Exercise 1: Consider the nonhomogeneous differential equation: y(o) y- 9y(4) = x³ + 2e¬3x (E)

Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

A:

Q: In the design of a certain computer application, a heat flow simulation is required. In the…

A: Given The 1-dimensional heat equation is given as follows ∂u∂t=∂2u∂x2 for all 0≤x≤10 & t≥0 it is…

Q: Solve the system graphica x+ys5 x+2y s 8 X20 y20

A:

Q: (b) Prove that for all sets A and B, (AN B)° = A¢ U B°.

A: We have to prove that for all sets A and B, A∩Bc=Ac∪Bc

Q: Show that if A and B are sets |A| = |B|, then |P(A)| = |P(B)|

A:

Q: 3)3 differant radical #'s rany is the set of all real #'s greater than o

A: Let us give three different examples of radical numbers in the next step.

Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…

Q: The graph of a function f is shown. (The dashed lines indicate horizontal asymptotes.) y4 1- Find…

A: We have to draw graph of y=|f(x)| from graph of y=f(x)

Q: 3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all…

A: We have to explain that n!+2, n!+3,…,n!+n-1,n!+n are all composite numbers.

Q: Evaluate the iterated integral. ra/2 7 cos (x + y + z) dz dx dy

A: To find the integral.

Q: Find the value of z for the probability statement: P (-z <Z<z) = 0.7887 %3D 1.25

A: Solution

Q: b) Consider the following linear programming problem: Min z = x1 + X2 s.t. 3x1 - 2x2 < 5 X1 + x2 < 3…

A: Let us consider the linear programming problem  Min. Z=f(x,y)s.t. g(x,y)≤bx,y≥0 Solving by graphical…

Q: Suppose that an object is thrown upward with an initial velocity of 64 feet per second off the edge…

A:

Q: Find the area. Use 3.14 for n. (Assume h = 0.8 m, and w = 2 m.) m2

A:

Q: 1. A graph of a function f (x) is given as follows. Sketch the graph of f(x) . State all the x and y…

A:

Q: Find and classify the critical points of f correct to three decimal places (as in this example). (If…

A: We have to find the critical points and then we can proceed further.

Q: Suppose you are using a triple integral in spherical coordinates to find the volume of the region…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3 2 Rank of the following matrix is A = |4 2 | 6. 7 4

A: To find The rank of a matrix.

Q: You are wallpapering two walls of a child's room. One wall measures 9 ft by 8 ft, and the other…

A:

Q: Betermine if the sets of vectors are linearly independent or dependent. Justify your answer. You may…

A: We Know that,

Q: If the Z-score of a certain number is -0.440, with a mean of 80.2 and standard deviation of 11.811,…

A: Given Z-score = -0.440 Mean = μ = 80.2 Standard deviation = σ = 11.811

Q: A punch-out card contains 100 spaces. One space pays $300, five spaces pay $20, and the others pay…

A: Probability tells about the possibility of happing something. Probability is computed by dividing…

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: 1 -1//2 1//2 Pi P2 1 1 0 0 18 0 -1//2 0 P4 P3 -1 1//2 0 1//2 1 0 -1 -1//2 12 Ps 0 P6

A: To solve the system of linear equations obtained below form the matrices; The given data is,…

Q: A certain city has two districts A and B. The populations of the districts are given in the table.…

A: Given, Table showing the population of two districts. No. of police officers employed= 40 We have to…

Q: 21. A die is rolled. What is the probability of getting a. an even number or a 3? b. an odd number…

A: Solution

Q: Which of the following is a correct conversion formula when changing from spherical to cylindrical…

A: Any point in the cylindrical coordinate system is represented as r, θ, z. Any point in the spherical…

Q: 1. A piece of property valued at $50,000 is divided among five players (P1, P2, P3, P4, P5) using…

A: Given: The value of current C-piece at the time it is the turn of other players P2, P3, P4, P5 is:…

Q: Use PMT to determine the regular payment amount, rounded to the nearest cent. The cost of a home is…

A:

Q: Question 2 Find the value of f(z) = z3 +z as z-i along the paths (a) parallel to the x-axis coming…

A: Given  f(z)  =  z3+ z To evaluate the limit of f as z → i  along two different paths

Q: Use a graph or level curves to find the local maximum and minimum values and saddle point(s) of the…

A:

Q: There is a 15x15 matrix as shown below 0.00 1.82 2.64 1.27 2.09 2.00 1.82 1.82 1.55 3.18 1.55 2.00…

A: Here, we are given the matrix t as the following. Matrix  t                           0 3.18…

Q: Sketch the graph of the following function, by determining the maximum/minimum point, the graph up…

A:

Q: 3. Find the value of ø(T) for a solution ø(x) to the initial value problem: y" + 25y = 10 cos 5x;…

A:

Q: The figure shows the region of integration for the integral. (x, y, z) dy dz dx Rewrite this…

A:

Q: A certain virus is known to spread among a population at a rate proportional to the fraction of the…

A:

Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

A:

Q: ntial equations: (x+2y) 1. = y de

A:

Q: 1. Please rewire the expression below without the summation operator.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: X, + X2 s 9 X, + 8x, s 16 0マx tx

A:

Q: QUESTION 3 Let E be the region in the first octant contained below the plane z=3 and above the cone…

A: We will find integral in all 3 co ordinate system and then compare .

Q: 2 1 2 3 4 5 6 7 8 2 to z = 7 using a Left Endpoint Approximate the area under the curve shown above…

A: The left point approximation of a function f(x) over the interval [a,b] with n subintervals is given…

Q: Question 1 Use Laplace Transform technique to solve the initial value problem y' + 2y = 26 sin 3t ,…

A:

Q: Find the perimeter of a triangle in which each side is ft. ft

A: Given each side of triangle is 523 ft.

Q: pand f(x) =5x as a half-range Fourier sine series in the range 0 < x <A , and sketch the function…

A:

Q: Find the series solution of x'y" + x(;+ 2x)y' + (x y = 0 using frobenius method

A:

Q: Solve the second-order difference equation Y=2=7Yt=1 + 10Y, = 4t + 8t

A: We solve  Yt+2 -7Yt+1+10Yt=4t+8t........(1)

Q: Suppose you bought a sofa for a total purchase price of $1,184.97. State taxes were 4%. What was the…

A: Solution :  Given that  Total purchase price = $1,184.97 Sales tax rate = 4%

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is O 5 4 O 2 None of the choices о

A:

Q: there is at most one polynomial of degree less than or equal to n_____ option,(a) which interpolated…

A: Using interpolation theory, We need to check which option is correct.