1. " Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. (a) ² = 4 + 4r²

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

A:

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

A:

Q: The following problem involves an equation of the form -= f(y). dy dt Sketch the graph of f(y)…

A: Given differential equation is dydt=y36−y2,   −∞<y0<∞

Q: A frog is at the bottom of a ten feet well. Each day it crawls 2 feet and loses its grip and slides…

A: See below

Q: Q3: If f is Riemann integrable fuction, then prove the following 1) [f] is Riemann integrable 2) f²…

A: Use the properties and definition of Riemann integral to prove this as in next step.

Q: Solve the following systems of linear equations via matrix algebra: –3x + 2y – z = –1 6x – 6y + 7z…

A:

Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :

Q: 3 By direct partial integration, Solve the following PDES 8- J 8²u axdy 2 = cosx cosy, x4(X₂ #) =X U…

A:

Q: The following problem involves an equation of the form = f(y). dy dt Sketch the graph of f(y) versus…

A:

Q: show that V(x, y) = x 'f (2x+y) is the general Solution of X dv dx 2x dv ду = V

A: Let us consider the partial differential equation Pux+Quy=R Using the Legendre equation solve the…

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: hat is grap

A: First of all, in graph there should be one edge from a typical vertex to another vertex. In brief, a…

Q: By Separation of variables, Solve the follow PDES :- ²4 d²4 dt² =43 2 dx² •o u(e,t) = u(s, t) =6…

A:

Q: 1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then An B = 0 and…

A:

Q: classify the following PDES :- 827 822 -2 +2 =X+3y ахг 82 дуг буду 2 2 X •х Ихх - 2ху Иху +Ў Цуу ох…

A:

Q: 3. Find a vector space basis for the following field field extensions: (a) Q(√2, √2) over Q. I

A:

Q: Obtain frequency response of the following system. Compute inverse Fourier transform of the…

A:

Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

A:

Q: Solve the following differential equations, giving y in terms of x. dy (iii) cotx + 2y = sin 2x. dx

A: Let us consider a differential equation of the form dydx+Py=Q where P and Q are function of x  To…

Q: 3. If $1000 is invested at 10% compounded continuously, the future value S at any time t (in years)…

A:

Q: A fireplace arch must be constructed in the shape of a semi-ellipse. The opening must be 60 cm high…

A:

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

A:

Q: Find the general Solution of the following PDES • 3 Их + 2 Иу SO > u(x,c) = чех (3У-2х)12 ans3-…

A: Given partial differential equations are , (.)    3ux+2uy = 0   ;    u(x,0) = 4e-x (.)…

Q: Please answer with complete solution. The task is to answer the question below: Let A be the…

A: Here given as R→u, v=u, v, u2-v2 Now draw qudrilatral on uv plane, That is v≤u≤3 and 0≤v≤1 Also,…

Q: The product of x++ x³ + 2x² and 2x² + 4x + 6 in z, [x]/is: 4x+1 X^2+2 5x^2+ 5x +1 None O

A:

Q: Given that a>5 and the equation ax -10x+c=0 has real root(s). What is the maximum value of integer…

A:

Q: Find the general Solution of the following PDES ди ди ay 9 2 -5х = 3e + 2e +u ucx;o) = > -5х-3у…

A:

Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π<x<π

A:

Q: Gauss - Jordan Elimination Equations: -3x + 5z -2=0 x + 2y = 1 - 4z -7y=3

A:

Q: B- Solve the differential equation (D² +1) y = x² cos 5x

A:

Q: dy Write down a differential equation of the form dt 13 solutions all approach y = as t → ∞o. 14 y =…

A: To answer the given question we will solve the differential equation dydt=ay+b and find the values…

Q: js(x) dx = (b-a) [ƒ(a) + f(b) -a) [¹ 2

A:

Q: What is the negation of the proposition/statement: 10 > 14 ?   10 < 14   10 ≥ 14   10 ≤ 14   10…

A: Given, proposition/statement is 10 &gt; 14  We have to find negation of the given…

Q: x - 1 5 = y - 2 3 Z - 2 1 2xy +z = 10

A: To find the solution of a system of equation is the values of the unknown for which the system of…

Q: 17. Ancient pyramid The Pyramid of the Moon at Teotihuacán in Mexico has a rectangular base. The…

A:

Q: 10. Write and simplify the integral that gives the arc length of the curve y = x³ +500 for -1 ≤ x ≤…

A: Consider the equation of the curve, y=x3+500 for -1≤x≤2. the arc length is defined by the formula,…

Q: 5 By Separation of variables, Solve the following PDES- ²4 dt² 4 ²4 dx² 0 o 2 u(e,t) = u(s, t) =6…

A:

Q: U (x, g) = x₁ - (100 /g) price of whine is It of buile price of ice rink is 10€ square meters income…

A: let's understand it From step were equation is: ∑i=11000100g2=μ(g) and we know that, μ(g)=10

Q: show that ф (x, y, z) = 8²4 PDE: аф дуг дуг + + даф x². 2 +у2 + Z2 =0 872 satisfies the

A:

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

A:

Q: 7. The coin is tossed twice. Which of the following is the correct representation of the sample…

A: ans 7  (a) {HH, HT,TH,TT} Ans 8 (d)   36 (6 into 6)

Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

A:

Q: 3. Integrate f 10(x+6) x² + 3x-10 2 dx by using partial fraction.

A:

Q: 55² +25-4 (5+₁) (S+₂) (S+ 3) Taking Laplace transform

A: First do partial fraction then find inverse Laplace transform by using standard formulas as in next…

Q: Let S be the unit sphere with outward normal. Consider the surface Problem 4. integral [₂ (z(3² − z²…

A: Using Gauss divergence theorem

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

A: Since

Q: Perform the following math operations to the given Matrices A- 0 2 L-24 B c= [1 2 -2] C= 0-1 O E= 2…

A: Solution :

Q: At 8 a.m., you place a certain amount of bacteria on a slide. Every hour, the area covered by the…

A: This is the problem of Modelling and differential equations.

Q: Find the Laplace transform L (cosht cos²t) @ & L (sinhst cashet) (2 3 L (sin't cos't)

A: Here we use the conversion of hyperbolic function to exponential function. And use some…