Let / be the line described by the Cartesian equations • X=1 y-11= 2(z-8) Let , be the line described by the Cartesian equations • X= 1 • y-11 = z-8 Compute the distance between and I2.

Q: Let R be a commutative ring with unity, I an arbitrary ideal in R and P1,P2,...,Pn prime ideals in…

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Q: Determine the equation of the normal line to the surface In (x + y) = Z 2 at the point (-1,2,0)

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Q: Let S be the quadric with equation 36x2 –4y2 –9z2 – 36x = 0. Sketch a graph of the surface with…

A: See answer below.

Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

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Q: The geometric object in 3-space represented by the equation (x +y +z)^2 = 81 is O a. the line…

A: This is quadratic equation.  When this quadratic expression can be factored in two linear factors…

Q: Find L{f(t)} of the following functions. Note: a, b, e, k and n are constants. (t+1 ,0<t <1 1. f(t)…

A: Laplace transferom of the function, using definition of the Laplace transferom

Q: Let R be a ring with unity which has exactly one maximal left ideal M. Show that the only…

A: Given: R is a ring with unity which has exactly one maximal left ideal M. To show: The only…

Q: How did you get 1=5a+5b I understand how you got all the values for the formula but why did you…

A: Solution

Q: Find the first three terms of the expansion (4 – 2x)°. 4°(1 – * + + .) 플 + 5x2 + .…) 2 а. b. 25(1 +…

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Q: Which one of the following series is divergent by comparison test? n=1 n°+ 8 8. n6 Σ 10 n=1 n+9 Σ n-…

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Q: Determine the linear approximation of f(x) = x° at x = 1. a. y= 8x +7 b. y=- 8 x - 7 C. Not in the…

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Q: Let i denote the square root of –1. For the two complex numbers z = 3e 3 and w = 6e'3 find z. w.…

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Q: Which of the forms would be most helpful in answering questions d-f

A: The various forms of a quadratic equation can be listed as follows. Standard form: f(x)=ax2+bx+c,…

Q: x³-10 Find the domain and the vertical asymptotes, if any, of the following function x2+17x+72 O a.…

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Q: iv) (8y? – t+3)dy + (3t² -y – 12)dt =0.

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Q: How to test the divisibility by a number using binomial theorem. Explain step by step.

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Q: You have 200 feet of fencing to enclose a rectangular plot that borders a river on two sides. If you…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 8x i + 8y…

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Q: 4. Рy/Оx? - 60у/дx - 5 %3D 0

A: 4 Given differential equation is ∂2y∂x2−6∂y∂x−5=0. We have to identify the order, degree, type of…

Q: Let A be an m x n matrix over C. The Moore-Penrose pseudo inverse matrix A+ is the unique n x m…

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Q: Let x and y be integers. Prove by the contrapositive that if x2 - y2 is even, the x + y is even

A: Let x and y be integers such that x2-y2 is even. We have to prove that x+y is even. Suppose that x+y…

Q: Find the isolated singularities for the holomorphic functions f, g, h. Determine the types and…

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Q: fined the genral solution 8) (D + D,)u = 0

A: Solution of the higher order homogeneous partial differential equation.

Q: very linear transformation = au + bv, y = cu + dv with ad – bc + 0 aps lines of the uv-plane onto…

A: Given, Linear Transformation x=au+bv and y=cu+dv maps lines of the u-v plane onto lines of the x-y…

Q: Consider the bases B= (u1, u2) and B' = {uj, u½} for R², where -[} »-H «-} «-[*] uj = u2 = %3D (a)…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: Let n be a positive integer and f (n) = -53n109 – n51 + 53. Then f (n) is O(logn) the above. None of…

A: Correct answer is O(n^110).

Q: (-2 1 Consider the matrix A 2 1 and vectors x = |1 and y: (-1 Let vector v be defined as v = (A – A'…

A: Here given matrix  A=-210021-100 Then  AT=-20-1120010 Thus A-AT=-210021-100--20-1120010=011-101-1-10

Q: Find the area of the region. Interior of r = 6 sin 0

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Q: If a line is parallel to the vector 4i + 1j + 4k and passes through the point P = (3, 7,9), then the…

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Q: Find the area Inside the lemniscate r = 6 cos 20 and outside the circle r = 3.

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Evaluate the surface integral fof the scalar feld 1-62+4 where S is the surface parametrised by (u,…

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Q: Q2/A) Find the particular solution for the following D.E., the boundary condition is (y-0 @x-0) dy =…

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Q: Problem 8. Consider the 3 x 3 symmetric matrix over R 2 2 -2 A = 2 2 -2 -2 -2 6 (i) Let X be an mxn…

A: The main objective is to determine the rank of matrix A and also find the P and Q matrices.

Q: (a) With the aid of software, find the eigenvalues of B and their algebraic and geometric…

A: Given matrix is B= 011-22-121-22-112-22-110021-1000

Q: 7. Match the function with its graph 1 1. f(z, y) = In(r² + y*), 2. f(1, y) 3. S(r, y) = y² – x²,…

A: This is a problem of multivariable calculus.

Q: nd the differential equation of a family of circles, each having its center on the line y = x and…

A: We have to find the differential equation of the family of circles from given data.

Q: where did you get the 657? the given was 675.

A: Solution

Q: Let II, be the plane with Cartesian equation z=0. Let II, be the plane with Cartesian equation x=0.…

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Q: - Sketch the graph of each function in [0,2n) by transforming its parent function. (a) y = cos(x) +1…

A: Use the following rules, to obtain the transformation of the parent function y=fx. Replace x by nx…

Q: Prove that the subgroup {o E S5 | o (5) = 5} of Sg is isomorphic to S4.

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Q: (2yt – 7y')dy + (y² – 5t)dt = 0.

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Q: B. Find the adjacency matrix of the following graphs. 1. 2.

A: 1 Consider the given graph We have to write the adjacency matrix. The adjacency matrix for the given…

Q: Prove that the number V7 lies between 1 and 2.

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Q: 3. (а) Let S be a two-dimensional subspace of R3. Let P be the projection matrix cor- responding to…

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Q: y" – y' – 2y = sin 3t y(0) = 1 and y'(0) = -1

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Q: A thermometer reading 70 degree Fahrenheit is placed in an oven preheated to a constant temperature.…

A: The differential equation is dTdt=kT−Tm. ⇒dTT−Tm=kdt Integrate both sides…

Q: Use integration by substitution or integration by parts as appropriate to evaluate Axsin (Bx) dx…

A: Here we use integration by substitution and then integration by parts

Q: d'r If r = (+ 2t)i – 3e-²j + 2 sin 5t k, find dt2 at t= 0. 12j -12j 12i -12k

A: Use the following formulae, to obtain the solution.…

Q: Suppose U1; U2; :::; Um are Önite-dimensional subspaces of V . Prove that U1 + U2 + ::: + Um is…

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Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

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