'Use Cartesian coordinates to evaluate III y² dV where D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 3x + 2y + z = 6. Use dV = dz dx dy. Draw the solid D.

Q: The differential equation: y' (t) − y(t) = 0 can be written in a vector equation: ´y' (t) 1 'y' (t)…

A: False

Q: 1. Find the Inverse Laplace Transforms 3) 3s³+3s s6

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Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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Q: 6. Show that the premises "If you send me an e-mail message, then I will finish writing the…

A: Let , p : You send me an e-mail message. q : I will finish writing the program. r : I will go to…

Q: Solve the initial value problem √y dx + (x - 2)dy = 0, y(3)=9 The solution is -2√y = In |x-2- -…

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given problem is to convert the given cylindrical and spherical coordinates equations to the…

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A: Given, Three dice are rolled. Sample space: n(s)=63=6×6×6=216 Thus, the sample space of three dice…

Q: A sign hangs from two wires. The left-hand wire makes an angle of 60° with the horizontal, and the…

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Q: 2x-y 2 2 + y+3x 3 2 =1

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Q: B) Solve the following equations: y=l+x+e="x

A: We have to find the general solution of the differential equation d3ydx3+27y=1+x+e-7x .

Q: Example 1.10 Use the power method to find the dominant eigenvalue and the corresponding eigen-…

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Q: Find the general and Singular Solution of the Following differential equation y²Lny = XyP+ P²

A: Let us start solving the problem step by step  Given differential equation is y^2ln y…

Q: 1. Let V be the set of all 2 x 2 matrices 4- such that the product abcd =0 with standard operations…

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Q: Question 3 [10] Solve the Laplace equation Vu= 0, (0<x<∞,0 <y<x), given that u(0, y) = 0 for every…

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Q: 13. Show that the following functions are contin- uous but not differentiable: (a) z (b) |z²2 (c)…

A: 13) We need to show that given functions are continuous but not differentiable. We know that , a…

Q: TRUE or FALSE: 1. There is no integer n such that 4 | (n^2-2) 2. The GCD of all prime numbers is 1.…

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Q: Let us solve the following equation via separation of variables 8²u(x, t) Ət² 8²u(x, t) dx² a) After…

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Q: دیا (a) | 4 25 53

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Q: The exponential model A-320 700241 describes the population, A. of a country in millions, t years…

A: We have given  Exponential model A = 320.7 e0.024t Where t is time in years  We have to find the…

Q: ntegers, fractions, multiples

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Q: ∞o ∞ Suppose an >0 and a diverges. Prove that n = 1 n=1 ∞ an an contrary suppose Σ converges, then I…

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Q: Let z = f(x, y) be a differentiable function defined for every point on the plane, and let u be a…

A: (a)Let the function f(x,y) be the height of a mountain range at each point X =(x,y). If you stand at…

Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: Solution

Q: A child enters a carousel that takes one minute to revolve once around. The child enters at the…

A: Please find attachment for the details solution

Q: 1. 10,20,30,40,50, 2.-2,-4,-6,-8,-10,

A: # as per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: Q1) Convert the point p = (2,) in the polar coordinate system to its Cartesian coordinate…

A: We know that conversion from polar coordinate (r, θ) to Cartesian coordinate (x, y) is as follows:…

Q: 3. Solve the system by using the matrix exponential -2 3 x' = [ X 5 -1 2 x (2) = (2] 4

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Q: Find the general and Singular Solution of the Following differential equation x² = 1 + P²

A: Given differential equation  x2=1+p2 Then  x=1+p2 Differentiating with respect to p ,we get…

Q: Q2. Find the convergence interval and radius of the series: √n (2x+5)* nal

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Q: II. SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere a² + y²…

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Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y²…

A: Volume =∭dzdxdyAccording to the given surfacesx2+y2+z2=4⇒z is from -4-x2-y2 to +4-x2-y2x2+y2=1⇒ x is…

Q: The function f(t) = 1500 represents the rate of flow of money in dollars per year. Assume a 15-year…

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Q: e of Php 100,000

A: Given as, Corporate bond= 8%, Face value= 100,000, Maturity= 5 years and 7%.

Q: 7. Study the Venn diagram below and then answer the following questions: 15 B A 9 4 8 300 7 5 2 1 10…

A: Only D and E asked and answered.

Q: 2x₁6x₂x3 = -38 Given the linear system -3x₁-x₂+7x₂=-34 -8x₁+x₂-2x3 = -20 , determine the values of…

A: 2x1- 6x2 -x3 = -38-3x1-x2+7x3 = -34-8x1 +x2 -2x3 =-20 We take x1=a,  x2=b,  x3=c for our convenience…

Q: Directions: Translate each argument into symbolic form (using the suggested letters) and determine…

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Q: about this lesson. In this section, you will be given tasks to showcase your skills and knowledge…

A: Exponents: The exponential form is written as ab, where b is a natural number. The number a is…

Q: lve for each interior

A: Given : The number of sides or regular polygon.

Q: Consider a fair coin tossed three times and three events are defined as follows: . E1: a head comes…

A: Solution : If two events are independent than, Probability of their intersection is equals to…

Q: 10.If a, b  and p are positive integers, what is the LCM of ap, bp^3 and a^2p^2 ? a.a^2bp^3 b.1…

A: LCM = Least common multiple GCD = greatest common divisor

Q: QUESTION 10 Let f(x) = sina and g(x) = cos x, and W = span{f,g}. 10.1 Use the Wronskian to show that…

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Q: Prove that using a proof by contraposition, “if n is an integer and ? 3 + 5 is odd, then n is even”

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Q: (B) Solve the following differential equation: 3y cos 3x dx - sin3x dy = 0

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Q: 1.4.5 only B Obtain the eigenvalues and corresponding eigenvectors of the matrices 2 2 1 0-2 -2 (a)…

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Q: 1. I. Evaluate each determinant. -3 -4 -5 3

A: Solution :  Given that  -5-33-4

Q: compare and state the conditions for a line segment to be parallel and line segment to be…

A: To compare and state the conditions for a line segment to be parallel and line segment to be…

Q: A) B) Solve the initial value problem Solve the differential equation y + 10y +34y = 0 dy e2x dx…

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Q: Explain the process of correctly determining Horizontal Shifts. Include a mathematical example to…

A: We have to determine the process of horizontal shift.

Q: Determine whether the given differential equation is separable. dy + 2 sin (x + y) = 0 dx

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Q: Draw a direction field for the given differential equation. Based on the direction field, determine…

A: Given,y' =y(y-6)2 At equilibrium points y' =0⇒y(y-6)2 =0 ⇒y =0 , 6thus, y =0 and y =6 are…