(b) Find for what value of the equation 12x²+36xy + y² + 6x + 6y + 3 = 0 represents a pair of straight lines.

Q: Let F(x,y)=√√y-x, then answer the following ( (1) Find the function's domain (2) Find the function's…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A:

Q: Determine whether the following ordinary differential equation cosh (3/y) - In(7y)y" = 11cos(4yx) -…

A:

Q: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

A:

Q: By direct partial integration, Solve the following PDES 8- • Xd²z ахду dz ду + =0 Z(X,0) = X+X =X+X,…

A:

Q: 4.By applying the Convolution Theorem to calculate L-1 is obtained: Determine the value of (a+b): a…

A: We have to find the solution.

Q: Partial Differential Equations Tutorial sheet classify the following PDES :- 227 822 827 ● +2 =x+3y…

A:

Q: The height, h, in centimetres, of a piston moving up and down in an engine cylinder can be modelled…

A: The main objective is to find the minimum height and period of h(t).

Q: 5 By Separation of variables, Solve the following PDES :- ²4 J² ● dt² dx² 0 o u(e,t) = u(s, t) =6…

A:

Q: from t = 7 to t = 9. X || 5 y = 5 ln((t/6)2 – 1) -

A: Given function is x=56t and y=5lnt62−1. We have to find the length of the curve defined by the…

Q: given the linear transformation T: R³ → R² where T (ED) - (₂) T (D-3 (²) and 7(i) = (²). T Find the…

A:

Q: (f) V = {x € R: In converges as noo}, W = R, T(x) = limn → In, I EV; (g) V =R%, W = R, T(x) = -1n,…

A:

Q: Assuming that the ratio of boys to girls is 2:3 in the children in all the years, how many more…

A:

Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable…

A:

Q: 8 {4} {{ {}₁ s² + a² s² +6² (1)

A: We have to find the value of a+b.

Q: g (right) = 9772 +98t + 99, ** <t <910

A:

Q: Solve the boundry-Valued PDE 24 = 4 24 = 484 ठेप ulog) = 86³4 using the genral method -12X-39 ans:…

A:

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a if and only if the…

A:

Q: Q4. A point is moving along a curve that is given as: R(1) = {cos 31 )i + (sin 31) j + (31)k. Find:…

A: Given position vector is R→t = cos3t i +sin3t j +3t k Function fx, y, z =x y z

Q: Does the following series converge or diverge? 4√√n Σ 3/2 10n +7n+7 n=1

A: Solution :-

Q: Let f: Q-Z be an epimorphism. Let A Q- Zb a) Show that f(n)-n for every n e Z.

A:

Q: There is a basis S = (U₁, U₂, U3) where u₁ = (1,1,1), u₂ = (0,1,1), u3 = (0,0,1). Convert these…

A:

Q: Let f: RR be a continuous 27-periodic function whose Fourier series is +∞ 1 1/2 + + /20 cos(nx). n=1…

A:

Q: show that Ф (x, y, z) = аф PDE : агф дуг + дуг I х2 +у2 +Z2 024 072 satisfies the

A:

Q: Given a function f: A→ R and a real number e that is a limit point of A. We say that ilm-f(x) = L…

A:

Q: 1. Find the complex Fourier series for the function f(x) = 2x where ƒ(x+T) = f(x) with T = 1. Graph…

A: We are given that f(x) = 2x, with a period 1.  The Fourier series expansion is defined as follows.

Q: What is the perimeter of region R? Enter the exact answer as an expression involving radicals and T.

A: To determine the perimeter of the given region R.

Q: k ΣΣ8.5 = k=4 j=4 = = n k 2j ΣΣΣn= k=4 j=7 h=6 = || = first step 2nd step 3rd step 4th step final…

A:

Q: Show your solutions to the following using Bisection Method and False Position Method. Write legibly…

A: As per the question we are given the following function : f(x) = 3x + sin x - ex And we have to find…

Q: 3 For which values of a € R the tangent plane to the graph of f(x, y) = 1 + sin(ax + y²) at the…

A: The given graph is                                f(x,y)=1+sin(αx+y2)

Q: Find the general Solution of the following PDES ди -5х ди ду -3x ucx;o) = зе 9 2 +4 , > idx + 2e…

A:

Q: (5 6 By Separation of variables, Solve the following PDES :- ²4 24 . 84² dx² 0 o u(e,t) = u(s, t) =6…

A:

Q: Graph each function over the indicated interval. X Г

A: 1. (a) Given,                    y=5x;     -2, 2

Q: By direct partial integration, Solve the following PDES 8- U (π, y) = 2 cosy 8²u axdy = CBX Cosy…

A: Solution :

Q: EXERCI ES 5.5.1 Find the range of uniform convergence of the Dirichlet series (-1)n-1 (a) (b) } (x)…

A: Please see the attachment  According to the guidelines we are supposed to do one problem.

Q: Let Xis Hilber @ 1| + |1

A:

Q: Determine the values of r for which the differential equation y" - y = 0 has solutions of the form y…

A: Given differential equation is y''-y=0. We have to find r such that y=ert is solution of this…

Q: Which of the following statement is always false? (a) For all integer x, [x] = [−x] (b) For all odd…

A: We have to check which of the given option is always false. a Given that  for all integers x,  x=−x.…

Q: It is known that the equation TL: R³ → R³ W₁ = x - 2y + 2z W₂ = 2x + y + z W3 = x + y a) Determine…

A:

Q: The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the…

A: Since

Q: 21 (AUC)n(BUC) 22 A-B B (((ANB)U(CNB))u(ANC))-((ANB)NC) 23

A: The union of two sets A and B , denoted by A∪B  is the set of all elements which are either in A or…

Q: Does the following series converge or diverge? 4√√n Σ 3/2 10n +7n+7 n=1 O The series diverges. The…

A:

Q: QUESTION 4 Calculate the area between y = 7 - x² and x-axis from x = -1 to x=2 as shown in Figure 1.…

A:

Q: Q3: A) Find the limits below 1) lim (x,y)—(0,0) x² + sin²y 2x2 + + y²

A:

Q: dV = r dz dr de where R: 0< Draw the solid R. z = √√3x² + 3y² and below the Duom solid

A: Using the volume of cylinder and the solid is given as,

Q: Gaussian Elimination Equations: 3X1 - 2x2 + x3 = 4 2x1 - 5x3 = 1 -3x2 + x3 = -1

A:

Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

Q: Find the wronskian of f1=x4, f2=-x4, f3=x2, f4=-x2

A:

Q: Consider the differential equation " - 4y + 5y = f(t). such that y(0)=0 y y'(0)-2. The function f(t)…

A:

Q: F:1: Solve 12(s+10)-140 (s+1)² +400)

A: