Evaluate [(-x+y + 2)dx + (x+y-2)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2, ₁)

Q: Consider the vectors. 6i- j, -8i + 4j (a) Find the dot product of the two vectors. -52 (b) Find the…

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Q: dy = -3, dt If z² = x³ + y², dx dt Please give an exact answer. Provide your answer below: dz = 2,…

A: We can solve as follows

Q: Evaluate (1 + i)(¹ - i). (1

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Q: Let g(x) = | f(t) dt, where f is the function whose graph is shown. y f 4 4 20 (a) Evaluate g(0),…

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Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: Select the conic section represented by the equation. 3x 2 + 2x - 5y + 7 = 0 line hyperbola circle…

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Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

Q: 4. (- FIND the center of mass of the lamina of density p if the lamina is shaped like the region…

A: A detailed solution is given below.

Q: By total differentiation, determine or find the approx. change in the length of the hypotenuse of a…

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Q: +² = x² dx

A: We have to solve the given differential equation

Q: (x, y) is equal [where we set It is known that the area of a polygon with vertices (x1.₁), (x2.2).…

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Q: 5. A line passes thru (3, 4) and cuts a right triangle with the coordinate axes in the second…

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Q: 10 Find the radius of x 2 + y 2 - 10x - 8y + 1 = 0. √41 2√10

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Q: 8) Find the unit tangent and unit normal vectors T(t) and N(t) for r(t) = (t, t², t²).

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Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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Q: 95 Μ: Μα (2) Σ k = (0) Σ 23 . = k=1 115 « Σ 6k +4 = k=1 k=1 95

A: Given problem:-

Q: Give a formula for the nth positive even integer: Here is a theorem: 1+ 2+3 + ... + n п(n+1) n = Use…

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Q: 109. ff(x)=x4 tan x³ -x In (1+x²), then the value of (b) 1 (c) da f(x) dx4 at x = 0, is: (d) 1 15

A: Use the properties of add and even function.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: For what values of x does the series converge conditionally? Σ (-1)^(4x+7)" n=0 OA. x = -2 3 OB. X=…

A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

Q: Evaluate the integral. (x3 – 6x)dx -2

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Q: 7) Find the unit tangent vector T(t) for the curve given by r(t) = 2 sintỉ+ 2 costj + tantk when t =…

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Q: In the triangle below, BA=u and BF=v. Express each of the following in terms of u and v. a) CD b)…

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Q: Find the area of the surface x²-6y-2z=0 that lies above the triangle bounded by the lines x = 4, y =…

A: Surface Area :        Surface Area = ∫∫R 1+zx2+zy2 dA

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

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Q: Find the y- coordinate of the Centroid of the planar region described by x² + y² ≤ 9π², y ≥ 0. Enter…

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Q: Perform the indicated operation if possible. If not possible, enter "DNE": -9 5 5 2 0 5 -2 -5-9 -7 4…

A: We have to perform the given operation.

Q: Problem 2. Do both parts. 12 4 8 Part (a) Find the sum: + ·+· 3 9 27 81 Part (b) Solve the equation…

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Q: Current Attempt in Progress Describe the graph of the equation. 14 sin 9t i + 14 cos 9t j r = It is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine whether the series converges absolutely, converges conditionally, ges. 4n Σ(-1)", n³+1 n=2

A: Use alternating series test for checking the convergence .

Q: A company selling baseball gloves has fixed costs of $1800, and it costs an additional $23.71 to…

A: This question is related to Cost and Revenue function, we will solve it using given information.

Q: A-28. 3. |A| = 3, B = 8, and the angle formed by A and B is 45°. Determine A - 2B

A: We have to solve above question

Q: 7. f(x) = x* - 4x³ +3x? +4x – 5 Domain: y Range: Rel. Maximum(s):. Rel. Minimum(s): End Behavior: As…

A: We have to find the graph, Domain, Range, relative maximum, relative minimum, End behaviour,…

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 6x + 17 between x =…

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Q: For what values of x is the function f(x) = |x2 − 9| differentiable? (Enter your answer using…

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Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: دی lim (4x) X18

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Q: Find the first 6 nonzero terms of the general series solution of the differential equation…

A: We have to find the general solution of the given differential equation.

Q: A 10-ft ladder is leaning against a house on flat ground. The house is to the left of the ladder.…

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Q: =H.w.2 Evaluate the following cartesian integrals by - changing them into equivalent Polar integrals…

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Q: A triangle has sides represented by the vectors (2, 1) and (3, 4). Determine the length of the third…

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Q: roblem 5. A cup of coffee has temperature of 200 degrees Fahrenheit and is placed in a room that has…

A: Topic:- Newton law of cooling

Q: Problem 2. Do both parts. 8 Part (a) Find the sum: 12 4 + +· 3 9 27 81 Part (b) Solve the equation…

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Q: A polynomial P is given. P(x)=x^3+64 A) find all zeros of P, real and complex, B)factor completely

A: Explanation of the answer is as follows

Q: Find the area that the curve encloses and then sketch it. r = 11(1 + cos ?)

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Q: Evaluate the indefinite integral given below. ∫ x(x+7)4 dx

A: Given query is to find the integration.

Q: A radar, using the polar coordinate system, detects that two airplanes are currently located at…

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs…

A: Explained below

Q: Create Representations to Communicate Math find the total surface area of each prism. 1. 2. 6 f 29…

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Q: A 42 cm piece of string whose length is given below is cut into two pieces. One piece is used to…

A: Here we have, A 42 cm piece of string whose length is given below is cut into two pieces. One piece…