Find an equation of the line in parametric form that passes through the vertex of the paraboloid z=x²-2x+y² +6y and the center of the ellipsoid 3x² +12x+4y² + z² = 0.

Q: ! d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A:

Q: It is the proportion of the variation in the dependent variable that is predictable from the…

A:

Q: in problems 1 and 12, list both the order of the DE and state whether the DE is linear of nonlinear.…

A:

Q: Which method is/are said to be direct method Gauss Elimination Gauss Jordan LU Decomposition method…

A:

Q: What is (are) the first name(s) of Fourier? A. Carlos Guiseppe B. Jacques Antoine C. Joseph Louis D.…

A:

Q: 3. Change the order of integration sin dydx. Hence, evaluate the integral. y

A: Sol ∫0π∫xπsinyydydxChange order of integration =∫0π∫0ysinyydxdy

Q: e. To solve the 2nd order ODE, xy" - (x + 1) y' - y = 0, by series method, the indicial roots are…

A:

Q: Find the matrix A of the quadratic form associated with the equation. 9x2 - 6xy +9y2 + 24z² - 29 = 0

A:

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the…

A: The ratio test: The convergence of the series: ∑i∞bi can be examined by evaluating the expression:…

Q: B. Find a general solution of the following differential equation using Lapla y" - 4y + 4y =…

A: y''-4y'+4y=3sin(2t) where y(0)=1 & y'(0)=1

Q: 1. Let matrices be 6 A = 10 -3 1 L-10 5 [5 a = 1 -2 -21 [2] 1 1 94 4 -4 B = 47 0 -40 b = [308] -4 0…

A: We know that a matrix of order m×n has m rows and n columns. There are certain rules to perform the…

Q: (b) Solve +4y=3u(t-5) sin(t-5) y(0) = 1, y'(0)=0 d²y dt² Oscillator with suddenly appearing…

A:

Q: Determine the values of a, if any, for which all solutions of the differential equation y" − (2a −…

A:

Q: Two matrices A and B are multiplied to get AB if O both are rectangular O both have same order O…

A: Necessary condition for multiplication of two matrices : If A and B are two matrices, then…

Q: Given that f(z)=z-ż where does f'(z) exist

A:

Q: 5) L (4 4 sinh 3 2t +3 sinh 2tỷ

A:

Q: When using Runge-Kutta method of order 4 to solve the initial-value problem: ý = cos 2t + sin 3t, 0…

A: K1= 0.25

Q: a) In a school of 36 students, 19 of them studies Music and 16 studies Art. Each student studies at…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: The Brute Force Bandits is a rock band planning a five city concert tour. The cities and distances…

A: A Hamiltonian path is a path that starts at any vertex of the graph and visits every vertex of the…

Q: 5. The linear least squares approximation which best fits the curve y= |x | over the interval -1 ≤ x…

A: Sol

Q: Determine the longest interval in which the initial value problem is certain to have a unique twice…

A:

Q: (3-1/2+1) ⁹

A:

Q: Problem 5. Find the Jordan canonical form of the following two matrices: 01 1 0 1 0 1 1 00 00111…

A: 5 Consider the given matrix A=0110100111000000000000000. We have to find the Jordan canonical form…

Q: Use the right endpoint sum to approximate the area under the curve f (x) = x^3 from x = 1 to x = 2…

A:

Q: Solve the initial value problem below using the method of Laplace transforms. y' +9y' + 18y = 160 e…

A: Some of the formula of Laplace transform are Leat=1s-aLy''=s2Y(s)-sy(0)-y'(0)L-11s-a=eat

Q: Solve the initial value problem y" - 4y' - 45y = 0, y(0) = : Find a so that the solution approaches…

A:

Q: . Use the result obtained in (i), and the method of Laplace transform to solve the following initial…

A:

Q: Let h(x) = f(g(x)). If ƒ(2) = −2,ƒ' (2) = -5, g(-6)= 2, and g'(-6) = 5, find h'(-6). Do not include…

A: It is known that: ddxf(gx)=f'(g(x))g'x.

Q: d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A:

Q: When using Runge-Kutta method of order 4 to solve the initial-value problem ý= 2, 0≤t≤ 1, y(0) = 0,…

A:

Q: Let f: R" x R → R define as follows f(x, y) = then f is

A: Given that: f:Rn×Rn→R define as follows fx,y=∑xiyi¯i=1n. The objective is to determine the value of…

Q: Determine the values of a, if any, for which all solutions of the differential equation y" (2a -…

A: Given differential equation is y'' -  2α-13  y' +  α2 -13α+ 36  y =0

Q: 3 (a) Find the volume of the solid that lies under the plane 3x+2y + z = 12 and TL above rectangular…

A: To find: The Volume under the plane 3x+2y+z=12 and above rectangular regionR=(x,y)|0≤x≤1, 0≤y≤π2. As…

Q: For each graph of f shown below, answer parts (a)-(d). -3 domain range -2 -1 y 15 10 5 1 f(x) = x¹…

A:

Q: i. Use partial fraction to find (1 1 sº(s – 5) -

A:

Q: QUESTION 3 Let A={1, 2, 3, 4) and B=(-1, 0, 2, 4, 5), and R = {(1,0), (1,2), (3, 1), (4,4)). Then R…

A:

Q: 1. 2. Find the interval of convergence of the series (-2)(x−1)ª 4* (k+1) k=l -x² Evaluate ¹* (x² +…

A: Using the results: Radius of convergence, Leibniz alternating series test, p-series diverge for p=1

Q: n 3. For nx n matrix A. define R₁ = -1,i+j laij 1, then each eigenvalue of A is either in one of the…

A:

Q: x³-2x-3-0 1.4 rations)

A:

Q: 62. A particle is moving on the x-axis with a velocity of v(t) = t² - 3t-18. For what values of t> 0…

A:

Q: According to determinant properties, multiple of one row is added to another row then determinant…

A: Given, If a multiple of one row of a matrix is added to another row

Q: Find the Fourier Series expansion of the function f(t) = t & f(t) = -2m(-1)" b. O a Ob O c Od c.…

A:

Q: Carbon-14 is a radioactive isotope of carbon that has a half-life of 5600 years. It is used…

A:

Q: If Use a Taylor Polynomial about II to approximate Cos 42° to an a ccuracy of 156

A:

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: Given three polynomials over 2₂. find (i) (ii) f(x) + g(x). f(x)h(x). f(x) = 6x³-5x² + 2x - 4, g(x)…

A: Please see the attachment

Q: Q5. B. Solve the following first order differential equation using Linear method? ty' +2y=t²-t+1…

A:

Q: (b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E) where {s, t} € E if and only if 7 | (s –…

A: The vertex set is: V=0, 1, 2, 3, …, 13 The graph G=V, E has the property that s, t∈E if and only if…

Q: A = 24 0 1 01 4 -1 3

A: In order to calculate the eigen value of the matrix A, we need to solve the equation: A-λI=0 for λ.…

Q: What is the correct translation of the statement "m varies directly to a" if k is the constant…

A: a is directly proportional to b means a∝b a is inversely proportional to b means a∝1b If k be the…