Volumes in cylindrical coordinates Use cylindrical coordinates to find the volume of the following solids.
32. The solid cylinder whose height is 4 and whose base is the disk
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- True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).arrow_forwardF43' in terms of F, F+1 F,+2]. (You don't need b) Work out a matrix equation that encodes this sequence in vector form for F+1 F42 to do this in Python.) Input as A the resulting matrix.arrow_forwardEquation does have x in it. Other.arrow_forward
- 3. Let A = {1, 2, 3} and B = {4,5}. a) Find A x B b) Find B x Aarrow_forwardThe compass gradient operators of size 3x3 are designed to measure gradients of edges oriented in eight directions: E, NE, N, NW, W, SW, S, and SE. i) Give the form of these eight operators using coefficients valued 0, 1 or – 1. ii) Specify the gradient vector direction of each mask, keeping in mind that the gradient direction is orthogonal to the edge direction.arrow_forward3: The function f(x)= max x, searches for the maximum value between a number. Prove formally that the function f(x) is convex.arrow_forward
- Python problem Problem statementDevelop a program that receives a matrix and determines whether it corresponds to a magic square. A magic square is one that the sum of its elements in each of the rows is equal to the sum of the elements in each of the columns and also equal to the sum of the elements of each of the diagonals. The condition that the numbers from 1 to n ** 2 are used must also be met, where n is the size of the magic square, which is a matrix of nxn. https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Magicsquareexample.svg/1200px-Magicsquareexample.svg.png EntryThe first line corresponds to the number n. After this, n lines, each line contains a list of integers separated by a space. DepartureIf the square is magic, it must print the value that has the sum of the numbers by columns, rows and main diagonals. If it is not a magic square, the word "Error" must be printed without quotation marks. Examples Input Example 1 416 3 2 135 10 11 89 6 7 124 15 14 1Output…arrow_forwardlet X = {0, 1}arrow_forwardcreate a program to solve for the determinant of a square matrix using Cramer's Rule. 2x2 and 3x3 matrix.arrow_forward
- HW7_2 This problem uses an interpolating polynomial to estimate the area under a curve. Fit the interpolating polynomial to the following set of points. These points are the actual values of f(x) = sin (e* – 2) 0.4 0.8 1.2 1.6 y -0.8415 |-0.4866 0.2236 0.9687 0.1874 a) Plot the function f(x) and the interpolating polynomial, using different colors. Use polyfit and polyval. Also include the data points using discrete point plotting. b) We wish to estimate the area under the curve, but this function is difficult to integrate. Hence, instead 1.6 of finding ° sin(e* – 2) dx (which is the same as finding the area under the curve sin (e* – 2) ), we will compute the area under the interpolating polynomial over the domain 0arrow_forwardPython numpy library functions to perform basic matrix operations are as follows.• C=numpy.add(A, B): Add two matrices A and B and store result in C.• C=numpy.subtract(A, B): Subtract matrix B from matrix A and store result in C.• C=numpy.divide(A, B): Divide matrix A by matrix B and store result in C.• C=numpy.multiply(A, B): Multiply matrix A by matrix B and store result in C.• C=numpy.sum(A): Form the sum of elements of matrix A and store result in c ∈ R.• C=numpy.sum(A, axis = 0): Form the column wise summation of matrix A andstore result in vector C.• C=numpy.sum(A, axis = 1): Form the row wise summation of matrix A, storeresult in vector C.Python code to show the implementation of these methods in a sample matrix.arrow_forwardQ10: Using (ode45, ode23, or ode15s), solve the below dynamic electrical system differential equation. 1. The charge Q(t) on the capacitor in the electrical circuit shown satisfies the differential equation where d²Q dQ 1 +R- + √ √e dt2 dt L = 0.5 R = 6.0 C= 0.02 and V(t) is the applied voltage. V(t) = V(t), henrys is the coil's inductance ohms is the resistor's resistance farads is the capacitor's capacitance ellee (i) Is the circuit oscillatory? (ii) If V(t) = 24 sin(10r) volts and Q(0) = 0 = Q'(0), find Q(t). (iii) Sketch the transient solution, the steady state solution, and the full solution Q(t).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr