1. Find all solutions to the system of congruence. (Use CRT) x = 1 (mod 2) x = 2 (mod 3) x = 3 (mod 5) x = 4 (mod 11)

Q: Consider C3 y-1 = 2². a. Sketch the graph of the right cylinder with directrix C3. b. Find the…

A: The curve given is as follows: C3: y-1=z2 (a) The graph of the right cylinder with directrix C3 is…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: A quadric surface is a graph of the function of two variables x and y in the three dimensional…

Q: x² T +3y² = z + 3. Consider the surface T with equation 3 1. Find the equation for the trace of T on…

A: Solution

Q: 3x 2x13x2x3 = 0

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Q: Determine the inverse Laplace transform of G (s) = 28 (8²-4)² Og(t) = t cosh 2t O g(t) = }t sinh 2t…

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Q: 5) Give the surface area and the volume of the shape shown. Show all your calculation neatly. a)…

A: Solution: Let distance between two nearest point in the diagram is a Now, there is a smallest cube…

Q: Problem 25. Find the Laurent expansion of f(z) = 1/[2(2-1)(z-2)] in i) 0 < 2 <1 ii) 1<|z| <2 2 < |z|…

A: This question from laurent series of complex analysis.

Q: The sum of the series n-n+1 n! is

A: Solution : To find, ∑n=0∞n2-n+1n! Taylor expansion of ex around 0 ex=∑n=0∞xnn! put x=1; e=∑n=0∞1n!

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: 5 (a) [√4x In (V√x)] idx…

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Q: (2, 0 <t < 2 f(t) = −1, 2 ≤ t < 3 <t (1, t≥ 3

A: To sketch and find the Laplace transform of the given break function.

Q: Consider the surface S given by 22² +2y² = a + 1 = 0. (a) Find the equations of the traces of S on…

A: A quadric surface is a graph of the function of two variables x and y in the three dimensional space…

Q: Find a solution to the given IVP using Laplace and Inverse Laplace Transforms y" + 3y' + 2y = 4t²,…

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Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: Determine if F=(e* cos y + yz)i + (xz-e* siny) j+(xy+z)k is conservative. If it is conservative,…

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Q: 9.W.1 The Gram matrix of an inner product on R² with respect to the standard basis is G = -1 12 Find…

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Q: Q2) Compute trigonometric Fourier series coefficients of following 2-periodic signal defined on the…

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Q: 5 4 3 2 -5 -4 -3 -2 -1 3 4 -1 -2 -3 -4 Use the graph of f(x) above to estimate the value of f'(1) to…

A: The value of f'(1) is equal to the slope of the tangent through the point x=1.

Q: For the following problems, find the general solution. 129. y”+5y+y=x+e

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Q: Let S be the quadric with equation 4x² - (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A: The trace of the surface: f(x,y,z)=0 on any plane is the projection of the surface on that plane.

Q: Sky Property cc, a real-estate developer is planning a new apartment complex consisting of 1-bedroom…

A: Consider a system of three linear simultaneous equations with three unknowns.…

Q: Determine the solution to the given ODE: y = √1 - y² over the interval from x=0 to 0.5 using a step…

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Q: Assume that the Taylor series centred at x = 0 of a function f(x) is Σo anx" Let g(x) = f(x³).…

A: The expansion f(x) is f(x)=∑n=0∞anxn Here a0=1, a2=2, a2=3, a4=4 Since  a0=1⇒f(0)=1…

Q: c). For each of the given paths, verify Green's Theorem by showing that [y³dx + xºdy=ff(xXx dA.…

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Q: identify and sketch the graph z = √(4 - y^2) in R^3

A: Given z=4-y2

Q: 34) True or False: The transformation shown below is a rotation.

A: Introduction: Symmetricity is very important in geometry. When a line divides a geometrical pattern…

Q: Solve for the determinants of the items using a combination of row operations and cofactor method.…

A: We need to determine , determinant of given matrix ,  B = 3-69-27-2015 Here , det(B) = 3-69-27-2015…

Q: Find the fourier transform of the following. functions by making use of Jordan's Lemma. a) 1 (x² +…

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Q: - 23 + 132-та -3 наха +2+12 (; +ана - -7³ 2 э

A: We have to write the given expression -λ3+13λ-12 as a product of linear factors. For this, we have…

Q: Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green. (a)…

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Q: 2. Consider the system of ordinary differential equations dy₁ dy₂ = -3y₁ + y₂, = y₁ − 3y₂, when x =…

A: The given system of differential equations is dy1dx = -3y1 + y2dy2dx = y1 -3 y2       when   x=0,…

Q: Solve the differential equation using inspection method d'y d³y dx5 dx³ = 24.

A: We have given a differential equation ,  d5ydx5 - d3ydx3 = 24 This would be written as ,  yv - y'''…

Q: d'y d³y - dx5 dx3 = 24.

A: Solution :-

Q: 9.M.4 Let A = AT be a symmetric matrix, λ be a real number, and v₁ and v2 be vectors such that Αυγ =…

A: It is finite dimensional vector space, so an inner product can be imposed.

Q: Please show full solution for thumbs up!

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Q: LUE OF MONEY It is now January 1, 2018, and you will need $1,000 on January 1, 2022, in 4 years. If…

A: Given: P=$750, t=3 years, FV=$1000, n=1 To find: r=?

Q: If the graph is Hamiltonian, find a Hamilton cycle; if the graph is Eulerian, find an Euler tour.

A: deg(d)+deg(h) = 4+4 =8 where d and h are not adjacent. Since deg(d)+deg(h) is not greater than the…

Q: describe xy - trace, xz - trace, yz - trace. draw each trace a) z^2 - 4x^2 = 9 - 4y^2 b) z^2 -…

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Q: be a linear operator on a vector space V(F). If = 0, t ce oft and null space of t. Also given an…

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Q: Provide all answers to four (4) decimal places. Applying the Gauss-Seidel method in solving the…

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Q: 6. Show that the closure Ỹ of a subspace Y of a normed space X is again a vector subspace.

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Q: 0 < x < 1 1< <2 2 <지

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Q: Find the least-squares solution * of the system H 831 || T 0 1 x || 8

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Q: Find the power series representation for f(x): = 2x (1-x²)² and then find its radius of convergence.

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Q: 3. Magkano ang nominal wage? Real wage = P10,200.00 CPI = P180.20

A: Here given  Real wage =10,200.00 CPI =180.20

Q: Find the length of the curve. Hand written plzz √2ti + etj + etk, 0 ≤t≤ 3

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Q: Use secant method to find the root of x^3 –x^2 – 3x – 3 with two initial points xa=3 and xb=2 and ∈=…

A: FIND THE ROOTS USING SECANT METHOD

Q: Determine the Laplace Transform of cos³3t

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Q: Find the length of the curve. Hand written plzz √2ti + etj + etk, 0 ≤t≤ 3

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Q: spac (a- Open and not closed, b- closed and not open, c- open and closed, d- Not open and not…

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Q: using the following: Line 1: x = 2 + t, y = 1 + t, z = 4 + 7t                                 Line…

A: Given of lines are: Line 1: x=2+t, y=1+t, z=4+7tLine 2: x=−4+5s,  y=2−2s, z=1−4s