Consider the vector field F(x, y, z) = (2ry³z, 3x²y²24, 4x²y³z³). (i) Show that F is a conservative vector field and find o such that F = Vo. (ii) Use this to evaluate F. dr, where 6 consists of the line segment from (1,0,-2) to (1,1,0) followed by the curve given given by r(t) = (e', cos(t), t) for 0 ≤ t ≤ 1.

Q: Question 11 Solve the differential equation. y' + y tan x = cos x A y=x sin x+c sin x (B) y=x cos x…

A:

Q: 2.4 х0.7 ww

A:

Q: The point P(4, -2) lies on the curve y = 2/(3 - x). (a) If Q is the point (x, 2/(3x)), use your…

A:

Q: 1. (a) Show that [(pq) Ag] →p is not a tautology. (b) Make up an example (i.e., particular English…

A: What is Tautology: A tautology is a formula or statement that is true under every conceivable…

Q: Let A = {Ba: a € A} be a family of sets and let G be a nonempty set. Prove Gn an (UB.) - U(GOB₂) =…

A: Given: A=Bα : α∈∆ be a family of sets and let G be a nonempty set. To prove: G∩∪α∈∆Bα=∪α∈∆G∩Bα

Q: Consider the differential equation for the function y, ty = 4y² + ty+ 16t², (a) Transform the…

A:

Q: Determine the domain of the following graph: -12-11-10-9-8-7-6-5-4-3-2 10 732 -8 -10 -11 2 3 4 5 6 7…

A: The way to identify the domain and range of functions is by using graphs. Because the domain refers…

Q: True or False Let A = {1,2} and B = {x,y,z). (2,z) € AxB

A:

Q: ⒸS&* dx + x ² dy + + sin(ty") de 3, Xe с: C: y=x² : 31 R(t) = (t₁, t², t²) t = [0, 1].

A:

Q: In this question, the domain of discourse is a set of students in a library. Define the following…

A: Given that:   B(x): Person x is reading a book   L(x): Person x is listening to music. Express the…

Q: Find the exponential Fourier series for the function f(t) = 2t ..............

A:

Q: The graph of the given function represents a function that is: th 3 2 + -3.5-3-2.5 2-1.5 -10 ++ -2…

A:

Q: -0. Consider the vector field F = (21, 3y, 4z) and the surface z = 4-2² - y², z≥ 0. Write down the…

A: Given : F=2x , 3y , 4z                       ,     z=4-x2-y2      , z≥0    Evaluate line integral…

Q: (1) Find the volume of the solid obtained by revolving about the y-axis the region bounded by y =…

A:

Q: x1 x₁ + 3x25x3 = 4 x₁ + 4x2 - 8x3 = 7 -3x17x2 + 9x3 = -6

A: We have the set of linear equations as x1+3x2-5x3=4x1+4x2-8x3=7-3x1-7x2+9x3=-6

Q: Show complete solution. Straight lines through the fixed point (h, k); h and k not to be eliminated…

A: What is Differential Equation: In mathematics, a differential equation is a relationship between the…

Q: Let E be the region in R³ bounded by the surfaces x² + y² = a², z = 0, and z = h. What does the…

A:

Q: 2

A:

Q: Solve the differential equation dy (y¹ x) PRESE = 1+x. dx Use the initial condition y(1) = 5.…

A: Solution:- solution:-y16xdydx=1+xDivide with xy16dydx=1+xx=1x+1y16dy=1x+1dxIntegrate both…

Q: 8. dy dx || = -X y

A:

Q: Suppose that f: R → R is a function such that f(x+y) = f(x) + f(y) for every x, y E R. Prove that f…

A:

Q: i) -21y² + 4xy + z². k) 424-20³-96x². j) 21²-201-22. 1) z²z+13x+36z.

A:

Q: If​ a, b, and c are digits for which the following​ holds, then a+b+c=​_____.     6 a 2 − 4 9 b   c…

A:

Q: A company's average cost per unit when x units are produced is defined to be Total cost Average cost…

A: Solution:- Average cost =Total Costx=7000x+85+0.5xa Total Cost = x * Average cost = 600…

Q: 2. 8²y at ₂0²y əx² Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Given,       ∂2y∂t2=a2∂2y∂x2.

Q: (a) What is the 2 × 2 matrix P that projects v = x y onto the x axis, i.e. takes x y to x 0 ? Is P…

A:

Q: Consider the following linear program. Max 1A + 2B 10 2A + 2B A, B 2 0 (a) Show the feasible region.…

A:

Q: Find the DE of each of the following by eliminating arbitrary constants. Reduce your final answer in…

A:

Q: x' = 3x,

A: Given Differential equation x'=3x and x(0)=2 Here we need to obtain the Solution for initial value…

Q: I.For each of the following propositions, construct a truth table and state whether the proposition…

A: As per Bartleby rules we have to answer only first three sub parts.

Q: Using Simpson method, find the values of A and B when h=1, Se (Ax² + 1)dx=40, and fi = 20. 3 eB 1

A: Simpson's Rule is given by:         ∫abfxdx≈h3fx0+4fx1+2fx2+4fx3+ . . . . +2fxn-2+4fxn-1+fxn…

Q: а. (1- 15 ) -1 x² b. 3 пx2 C. Зу 4х -8 d. 4(y-5) 3x-6

A:

Q: During the first year, the value of an investment rose by 12%. During the second year, the value of…

A:

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A:

Q: Consider the interval I = [0, 10]. Since the rational numbers in this interval form a countable set,…

A: B

Q: Determine the reactions at A and E if P = 920 N. The reactions are positive if to the right or up,…

A:

Q: The following graph shows the approximate number (in thousands) of people who immigrated to Ireland…

A: The main objective is to find greatest and least average rate of change of l(t) during 2-year…

Q: 3

A:

Q: Solve for A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right…

A:

Q: - Complet X f(x) the following table: 0.0.5. O - J 2.71828 1.75 -5.75460

A: 3a+2.75b+4.0625c=8.47288→(1) Calculate Fitting second degree parabola - Curve fitting using Least…

Q: Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use…

A: Given dydx=x(y-8)2-6 We know that slope of linear equation id the it's derivative So, m=dydx

Q: Give the state space forms of the following equations. Superscripts with parentheses are the orders…

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

Q: A balloon ascending at the rate of 12 ft/sec is at a height 80 ft above the ground when a package is…

A: Sol:-v0=12 ft/secHeight = h = 80 ftThen, y-y0=v0t-12gt2

Q: Find formulas for the coefficients of the Fourier series of the function 50 f(x) = = { -1<x<0 0<x< 1

A: Since you have asked multiple questions, we will solve the Question Q1 (a) for you. If you want any…

Q: Find the function f at z=10 which is analytical in a region R, such that its contour integral…

A:

Q: 1. Determine the span of solution of the system 2w-8x-2y+8z = 0 = 0 -w+3x+2y+8z

A:

Q: The price of an item last year was $1.75. This year, the price of the same item increased by $2.26.…

A: Using the definition of % we can find the solution.

Q: The owner of a skating rink rents the rink for parties at $240 if 20 or fewer skaters attend, so…

A:

Q: A room has a width of 14.1 feet, a length of 15.5 feet, and a ceiling height of 12.0 ft. You plan to…

A: We know that 1 feet = 0.3048 meter. Also 1 sq feet = 0.092903 sq meter.

Q: Translate Vay[(Q(x) → (C(y) ^ H(x, y))] into words.

A: