Given the differential equation y'-y=3 and the initial condition y(0)=a, what is the value of a that would give this particular solution: U 3e O -2 O 2 3. 0.

Q: 2. All of the following relations is a function EXCEPT ONE. O (6,7), (7.9). (6,11), (7,13)) O ((3,6)...

A: In the relation {(6,7),(7,9),(6,11),(7,13)} The 6 has images 7 and 11 as (6,7) and (6,11) are in the...

Q: Q3 (a) A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable...

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Q: Q3/ Determine whether the following functions are harmonic or not. 1. 3xy + 5xy - 2y 2. 3x²y + 2x - ...

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Q: Solve for the Maclaurin series expansion of ex and use the series to evaluate e0.77. What is the of ...

A: The solution of given problem is followed by

Q: Consider the following matrix A= 2 3 4

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Q: B. Determine whether each statement is correct by use of inductive reasoning. Write CORRECT if the c...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub-...

Q: 2. Prove each of the following statements using a direct proof, a proof by contrapositive, a proof b...

A: There are many methods to prove a statement. In direct proof we assume the first part of the stateme...

Q: 1. Let (A, B, C) be a partition of S = and (2) d e A. What can we say about |C|, the size of C? Just...

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Q: at an restaurant an appetizer costs $8.00 and an entree costs $22.If a family of 7 all order an appe...

A: Given that at an restaurant an appetizer costs $8.00 and an entree costs $22.If a family of 7 all or...

Q: Sketch the phase line for the given differential equation. Identify the equilibrium points as stable...

A: To sketch the phase line for the below differential equation and to identify the equilibrium points....

Q: Find the coordinates of vector u=(4,5) with respect to linear basis ((2,1),(1,-1) ? a. 2 b. 3 • 2 O ...

A: Here we use linear combination to solve this 

Q: 2.) Solve for n in the equation: 3(,C,) = 5(.., Cs) (Show yourself work for reducing factorial expre...

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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x + y ...

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Q: Q2/(a): Evaluate the double integral 3xy2 dA over the reetangle R = ((x, y): 3 sxS 2, 0sys1, dA = dy...

A: To evaluate the double integral. 

Q: Consider the iteratively defined sequence (x,), where x41 = 3 - 2 and x = 3. Use the Monotone Conver...

A: Monotone convergence theorem: If a sequence monotone and bounded then it is convergent.   If the seq...

Q: 2. Even and Odd (a) Use a direct proof to show that the sum of two odd integers is even. (b) and n, ...

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Q: Calculate the particular solution associated with the following dynamical equation 2 x(t) + a ¿(t) =...

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Q: (a) Suppose that T : R° → R° has a 5-dimensional eigenspace for the eigenvalue 1. Then show that eit...

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Q: Calculate the integral of - e2x -dx. 3x +8

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Q: A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable level ...

A: Given: The differential equation that governs the concentration C of the pollutant as a function of ...

Q: 8. Prove the following (I +CD)-\C = C(I+ DC)-1 by expressing the C + CDO in two forms. i

A: To prove the below equation by expressing C+CDC in two forms. 1+CD−1C=C1+DC−1

Q: Assume x is a particular real number and use De Morgan’s laws to write negations for these statement...

A: Given x is a particular real number. 1 Given 1>x≥-3. We have to write the negations for the given...

Q: {:} -1 1 and e2 = 3 and y2 = and let T: R2-→R? be a linear transformation that maps e, into y, and m...

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Q: Q2: matrix P which is the augmente linear System s in Xi, XQ, X3& XL -53 -| -6 -7 P=/ -3 -2 6 4 -5on...

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Q: How many ways are there to pick 9 balls from large piles of (identical) red, white and blue balls, p...

A: To determine the number of ways to pick 9 balls from large piles of red, white, and blue balls, plus...

Q: 11 4 -2 3 - 1 - 15 - 5 3 -8 Let b = and let A = Is b in the range of the transformation XHAX? If so,...

A: Given b=11−152315 and A=4−23−1−53−80−8103−135−380. Let T:R4→R4 be a linear transformation defined by...

Q: the Gaussian Elimanation (a) to write the following and (b) use part (a) to solve for x1,x2, x3, X4,...

A: Introduction:  

Q: The augmented matrices that follow are in reduce row echelon form. In each case, find the solutio se...

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Q: Consider the Following matrix A= 2 3 4 C) Find the Pollowing Funchon f A. At Sin(At)

A: we love this problem with the help of series expansion of ex and sinx

Q: Consider as following ordinary differential equations dy - 2y + 3y and dt dy = e" – 1. dt %3D Determ...

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Q: M. 2x+46 3x- 6

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Q: Given a linear basis v,,..,v, for a vector space V, if (v,,v, =0 for ij then the linear basis is cal...

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Q: Plot a graph for a linear equation in two variables 6x+9y-12=0.

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Q: Disprove the following statement. For all sets A, B, and C of some universe U, (AAB)U (ANBNC) = (ANB...

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Q: Can someone please explain step by step how i'm supposed to expand this integral? In the radical the...

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Q: polynomial in V2+i and compute the conjugates of i over Express i as a Q(/2 + i).

A: As per the question we have to express i as a polynomial in (√2 + i) and then compute its conjugate ...

Q: Find L {(2 - 3)}. 2(n!) 2 3 - sn+1 O 4(2n)! 12(n!) 9. - s2n+1 sn+1 O 4(n²)! sn2+1 12n! 9. - sn+1 O 4...

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Q: The temperature distribution u(x, t) of the one-dimensional gold rod is governed by the heat equatio...

A: Given : temperature distribution ux, t of the one-dimensional gold rod is governed by the heat equat...

Q: Assume that A is a matrix with four rows. Find the elementary matrix E such that E A gives the matri...

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Q: A= • MI

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Q: How many four-letter words (including nonsense words) can be made from the letters of the word "CHEM...

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Q: Drive Rent-A-Truck company plans to spend $13 million on 320 new vehicles. Each commercial van will ...

A: Introduction: A linear equation is an equation with the highest degree of one. This means that in a ...

Q: Ordinary Differential Equations M- 06. Solve the following initial value problem over the interval f...

A: We can solve this by using formula which ask in question

Q: The temperature distribution u(x,t) of the one-dimensional gold rod is governed by the heat equation...

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Q: A point P is moving along the curve whose equation is f(x) = lae2x+3 . By using second derivative fo...

A: The equation of the curve is as follows: fx=4e2x+3 The values for x and fx with step size of h=0.05....

Q: rove the following statement. Ve >1 3d 21 Vx >d: c< 3r.

A: Introduction: A grouping of objects. The set's specific objects are referred to as its elements or m...

Q: Use the inverse Fourier sine transformation to find f(x) from F, (a)= Le™, ,a>0

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Q: Show that if T: Rº → R® has 6 distinct eigenvalues and S has the same eigenvectors as T , then ST = ...

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Q: 1. Detemine, whether and-5 are roots of the equation 10a –5 = 2a3 - a?.

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Q: You are given: i. A survival model is defined by u (x) = 0<z<w. %3D 3(w-z) ii. The median age is 63....

A: Explanation we have given the survival mode defined by μ(x)=13(ω-x),0≤x≤ω The median age = 63 To fin...