Solve, graph, and explain the graph of the parabolas: a) y=x² +7x-9 b) u=-3x² + 4x - 20

Q: Find the area of the region which is inside the polar curve r = 9 cos(8), and outside the curve = 6…

A:

Q: n= (-1)" n2 +1' M8 n=1 1 12 +1

A: (1) Exponential Fourier coefficients:Hence,

Q: 4. Use variation of parameters m y"+y' = ln x

A:

Q: 3. Iff= {(-7, 1), (-5, 8), (3, 11), (5, -1)} and g = {(-6, 4), (-5, 3), (-1, 7), (5,5)}, what is f +…

A: Given that, f={(-7, 1), (-5, 8), (3, 11), (5, -1)} and g={(-6, 4), (-5, 3), (-1, 7), (5, 5)}

Q: For the system of differential equations, [23 v(t)= Determine a general solution to the system by…

A:

Q: i) Consider maximising the function f(x, y) = 2x + 3y subject to the simultaneous constraints x…

A: Since you have posted a multiple question according to guidelines I will solve first(i)  question…

Q: Thm The Arigonometric pdynomial of degree k minimbing (y₁ - S, (x₂)) ² is k. Sk(x) = a + Σ (a;…

A: So for the given problem n= 6,k=2So the interval divided into 5 parts so that there are 6 points in…

Q: 1. Determine the Laplace transform. a) L[tsin(2t)]

A:

Q: (e) Using parts (a) and (b), show that the equation tan(3r) = √2r+1 has a unique solution on (0, 1).…

A:

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A:

Q: 6. Use the graph of f(x) given below to sketch a graph of f'(x). f(x)

A:

Q: 3) Find the inverse Laplace t 1 {{}}}}}

A:

Q: Solve the initial value problem 32 *-(11) *. - (1¹) y' = y, y (0) = 2

A:

Q: Which of the following diverge? Σο(-1) 2 n! 2 |||. Σn=1 3n+1 O II and III OI and III III only 1. Σ1…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: a) one of the three men is guilty, the two innocent men are telling the truth, but the statements of…

A: a) If one of the three men is guilty, the two innocent men are telling the truth, but the statements…

Q: Let G be a bipartite Prove that a(G) = graph of order n. if and only if G has a perfect matching.

A: Let G be a bipartite graph of order n. We need to prove that  if and only if G has a perfect…

Q: Let and W = V = X V = R³ y : : Z -2-zy=0} 2x 2x - 3z + 2zy = Is W a subspace of V? Justify your…

A:

Q: Suppose we want to approximate the integral widths. Answer: 10 Write out this sum, using function…

A:

Q: Use MP, MT, DS, and HS to prove that the following arguments are valid. (1) 1. R (10) 1. (ADB) C DVA…

A:

Q: Question 2 Use Green's function to solve the following problem y"+y = 2, y'(0) = 0, y(T) = 0.

A:

Q: 9. Find the area between the cubic xy² = a³ and the lines y = a and x = 0. 10. Find the area bounded…

A:

Q: Consider the following equation and the initial conditions y" + 2 = 24 sin² (2) + 40 cos³ (7), 4…

A:

Q: Problem 7 Let A = be a 2 x 2-matrix such that det(A) = 0. a) Show that there is a non-zero vector u…

A:

Q: Question 1. Find the matrix representation of the linear transformation T(f(t)) f(3t-2) from P₂ to…

A: We have to find the matrix representation of the linear transformation T(f(t)) = f(3t - 2) from P2…

Q: how that there are arbitrarily large gaps in the sequence of primes, i.e., that for any natural…

A: The idea is to use factorials

Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

A:

Q: Consider the following function of two choice variables Z=f(x,y) Write down the first order and the…

A: Given Information:The function is of the two choice of variables.To write:The first order and the…

Q: 02: Consider a system having the following characteristic equation. P(s) = s + s7 + 12s6 +22s5 +39s…

A: To construct the Routh-Hurwitz table from the given characteristic equation, which is:We need to…

Q: Express the limit as a definite integral on the given interval. Assume that the interval [a, b] is…

A:

Q: Use MP, MT, DS, and HS to prove that the following arguments are valid. (1) 1. R 2. SDR/.. ~ S (2)…

A: We solved the problem by using only the eight inference rules.

Q: Problem 1 Find the eigenvalues of the following symmetric matrix, an orthonormal basis for each…

A:

Q: 9*. dx dt = -x - 5y, dy dt · = x+y.

A:

Q: Find the flux of F(x, y, z) = xi+yj - zk outward through the shpere x² + y² + z² = 4. (Hint:…

A:

Q: How would you write this as a product of disjoint cycles?

A: LetWe have to write  as a product of disjoint cycles.

Q: 5. How many nonnegative integer solutions are there to x+y+z+w = 7? Explain your reasoning.

A:

Q: O Solve the following differential equation by finding a series solution: y" - xy' = 0

A: We have to solve the following differential equation by finding a series solution:y" - xy' = 0.

Q: Find the general solution of the given system. 5 -x + 4y 2 (x(t), y(t)) = dx dt dy dt 4 = 3 =-X - 3y

A:

Q: 2. A tank containing 100 gallons of water initially has 10lbs of salt dissolved in it. A solution…

A: Before more salt is added to the tank at time t=0:The volume of brine V(0)=100 gal.The quantity of…

Q: Solve the equation xy" + y = 0, in terms of Bessel's functions. x > 0,

A: Bessel equation is given byIt's solution is given bywhere  is Bessel function of order n.

Q: Is the value x = -12 the last value of the function's domain is 6 ≤ x ≤ 12 Is the function…

A: In given figure of graph of function,[-6,12) is domain of function. x=12 is not included in the…

Q: J. (a) In how many ways can the letter of the word BECOMING be arranged in a row? (b) In how many…

A:

Q: Find the radius of convergence and interval of convergence of the following power series 2 ³3

A:

Q: Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = 0 have nontrivial…

A:

Q: Find eigenvalues and eigenfunctions of the boundary value problem x²y" = xy, y(1) = 0, y(2) = 0.

A: Rewrite the equationx2y″−λy=0 Which is Euler differential equation.Then the corresponding quadratic…

Q: Find two LI solutions of the ODE She x(x - 1)y" + (3x - 1)y' + y = 0

A: We have to solve the differential equation and find two linearly independent solution

Q: Solve an initial value problem y' = 5y + cos(t), y(0) = 0.

A:

Q: dz dt dp dt 2x - x² - xp x2 =p-z²p

A:

Q: How many subsets of {0,1,...,10} have cardinality 1 or more?

A: Let  We have to find the number of subsets of that have cardinality 1 or more.We know thatIf A is…

Q: A 100-gal tank is used to hold 5 lb of salt dissolved in 50 gallons of water. A solution of salt per…

A:

Q: McJester's Burger Hut plans to expand by opening several new restaurants.  The chain operates two…

A: McJester's Burger Hut plans to expand by opening several new restaurants.  The chain operates two…