Show clear and detailed solutions • Determine and draw the graph of the following equation in R3 : x2 + 2y? + z2 – 8x + 12y – 2z + 35 = 0 - -

Q: 2. Let A = (1,0, 2) and B= (6,-2, 3). Solve for projAB.

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Q: d²y What is the particular solution to the differential equation x dx? dy x² with y = 0 and dy = 1…

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Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

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Q: n each part below, give an example of a function which satisfies the given criteria. Justify that…

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Q: Question 6 Find the solution. (4D3+12D2+13D+10)y = 0. /½(c,cosx+c_sinx) + cge -2x y = c ,xe-2* + e A…

A: Solution of the Homogeneous differential equation

Q: p3 – 4x2 (x + 2)² ’ x(x+8)(x – 2) (x + 2)³ 8(7x – 4) (x + 2)4 - - - f(x) = with f'(x) = and f"(x) =…

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Q: Find the solution. (x+e) dy - dx =0 (A y=ce" + ye B x=ce" + ye" x=ce + ye D y=ce" +xe

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Q: max2 =2%+31 -51y Sito XitXz tXg =7 メ2-5Y2+X フe メoxe F (usighe Using M-Eechnifue

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Q: H13. estimate intervals to the approximate the Minimam number of Sub Velue of (ax 4) dx with an…

A: (a) We have fx = 2x2+4 then f'(x) = 4x, and f''(x) = 4 Note: We have second degree function.

Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y” = 0.

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Q: I. Solve the following problem, complete with free body diagrams, clear solutions, and complete…

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Q: 12. In a standard deck of 52 cards, each card has a suit and a rank. A, hearts ♡, clubs , and…

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Q: Let A (1,0, 2) and B= (6,-2, 3). Solve for proj,B.

A: Given vectors are A = 1, 0, 2 and  B = 6, -2, 3

Q: Express the sum of integrals as an iterated integral in polar coordinates: r2/3 r4+V16–x² x dx dy +…

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Q: 1. Let n be a natural number with n > 1. (a) Suppose n is prime. Prove that if ab = 0 (mod n), then…

A: In 1)  (a) we need to prove that ab≡0 ( mod n), then a≡0 (mod n ) or b≡0 (mod n ).     In (b) We…

Q: Solve for the domain and range of. f(x.y,z) = 4-x2-y?

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Q: 2. Use zero- through fourth-order Taylor series expansions to predict f(2.5) for f(x) = ln x using a…

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Q: Generate the 6th degree Legendre polynomial.

A: Solution

Q: exercise Find the laplace of each f(t) 2. sin8t sin6t

A: We have to find the Laplace transform of ft=sin8tsin6t

Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 (A -e "cos3t 3 1 B -e -'sin9t 3 3r -e"cost D -e…

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Q: 2s + 3 Find the Inverse Laplace Transform of (s+4)3 A e"(2cos2t +- sin2t) 2 (cos2t+ -sin21) (2cos21+…

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Q: Use the Newton Raphson Method to find the root of f(x) using 2.2 as the starting value of x. Iterate…

A: f(x) = tan-1x2+x-6 then f'(x) = 2x+11+x2+x-62

Q: х — 3 2. Graph the function f(x) = Identify asymptotes and holes in the х2 — 4х + 3 graph. Answer:…

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Q: Question 8 Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general…

A: Given is an IVP with initial conditions   To Find:  Solution to given IVP with initial conditions…

Q: Use the Newton Raphson Method to find the root of f(x) using 2.2 as the starting value of x. Iterate…

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Q: Find the solution. y'-y = -xy1/2 -ху

A: This is Bernoulli type differential equation.

Q: Find the Laplace Transform of e 2 cos3t + 5e 2 sin3t - s+2 + s2+9 15 A. g²+9 (s+2) + 15 (s2+4s) + 13…

A: To find the laplace transform of given function first we will use the linearity property of laplace…

Q: Find the solution. y" - 2y'- 2y = 0

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Q: 94: For the system presented by the function x +y+ 2 4xy. Calculate all the possible points at which…

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Q: 8. PROVE: Suppose that S CR is connected, and that f : R → R is continuous. Then f(S) is connected.…

A: We want to prove f(S) is connected.

Q: c) Find u (v x w) if u = [0,0, p], v = [0, q, 0] and w = [r,0,0]. %3D

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Q: How long is this side? 1.7 cm 71° 21 2.2 cm 1.7 cm 4.3 cm 53° 37 2.1 cm 3.2 cm 2.9 сm 42 3.8 cm 3.6…

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Q: Integrate f(x) from x = 2 to 8 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000 + 24583x –…

A: We have fx=5000+24583x-7418x2+766x3-31x4+0.44x5 and x is from 2 to 8 The formula to integrate…

Q: Approximate the roots of the polynomial f(x) = X³ - 7X + 6 using False-position method.

A: We will find Approximate the roots of polynomial f(x) = x3-7x+6 using False-position method. steps…

Q: Which of the following operations on a matrix may not be an elementary operation row ...

A: Which of the following is not a elementary row operation on a matrix.

Q: Find the solution. (x³ + 3y) dx – xdy = 0

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Q: Using Bisection method find the solution of h (x): = xcos2x +1 = (x - 2)2. Use as initial values and…

A: given method hx=xcos2x+1=x-22 use as initial values π2 and 5π6. stop iteration if the error is less…

Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: Question 16 Find the Laplace Transform of e4t + 5 A + s- 4 B s+4 C s-4 D) s+4 s2 - + +

A: The solution is given as

Q: Question 2. Approximate the roots of the polynomial f(x) = X° - 7X + 6 using False-position method.

A: To approximate the root of the equation using false position method .

Q: (b) y = 4xª+(3+51)x³+5x²-(100+1)x-400. What is the slope of the tangent on this curve at x=2.5?

A: Given curve,  y= 4x4+(3+51)x3+5x2-(100+1)x-400 To find the slope of the tangent on this curve at…

Q: 4. Draw the logic diagram corresponding to the following Boolean Expression. a) (P+ R)• (Q ® R))+ (P…

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Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: Let u = (-5,-2, 4), v = (3,6,-5) and w (-7,1,-8). (a) Calculate (u x v). w and hence find the volume…

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Q: Embassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and…

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Q: Solve y" + 4y —и(( — 1) + 6(t — 2), у(0) — 1, у (0) — — 1. |

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Q: Question 1: 1- Evaluate xp 1+ x

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Q: . ndS over the 2 = 9, where F = is the unit outw

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Q: Consider the following IVP: y +y = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: Find the solution. dy y dx A y = y = -x+ cx-8 y = y-2 -| 00 B.

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