, and thus there are in the second month three pairs;of these in one month two are pregnant, and in the third month 2pairs of rabbits are born, and thus there are 5 pairs in the month;...Explain how the rabbits reproduce. Create a list F where F[x] is the number ofrabbits in month x. (so F[0]=1, F[1]=2) Find F[12]. Find F[100].[Unbalanced Rod] Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure below. -1". /10 2 3 12 2 4 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). where 0 ≤ Pi≤n-1 is the position of weight along the rod. For example, in the figure shown above, the center of mass is computed as C= C = i Wi Pi Σi Wi 10 0+2 1+3·2+4·3+12.4 +2.5 10+2+3+4+12+2 78 33 The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c. Answer the following questions. 1. Describe a greedy algorithm that finds the assignments that…
