Question 18 If F is a conservative vector field in R³ and C is a loop (curve whose initial and terminal points are the same), then what must be true about this integral? Sc Fodr O the length of C O negative O positive 00

Q: con 2. 體 + dt +13y = 3sin(2t)

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Q: Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  to find the rate…

Q: Use a triple integral to find the volume of the region bounded by 5x + 6y, z = 7, and the planes x =…

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Q: Solve simultaneously x (t) + x' (t) − y (t) + z' (t) = 4 y' (t) + z(t) = 0 2x(t)+y(t)+z(t)=0 where x…

A: Given the system of differential equations x(t)+x'(t)-y(t)+z'(t) = 4  ......(1) y'(t)+z(t) = 0…

Q: √x + 1 / dx X (Hint: Let x + 1 = u².)

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

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Q: The region D bounded by y=0, x=y - 1, X x = as given in the following figure. YA 3.0+ 2.5- 2.0+ 1.5+…

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Q: Find the solution of the given initial value problem. ty' + 4y = t² − t +7, y(1) = 2, t>0 Y

A: We know that a differential equation of the form y'+P(t)·y=Q(t) has Integrating Factor (I.F.) =…

Q: hand written plz 5. Let D be the region bounded by the lines y = x, x=3 and the curve y = (a) Sketch…

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Q: S 7. Evaluate 8. Evaluate 9. Evaluate (cos x - sin x) dx cot²x dx (sin x + x) dx

A: Given problems:- Solve the following using the theorems on differentiation. 7. ∫ (cos(x) -sin(x) dx…

Q: Consider the following. '6 dt Jo 36 + t² Let t = 6 tan(0) and determine the following.

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Q: 1 x √x²+3 igonometric substitution to find f

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Q: Without using a calculator, compute the sine and cosine of 210° by using the reference angle. What…

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Q: Question 2 Use Euler's method with step length h = 0.5 and determine an approximate value for y(3)…

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Q: X=(1)+ wam (xf pulf Z-x7=(x)₂ + £I-E#

A: Topic = Integration

Q: Find the solution of the given initial value problem. 9 cos t y' y = y(π) = 0, t-9, t> 0 y(t) = =

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Q: 2xy-9x² + (2y + x² + 1) = 0 d.x

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Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

Q: Please

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Q: of 14 that Suppose newly-baked cupcakes are taken out of the oven which is set at 100 degrees. Room…

A: We will use Newton's law of cooling to solve this question.

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: Find f(t). f(t) = = - 3s 1 - s²(s + 1)³

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Q: The region trapped between y = 4x - 2x² and y 4x-2x² - 2x² - ³ is shown below. a) Set up the…

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Q: An airplane takes off from an airport at sea level and its altitude (in feet) at time t (in seconds)…

A: The given equation is: h=3400lnt+1   ...1   As we know that; The Power Law: ddxxn=nxn-1 The Chain…

Q: This triple integral represents the volume of a cylinder. O True O False 2π V = f²f²f² r dz dr de

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Q: Solve (D³ + 3D² + 16D - 20)y=0 when x = 0, y = 1, y = 0, y" = 1

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Q: 3. An open rectangular box w/ square ends to hold 6400 cu ft, is to be built at a cost of Php 75.00…

A: Given: An open rectangular box  square ends to hold 6400 cu ft,Cost for base end = Php.75Cost for…

Q: 3 2x² + 5 can be split into simpler fractions using partial fractions decomposition. Set up the very…

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Q: Let x = [X₁ X2 X3]. Find the matrix A such that the system x' (t) = Ax(t) + f(t) is equivalent to…

A: Here is the solution of the given problem. Differential equation to system of differential equation.

Q: Analyze and sketch:  x- and y-intercepts  Critical Numbers  Table for increase/decrease + local…

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Q: QUESTION 2 Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

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Q: =: Triangle may not be drawn to scale. pose a = 3 and b = 8. an exact value or give at least two…

A: Please refer to the image below

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: 8) If f(x) = x(x-1)^3 , then which of the following statements is correct? A) f(x) has a point of…

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Q: Assume that x and y are both differentiable functions of t and are related by the equation y = cos…

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Q: show that V(x,y) = x 'f (2x+y) is the general Solution of 9 dv X du 2x = V dx 1 ay

A: Given: V(x, y)=xf(2x+y) Find: the general solution of Xdv/dx - 2XdV/dy= V

Q: y = log sin x (csc 4x)

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Q: Find all the critical points of the following functions and classify them as local maximum, local…

A: First we need to find the critical point and then we should apply the conditions to approach it as a…

Q: Use the graph below to fill in each entry of the grid with positive, negative or zero. y = f(x) f''…

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Q: Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following…

A: I have just use the methods and easily find the all solutions. Main solutions are in the boxes.

Q: dx | | dt dy dt dz dt = 3x + 2y + 4z = 2x + 2z = 4x + 2y + 3z

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Q: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

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Q: Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following…

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Q: Find the general Solution of the following PDES Du -5X -3x = 2 +4, исx; c) = 32 + 2e du ду 3e Dx…

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Q: In cylindrical coordinates, the equation below describes what? O a vertical plane O a horizontal…

A: Given :   r=5

Q: convert the following differential equation into a Perfect equation and then Find its general…

A: To find the solution of the given differential equation.

Q: Evaluate the triple integral. [[[_xy sin(yz) dv, G where G is the rectangular box defined by the…

A: The given triple integral is evaluated below.

Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

A: Please refer to the image below

Q: VI. Consider the conservative vector field 1. F(x, y, z) = (z cos(rz) -y sin(ry), 2y cos(ry) - ry²…

A: Solved below.