Circular Disk Method 1. R:y = Vx,y = 4, y – axis axis of revolution: y = 4

Q: 2.f (t) = cosh wt sin wt

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Q: Determine whether the function involving the n × n matrix A is a linear transformation. T: Mn,n -…

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Q: find Fourier series on [0,2n] -1 0<x<T (8) f(x) = 1 てくx<2元

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Q: Given the diagram of the rectangular prism, determine expressions for the listed vectors in terms of…

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Q: Part 2. Prove that the following are equivalent A. by Constructing a truth table 1. [p V (~p ^q)] +…

A: We will use truth tables and rule of replacements here

Q: Answer the following, being sure to carefully justify your answers. (a) Describe the orbit…

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Q: What is the argument of 2 3-j ? none of the choices 7. 12

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Q: Determine the lowest positive root of f (x) = 8 sin(x)e–x − 1  Using the Newton-Raphson method…

A: The function given is as follows: fx=8e-xsinx-1 (a) We are asked to find the least positive root…

Q: A student's grades for a math course are given below. 1. Percentage of Final Grade Student Grade…

A: Solution

Q: if 0s1<3 12. Compute the Laplace Transform of K) = - if t2 3 A) 1 B) 1 C) 1 D) +

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Q: Express the given power series as a series with generic term x^. n=8 Σ

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Q: Problem 3 The Silly Nut Company makes two mixtures of nuts: Mixture A and Mixture B. A pound of…

A: We have to find the number of pounds of each mixture A and B that the company should make to…

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

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Q: Q2. Evaluate | ydA in two different ways. Here R is the region in the first quadrant bounded by the…

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Q: Working directly from the e-N definition of convergence (without using any rules for limits), prove…

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Q: 1) = det(A) for any A E M2,2(R). Is ƒ a linear transformation? [b11 b12] [b21 b22 a12 A = a21 and B…

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Q: Determine whether the function is a linear transformation. T: R2 → R2, T(x, y) = (x, 4)

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Q: 10. Three circles of radii 115, 150, and 225 m are tangent to each other formed by joining the…

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Q: Prove that the transformation below is LINEAR. T:R² – → R3 R³ T(x,y) = (x + y, 3y, 2x – y)

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Q: Show that if m is a positive integer, then p(m²) = m· ¢(m). Hint: consider the prime factorization…

A: Introduction: The phi function of Euler denoted by ϕ is one of the most important number-theoretic…

Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: Find the median and mode for the data in the table below: interval frequency 0-10 10-20 20-30 4…

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Q: -2 A = b, b2 1

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Q: ý = -9y + 4t + 3

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Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i +4 sin(t)j+tk; t = - 6. T;)- .2 NE) -

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Q: Find the Fourier cosine and sine integral representation

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Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Question 1 1 -2 1 -1 1 2 -1 Let A = and assume that 1 2 -1 -1 -2 1 1 100 -2 1 1 -1 1 1 -1 В - is row…

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Q: A company manufactures two products: Product A and Product B. Product A is produced at quantity q1…

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Q: Determine if the function is continuos. If the function is not continuous, find the x-axis location…

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Q: (B) = 10 and n(A N B) = 4, what is n(A u

A: n(A U B)=12

Q: Evaluate the line integral / -ydx + xdy along the curve C : y? = 6x from (6,6) to (0,0). NOTE: Enter…

A: We have to find the line integral ∫C-ydx+xdy along the curve C: y2=6x from (6,6) to (0,0).

Q: -11 5]SX1 -8

A: This is a problem of stability analysis.

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: The given points are P0, 0, 0 and Q4, 6, 6. Let us denote  x1, y1, z1=0, 0, 0 and x2, y2, z2=4, 6,…

Q: Which of these graphs have the property that the removal of any vertex and all edges incident with…

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Q: Show that if a and b are integers and m and n are positive integers such that n|m, then If a = b(mod…

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Q: Consider the initial value problem y' = x(y+ x) – 2, y(0) = 2 Use Euler's method with step sizes h…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: For the following matrix 3 2 A = 3 7 -2 -3 2 8 10 20 || -10. Find approximate value for the…

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Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

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Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: Note: Round off your answer to 4 decimal places only 16 1 -5 4 X1 3 -4 -3 -2 -8 -1 X2 -7 6. 15 11 X3…

A: To solve for x4.

Q: 8. In the prism, assume all dimensions have different lengths. a. State 3 equal vectors to DC. b.…

A: The 3 equal vectors to DC→ are HG→, EF→ and AB→ Since they have same magnitude and the same…

Q: Determine the vector field of FF. F(x,y)=8i−4j

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Q: 2.f(t) = cosh wt sin wt

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Q: Assume that the function f : R → R is differentiable. 1. Show that the function u(x, y) = f(x+y)e¬¤…

A: (1) To show:  u(x,y)=f(x+y)e-x is a solution of ∂u∂x-∂u∂y=-u. (2) To find: A function f such that…

Q: 2. Show that the following graph is not planar. USM 1999 083 IVERS

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Q: Question 7 If the heights of women are normally distributed with a mean of 64 inches and a standard…

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Q: 'ind the inverse Laplace transform of 1 H(s) : 1 2 + 4 1 -4s %3D

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Q: Find approximate value of the following integral by using the Simpson method for n = 6. S° 10 sin…

A: I have rounded the final answer upto four decimal places.

Q: Use Gauss's Theorem to find the surface integral OF •dS across the positively-oriented S sphere of…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.