du at u(o₁t) = du (πT₁E) = 0 ди dx and I.C₁ u(x₁0) = 3 sin (5x) HW: solve heat eq. ax² with b.Cs:

Q: Use two truth tables to show that each of the propositions are equivalent.  f. (p /\ q) /\ r and p…

A: Remember the truth table for p∧q pp qq p \wedge qp∧q True True True True False False False…

Q: Resolve yDx-2(x + y)Dy = 0 O x² + 2y = cy² ○ x + 2 = cy² O x + 2y = cy² Ox+2y=c

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Q: 2 f(t) = ½ (4-³)² u(t-3)

A: As per the question we have to find the graph of the Laplace transform of the following function :…

Q: Hand written plzz : Find the Laplace transform F(s) = {f(t)} of the function f(t) = (8-t) [U(t-4) -…

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Q: The paper speed of a given recording machine (say, an EKG) is 25mm/sec. This means that, at every…

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Q: (c) Every element in the set {0, 1, 2} is greater than or equal to half of its square. i. Original…

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Q: Let f(x) (x² + 1) cosh x² 1. It's true that Of is an infinitesimal, non-comparable with 1 ○ 13 24x4…

A: As per the question we are given a function f(x) and we have to investigate its asymptotic behaviour…

Q: The particular solution of the differential equation: (x + 2)² d²-(x + 2) dx +y = (b + 1)(b +…

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Q: 2. Solve the following LPP using Simplex method. Max P 12X + 16Y Subject to: 10x + 20y =0 and Y >= 0

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Q: (d) Find the approximate solution of the system of equations (using the projection matrix) 3 4 J]-[…

A: Least-square solution: The least-square solution of Ax=b coincides with solutions of the normal…

Q: Q. Show that (2) + ل ( ) + y , (4) y₂ + (1) Dy+ y = D

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Q: y(x) Use Euler's method with step size 1 to estimate is the solution of the problem y + 3x²y = x²…

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Q: P6.3 Simplify the following Boolean expression using Boolean algebra laws: (a(a+b))' + ba'

A: Given Boolean expression is aa+b'+ba'. We have to simplify the given Boolean expression using…

Q: (laplace transform) 3u If L (e³t) = ¹, then L( e³u du) is... S-3'

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Q: Let f(x): e² sin³ (4) x6 sec(x − 2) a. Solve for f'(x) without using quotient rule or product rule.…

A: As per the question we are given the function f(x) and we have to find its derivative f'(x)  without…

Q: c) Use Secant Method to find the root of f(x)= x -x-1 with two initial points x, = 1 and=1.5 and =…

A: Secant method Steps  Step-1: Find points x0 and x1 such that x0<x1 and f(x0)⋅f(x1)<0.…

Q: Solve the formula for the specified variable.  p=rc for r r=    Solve the formula for x. Ax+By=C x=

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Q: (c) Show that if a <r < [b], then 1 2πi √₁₂ (z − a) (z - b) -dz a 'b' - where y denotes the circle…

A: First I introduce about Cauchy's Residue theorem: If f(z) is analytic function inside and on a…

Q: Use two truth tables to show that each of the propositions are equivalent.  h) p \/ (q \/ r) and (p…

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Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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Q: Give examples of the following, and provide justification as to why your answers are examples of the…

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Q: Solve the following LPP using Simplex method.     Max P = 12X + 16Y     Subject to:            10x…

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Q: (c) y(0) = -5 10 -10 O (d) y(8) -5. 10 -5 -10 -10 O -10 -5 -5 0 y 0 5 10 10 X X -10) O 10 O 10 5 0…

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Q: Solve the given differential equations: 1. 3x²y dx − (x³ + y³)dy = 0, y(1) = −2

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Q: 15. A flow rate of 32 microdrops per minute on a gravity system is equivalent to how many…

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Q: 4. Consider the vector field given in Cartesian coordinates by A(r) = (x² + y³, 3xy², z²). (a)…

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Q: Evaluate the given function by using three terms of the appropriate Taylor series. √16.2 √16.2=…

A: Consider a function f(x)=√x

Q: 12y 3p A) For the joint probability p(A.B)-5p 4y. Find P(A). P(B), P(A/B), and 13p 7pl P(B/A), if y…

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Q: (z-3√2)² Allow T to be the surface with equation 1 42 3² 1. Provide the equations of the traces of T…

A: here we use general equation of ellipse to conclude that the trace is elliptical.

Q: 14) Let C: r(t), t € [a, b], be a regular curve in R³, oriented from the point P = r(a), to the…

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Q: Nx - My xM - YN has an integrating factor of the form a(zh Find an integrating factor and solve the…

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Q: 3) Consider the curve C which is the intersection of the surfaces shown in the attached figure. 1 If…

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Q: Integers Fractions Negative Positive Figure 4 The real number system Exercise 5 Copy and complete…

A: We need to complete the table.

Q: P(1,0, 12). Consider h(x, y, z) = cos (ry) + e + In (az) at the point P llowing: it vector in the…

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Q: - The multiplication error is lx*y* - xyl ture false O

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Q: island has 12 fur seal rookies(breeding places). To estimate the fur seal pup population in Rookery…

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Q: Q2) Determine the traction vector, considering the following input data: 30 15 12 o 15 24 18 n=…

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Q: Find the derivative dv/dpsi of v(x) V()| V(vi) where V(y) = (1 - e-√2 and 16 V (vi) = (1 - e-√2…

A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…

Q: For the shown function, calculate the location of for the shaded region. Express your answer in…

A: x- is the x coordinate of centroid

Q: Define fet)= et +etcost if t>#7/2 solve y(3) - 2y (2) + ý' - 2y = f(t) y(0) = 1₂ y'(o) = 2, y"(0) =…

A: Given differential equation is y3 -2y2 +y' -2y =ft   with   y0=1,  y'0=2,  y''0=4Here, ft = e2t if…

Q: Q2 Find the points of intersection of the polar curves r=1+cos and r= -cos

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Q: 3 By direct partial integration, Solve the following PDES 8- 82 Z 5 4 BB =0, Z(X₂0) = X²+X, Z (2,y)=…

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Q: (1) 1 = (2) 1 = √ z²dz, C: z(t) = t² + it (0 ≤ t ≤ 1) zdz, C:z(t) = t² + it (0 ≤ t ≤ 1)

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Q: Q 1 Find all points in the first quadrant where r = 2sin(30) and = 1 intersect. r=2sin(30) +

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Q: A system of linear equations reduces to the following augmented matrix: x y Z I cc What are the…

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Q: Problem 4: Solve the initial boundary value problem: 3π u₁=Uxx +€¹¹cos(x)+1, 00 BC: u(0, t) = 1,…

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Q: After a 80% ​reduction, you purchase a new sofa on sale for ​$148. What was the original price of…

A: Given reduction is 80% and after reduction price of sofa is $148

Q: what about part c,d,e?

A: (c) write the contrapositive of the statement  if n2 is a rational number than 2n-1&lt;n2 solution…

Q: fCt = [ Htu (t-π) Jun (37)

A: As per the question we are given the following function : f(t) = [1+u(t-π)]sin(3t) And we have to…

Q: Using Intermediate Value Theorem, check whether f(x) = x³ + 3x-5 contains real root in interval: i)…

A: Intermediate value theorem