1. Perform the following calculations in R/RStudio using this R markdown template and write your R code in the code chunk provided: √20 and y1+ Find the value for y # Write your R code here 2. Write the R code (in the code chunk provided) to find the descriptiopn of the "plot" function. # Write your R code here 3. Generate the variables w and z using the R code below. Then, make the plot of w against z (i.e., on the xy plane). Write your R code in the code chunk provided. w <- rnorm (50) z <- rnorm (w) # Write your R code here

Q: Find the domain of the following function. Make a sketch of the domain in the xy-plane. f(x.y) = /x-…

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Q: 8. (S.15). Write P20 r2+2r-1 as a linear combination of the polynomials P21 r-r- 2, P22 2r2-r+3, P23…

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Q: If a=[5,-2,4] and [0,-2,3], find a -16 O [-2,15,10] [2,-15,-10] O [-2,-15,10] 10 xò.

A: a→=[5,-2,4]b→=[0,-2,3]

Q: Find a polynomial that interpolates the following data points: (-1, −10), (1, 6), (2, 5).

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Q: Explain the problems with the Lagrange form of the interpolating polynomial?

A: Lagrange polynomials are used for polynomial interpolation.

Q: Jc = − xj; P(−2, −4), Q(-2,-2)

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Q: 2. Express the following function in standard form using completing the square: f(x) = - 2x2 - 12 x…

A: Consider the general form of the parabola , y=a(x-h)+k  Axes of symmetry is x=h Vertex is (h,k)…

Q: 5. Let f(x) = 4x²/3 – x4/3. a) Find the domain of f. Domain: b) Find the x-intercept(s) and…

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Q: 2x² – 7x – 3

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Q: Find the following dot product. (-19,3) · (16,-6)

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Q: . Find x and y, if DE is a median

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Q: Construct the highest degree Lagrange Interpolation Polynomial. Xi yi 1 3 -1 -2 3 100

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Q: Find the vertex of the function: y = 2Vx + 9- 2 O (9,-2) O (-9,-2) O (-9,2) O (9,2)

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Q: B: Draw the function y = √√x-8

A: First we compare this equation with general equation of parabola then transform.

Q: 1. For the following graphs, write the functions in factored form and then write them in standard…

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Q: C is the center of the circle with  AB  and AD as points of tangency.   Whats the value of the…

A: Circle Question

Q: 2. Write a computer code that interpolates the function f(x) = 1+2 at the points -5, -4, -3, -2, -1,…

A: Here is the code:import numpy as np import matplotlib.pyplot as plt # Define the function def f(x):…

Q: Q4. Find the interpolating polynomial of least degree that interpolates these sets of data: 3 7 a)…

A: The objective is to find the interpolating polynomial of the least degree. (a)Given data is x 3 7…

Q: Find the interpolating polynomial of degree at most 2 that passes through the points (-2, 14), (1,…

A: Using Lagrange interpolating polynomial.

Q: Graph the following points on the coordinate plane. Find the distance between the points. Show your…

A: To graph the following points on the coordinate plane and the distance between the points (4,3) and…

Q: 4) Plot the function V2 – x² , also find the domain and range of the function.

A: Let y = 2-x2, then we have to find the values of x that make the expression meaningful and the…

Q: If BD = p- 7 and BF = 6p - 97, find BF in parallelogram CDEF. D. BF C.

A: Given : CDEF is a parallelgram  The diagonals of a parallelgram are bisected by the point of their…

Q: 3. Find both linear and quadratic interpolating polynomials for the points (-2,-13) , (-1,-3) ,…

A: We take given pairs of points as (x, y) x y -2 -13 -1 -3 1 -1 2 -9 3 17 We have…

Q: Write an expression for the distance w in terms of y. +2x²-2 y=4 W 1 -3 -2 3 3 N → O 2

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Q: Find the midpoint of the segment whose endpoints are (-6, -8) and (3, 6). SHOW YOUR WORK.

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