Plot the function f(x) = sin(2x) cos² (0.5x) and its derivative, both on the same plot, for -π≤x≤2. Plot the function with a solid line and the deriv- ative with a dashed line. Add a legend and label the axes.
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- Provide a contour map for f(x;y) = xy2:Be sure to specify the values of your contours. The bookdoesn't, which makes them far less useful.Although the plot function is designed primarily for plotting standard xy graphs, it can be adapted for other kinds of plotting as well. b. Make a plot of the curve, which is defined parametrically by the equations x = 2cosθ + cos2θ, y = 2sinθ - sin2θ, where 0 < θ < 2π. Take a set of values of θ between zero and 2π and calculate x and y for each from the equations above, then plot y as a function of x. b. Taking this approach a step further, one can make a polar plot r = f(θ) for some function f by calculating r for a range of values of θ and then converting r and θ to Cartesian coordinates using the standard equations x = r cosθ, y = r sinθ. Use this method to make a plot of the function r = ecosθ – 2 cos(4θ) + sin5 (θ/12) in the range 0 <= θ <= 24π. use python code to answer the highlight oneThe shape of a limacon can be defined parametrically as r = r0 + cos θ, x = r cos θ, y = r sin θ. When r0 = 1, this curve is called a cardioid. Use this definition to plot the shape of a limacon for r0 = 0.8, r0 = 1.0, and r0 = 1.2. Be sure to use enough points that the curve is closed and appears smooth (except for the cusp in the cardioid). Use a legend to identify which curve is which. use phyton language import mathimport numpy as npimport matplotlib.pyplot as plt%matplotlib inline
- Plot the function f(x) = x4 − 3x3 + 10x2 − x − 2 for −6 ≤ x ≤ 6.Draw the function as a solid black 2-point-wide line, and turn on the grid. Be sure to include a title and axis labels, and include the equation for the function being plotted in the title string.For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.Suppose images f(x,y) and g(x,y) have histograms h; and hg. Suppose you form image k(x,y) as the sum of these two images: k(x,y) = f(x,y) + g(x,y). (a) Under what conditions (on images f and g) can you determine the histogram hų of image k in terms of the histograms hf and hg? (That is, under what conditions can you determine hu if you are only given hj and he? Hint: this turns out to be fairly restrictive.) (b) Explain how you would derive hỵ in this case.
- Scale a line between (2,1) and (4,1) to twice its length and draw a line before and after scaling.Simplify the following Boolean functlons using four-variable maps. d. F(A, B, C, D) = ∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)The attatched image is the 2D profile of an image, showing I(x,y). True or False: The spatial frequency in the x direction (kx) is π; the spatial frequency in the y direction (ky) is π; and the inital phase is π. To create this 2D intensity, we need to add together multiple 2D sine waves. The Fourier transformation of this image will contain a single peak at a single frequency (not counting peaks at zero and the overtones) The wave in the 2D profile is plotted for 3 wavelengths
- Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y 5mx 1b, where b is the y-intercept. If l passes through the point (x0, y0,), the equation of l can be written as y 2y0 5m(x 2x0 ). If (x1, y1) and (x2, y2) are two points in the x-y plane and x1 ≠ x2, the slope of line passing through these points is m 5(y2 2y1 )/(x2 2x1 ). Write a program that prompts the user two points in the x-y plane. The program outputs the equation of the line and uses if statements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If l is a non-vertical line, output its equation in the form y 5mx 1b.This is energyBalance.m in the first image in the second image are the questions according from image 1Wirte a matlab code to plot the 3D image of a helix: Use the following parameters and equations that define the axes in 3D: p=0.199; Pitch distance (distance between the turns)a=0.02999500; Radius of the helis wireb=0.191; Radius of the helixn = 5, is the number of helis turns. δ = atan(p/(2*pi*b)); The pitch anglex’ = b + a cos(Ө)y’ = -a sin(Ө) sin(δ)x = x’ sin(ф)+y’ cos(ф);y =-x’ cos(ф)+y’ sin(ф);z = p*ф/(2*pi)+a*sin(Ө)*cos(δ);