Showthat S subring of RIKRZ+R3

Q: determine if the points (1, 3, 3), (3, -1, 5), (5, 2, 0), and (3, 3, 4) lie in the same plane.

A: We will have to check whether the points (1,3,3), (3,-1,5), (5,2,0), (3,3,4) lie on the same plane…

Q: Describe in words the region of R3 represented by the equation. x² + y2 + z² = 36 The equation x2 +…

A: Given equation is x2+y2+z2=36. We have o describe in words the region of R3 represented by the…

Q: e.Solve the diffusion problem uų

A: Given,           ut=uxx in 0<x<1                    ...(1)            u(0, t)=u(1, t)=0…

Q: Sketch the triangle with vertices O, P = (7, 0, 7) and Q = (3,0, 3) and compute its area using…

A: To find the area of the triangle using cross product method when it's vertices are given .

Q: Find a general solution of the equation: 3x?y" + 2xy' – 2y = 0

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Q: 4. The area of the region between the curve y=x and the line y=4 is divided into equal partitions by…

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Q: Question 1 f(x) = e²* – x,xo = 0, x1 = 1.25 and x2 = 1.6. %3! %3D a. Construct the interpolating…

A: (a) We can use Lagrange interpolating polynomial method to find P2(x) using given nodes.

Q: 2. a) Estimate the area bounded by the curve and the x-axis on [1, 6] using the 5 equal subintervals…

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subparts as…

Q: ) If we substitute the polar coordinate x = r.cos0 & y = r.sin0 continuous function w-f(x,y) that…

A: Here we use basic chain rule to Show this

Q: Question* The Laplace transform of f(t) = et-2 cos(2t-4) u(t- 2)-e-(cos(3t) - 1)

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Q: The employees of a company were asked how long it took (in minutes) to commute to work. The results…

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Q: Evaluate the integral: 3 I= S (³ + 6) [8 (t) + 135 (t – 1)] dt. . -1 Express your answer using three…

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Q: Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

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Q: Let 9 P = 15 2e3t – 6e 3et – -4e3t + 2e -6e3t + 5e¯ ỹ1(t) [3e - 15e+| V2(t) = a. Show that j1 (t) is…

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Q: Find a particular solution to -8.5et y" – 4y/ + 4y t² +1 Yp %3D

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Q: s+1) (a) L-1 4s2 +1 (b) L-1 s4 + s] (e) E{/ c{[e cos(r) dr.

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Q: Find a particular solution to -18.5e-21 y" +4y +4y = t2 + 1 Yp =…

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Q: Problem 3 Let R be the relation on the set of ordered pairs of positive integers such that (a, b),…

A: As a+b = b+a, ((a,b),(a,b)) € R.  Hence, R is reflexive.  Let, ((a,b),(c,d)) € R      => a+d =…

Q: A tank initially contains 100L of brine in which there dissolved 20kg of salt. Pure water flows into…

A: Use the integration techniques to solve the question.

Q: initial value pr '(0) = 0 (upto

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Q: 9. Use the method of undetermined coefficients to solve the given system -4 X + 4t +9e X' %3D

A: To find- Use the method of undetermined coefficients to solve the given system X' = 1-441X + 4t +…

Q: for which all the Ei en below are real is 4 1

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Q: b1) The Fourier coefficient of Fourier series of the function f(x) = x + x²,-2<x< 2 is

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Q: A raft is floating on the ocean. Its distance compared to the height of the dock is recorded over…

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Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

A: using newton's backward difference formula find the approximate value of y-13 given y -0.75 -0.50…

Q: e relation on the set of ordered pairs of positive in +c. Show that R is an equivalence relation.

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Q: Al is at the point (0,6) and Bob is at the point (8,0). They are both running towards the origin. Al…

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Q: 4. The area of the region between the curve y=x* and the line y%3D4 is divided into equal partitions…

A: Given curves are y=x2 and y=4.Also given that y=c divided into equal parts of the area.

Q: is solved by New e initial guess of iterations would

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Q: , Find the antiderivati 4x3/2 –1

A: Introduction: We know that the antiderivative of some functions is as follows:…

Q: For non-null matrices A and B, of the same order, which of the following statements is true? А. А -…

A: We want to find true statement.

Q: Write an iterated integral for dA over the region R bounded by y = Vx, y = 0, and x = 32 using R a.…

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Q: Round-off intermediate values to 7 decimal places, and 5 decimal places for the final answer.…

A: The Approximate Root of equation is -0.40152 (Correct upto 7-digit and Round-off 5 decimal place)…

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: Use Mathematical Induction to show that 512|8 · 5" + 6 · 32n – 80n – 14 for all n E N.

A: We have to show that 512|8⋅5n+6⋅32n−80n−14 by using principal of mathematical induction. Let…

Q: nts, in a line, or in a circle? sphere intersects the xz-plane ? sphere intersects the yz-plane ?

A: Introduction: If (a, b, c) is the sphere's center, r is the radius, and x, y, and z are the…

Q: 2) Determine if F is a conservative vector field. If so, find a function f such that F = Vf. b. F=…

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Q: Let A = -2 Which of the following is true? 1 A is not diagonalizable O A is diagonalizable None of…

A: Given matrix is A=−2411. We have to check which of the given option is correct. First find the…

Q: At time t = 0, a storage tank is empty and begins filling with water. For t> 0 hours, the depth of…

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Q: Define T: R R by T(x)= Ax, where A is the matrix defined below. Find a basis B for R with the…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Write an equivalent integrals for the function f(x,y)=D4x+y for the following base (2,4) y= 2x y

A: Let us considre the function z=f(x,y) the integral under the region R  xy-plane is obtained as…

Q: Prove that is a function f is harmonic =0, then - dx -Ldy =0.

A: Given function f is harmonic such that ∂2f∂x2+∂2f∂y2=0

Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75)…

A: Here              x0=-0.75, x1=-0.50, x2=-0.25, x3=0.and y0=-0.07181, y1=-0.02475, y2=0.33494,…

Q: AutoSave Off 10-02 task Draw Design Layout References Mailings Review View Help File Home Insert…

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Q: Write the augmented matrix as a system of equations 1 0 -2 100 0 1 1 150 1 300 y+ = Z

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Q: Tacoma's population in 2000 was about 194 thousand, and has been growing by about 10% each year. a.…

A: Given Total population =194000 in 2000 Growth rate =10% We have to find time when given population…

Q: Q2/ Complete the following table to find the values a, b,c and s

A: # the value 308 is given incorrect . it should be 3162-2845=317 so taking value 317 for calculation…

Q: 22.37 Amount 24 spent on 27.61 20 entertainment 20.03 (in dollars ) 16 29.07 23.43 2.

A: In this equation, the equation of the line of best fit is given. The observed amount, the predicted…