1. Solve the non-homogenous boundary value problem ut (x, t) = kuxx (x, t) + x, 0 0 u(0, t) = 0, u(1, t) = 0 and u(x, 0) = p, where p is constant. You may want to use X = ∞ n=1 (−1)n+1 NT 2- -sin(nπx), (0< x < 1).

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Q: Translate the number 203,651 into Babylonian numerals.

A: Now,  Given to translate 203,651 into Babylonian numericals.

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Q: Solve the DE 2x dx= – XÂY việc s y² Ax-Aretan (y/x) +C Bx²y=x+Cy Ⓒx²=y+Cx (D) xẻ=Arcun(x/y)+C by…

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Q: Let a, b, c be positive integers such that a is a multiple of c and a2 + b2 is not a multiple of c.…

A: a, b, c are positive integers such that a is a multiple of c.  =&gt; there exists some integer x…

Q: Find the general solution of the linear differential equation ydx + xdy - x^3e^(-x^2)dx + 2x^2ydx =

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Q: Which, if any, of the given differential equations is exact? Show how you test each equation, but do…

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Q: for all natural numbers m, n, p, we have that if p | (m * n) then either p | m or p | n" Try…

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Q: Let T (c, d) mean “c is taller than d,” G(c) mean “c is a giraffe,” N (c) mean “c is a gnu,” L(c)…

A: Given: Tc,d means c is taller than d. Gc means c is a giraffe. Nc means c is a gnu. Lc means c is a…

Q: Let H= Span(v₁,v₂) and K= Span{v3.V4), where V₁, V₂, V3, and v4 are given below. 5 0 V₂ = 3 -20 6 8…

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Q: FIND THE HOMOGENEOUS UNEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS WHOSE GENERAL SOLUTION…

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Q: On the measurable space (R, B(R)), let µ: B (R) → R be defined as: u(A) = The number of all rational…

A: It is given that, ℝ, Bℝ is a measurable space and μ : Bℝ → ℝ¯ be defined as ;     μA = The number of…

Q: Compute L{t sin (4t)};

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Q: Fred's final markin an online course was determined entirely by two exams. The mid-term exam was out…

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Q: PLEASE

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Q: d.     a specific element of R3 that is not in V.    e.     a specific element of v in V for which…

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Q: Recall that N = {1, 2, 3, . . .}. Prove that {8n − 3 : n ∈ N} ⊆ {4m + 1 : m ∈ N}

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Q: Derive the three-point central formula that approximate the derivative of a function f(x) is a point…

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Q: Is S closed under addition, scalar multiplication, and is S a subspace of V? V = R2, S = { (n,n) |…

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Q: College radio surveyed 215. Make a Venn diagram is 26 like classical, 145 like rap and 171 like both

A: We have to solve given Questions.

Q: 4. How many 6-digit numbers (using 1,2,3, ... ,9) are there if repetition is not allowed? How many…

A: We know that the number of ways of selecting r items from a set of n items is given by the following…

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Q: preimage, E(-2,-4), is reflected over the y-axis? a) (2,4) b) (4.-2) c) (4,2) d) (2,4)

A: Note: When we reflect any point about y-axis, the y-coordinate remains same, but the x-coordinate is…

Q: Use the graphing technique to solve the LP problem below. Maximize p-3x+y S.T. 2x-Sy ≤ 10 5x - 2y2…

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Q: Let f(x) = (6 + 5x) f(x) has one critical value at A = For x A, f(x) is [Select an answer Soloct an…

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Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = x³y². The directional…

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Q: Consider the function f(x) = 5(x − 3). For this function there are two important open intervals: ( −…

A: fx=5x-323 For critical point  f'x=0∴f'x=103x-3-13 ∴103x-3-13=0 , has no solution. f'3 is undefined.…

Q: Solve the system of equations by graphing:

A: first we draw these two graph  given y=2x+1 and  -4x+8y=-16 on simplifying -x+2y=-4 y=-2+x/2

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Q: Let a and b belong to some extension field of F and let b be algebraicover F. Prove that [F(a,…

A: Given: A field F and a and b belong to some extension field of F and b is algebraic over F. To…

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Q: Consider the solid under the graph of z = e above the disk x² + y² ≤ a², where a > 0. (a) Set up the…

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Q: 22. C/Gy" + 4y + 3y = -e (2+8x), y(0) = 1, y'(0) = 2

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Q: 4e4* sin(2y) Given f(x, y) = 4e4x then Vƒ(0,7) - [ 2

A: The operator ∇ is defined as: ∇=i^∂∂x+j^∂∂y. Hence, the gradient of f can be written as:…

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Q: QUESTION 2 8 Find the eigenvalues and eigenvectors of matrix B, where B 1 1+2 2 5 6 3 5 8-2i

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Q: Which statement most accurately describes the graph of the solutions to the inequality…

A: Try to graph the 17x-3y=42   then look at graph of 17x-3y=c by changing c.

Q: Change from rectangular to spherical coordinates. (Let p ≥ 0, 0 ≤ 0 ≤ 2π, and 0 ≤ y ≤ ñ.) (a) (0, 3,…

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Q: 1. (Section 16.4) The following integral gives the volume of a solid (a) Graph the solid. 1 1-1-2-y…

A: A volume integral involves the integration with respect to the product of the variables x,y, and z.…

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A: To Find: The point on the surface of z=-3x2+3y2 at which the vector n=-24,12,1 is normal to the…

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Q: You deposit $100 each month into an account earning 4% interest compounded monthly. a) How much will…

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