Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

Q: Solve the following differential equations of 1-' 4. (2xy²-2y)dx+(3x²y-4x)dy=0 ( 7

A: The solution is given in the next step.

Q: Consider the vector between (-2,-5, -3) and (5, 10,7). 1. The vector is 2. The length of vis 3. If…

A: Consider the vector between (-2,-5, -3) and (5, 10,7).

Q: 3. Find the quotient and the remainder for (x4 + 8x² − 6x − 3 ) ÷ (x+2).

A: 3. A polynomial p(x) can be written as p(x)=q(x)d(x)+r(x)⇒p(x)d(x)=q(x)+r(x)d(x) Where, d(x) is…

Q: Solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is…

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Q: ) identify the technique of integration most appropriate b.) Find the average value

A: Here we have to use the concept of integration

Q: Epa is investing $2500 at 6% per annum, with interest compounded continuously. She wants to come up…

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Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

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Q: Suppose that f(x, y) = x +y on the domain D = {(x, y) | 1 ≤ x ≤ 2, x² ≤ y ≤ 4}. D Then the double…

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Q: Determine which numbers could not be used to represent the probability of an event. Select all that…

A: Here we have to determine which numbers could not be used to represent the probability of an event.…

Q: 2/5 Find the cost function if the marginal cost function is given by C'(x)=x +3 and 32 units cost…

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Q: The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x) = x(40x²…

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 2 + 5x² + 4y², the planes x = 4…

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Q: Determine whether the series sum. 1 12 16 3 4 The series is divergent. n=1 4n-1 is convergent or…

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Q: Convert the following double integral to polar coordinates (do not evaluate). 2 √√4-1² X dxdy = 1+…

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Q: 5. y = log(7x + 3). 4²x¹+8

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Q: Rewrite the following equation with the variables separated: y' = dy cos y = (3x + 5) dx dy = cos y…

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Q: Use the derivative of a function definition to find f ′(a) at the given number a. f(x) = (5x+6)1/2…

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Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: x-1 +1 1-z Q1) Find equation of plane normal to line *-¹ == and pass through line 3 2 1 x=y=2.

A: Concept: The standard form of the line is x-x0a=y-y0b=z-z0c Here a, b c represents the normal…

Q: Which one of the following functions is odd? Oy = 3x² = Oy y = 3x y = x³ Oy=3+x What is the parent…

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Q: Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of…

A: yes

Q: Which of the following integrals is convergent? Select the correct answers. .24 0 of OP 0 2 X dx dx…

A: We have to find which of the following integral is convergent. (a).…

Q: Q2-Solve the differential equation dy = y - xcos² (2 dx x

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Q: 5) The function A(x) = A₂e-0.0077x models the amount in pounds of a particular radioactive material…

A: Both 5 and 6 has been solved as per the request of the student.

Q: The approximate rate of change in the number (in billions) of monthly text messages is given by the…

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Q: This is the graph of the quadratic function rx)=-x²+bx+c 3 (The scale on the x-axis is not…

A: Given graph:-

Q: 1) An ostrich runs along a mountain path with coordinates given by r(t) = ( a) What is the change in…

A: According to the guidelines in case of multipart question, we are only allowed to solve first three…

Q: رد البر A Polynomial of the third degree reculting from the Tyler series of the function fix)=√x+1…

A: The given function is f(x)=sqrt(x+1), x0=1.

Q: Q5: Find the sums of the following (geometric series): 3n-1 1 6n-1 n=1

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Q: determine the instantaneous rate of change for the function f(x)=7^x + 9log(x^x) at x=4

A: This question can be solved using the concept of derivative of a function at a point.

Q: (i) Find f(4). Select the correct choice below, and fill in the answer box if necessary. OA. f(4)=…

A: We have to find the limits.

Q: Solve the following differential equations of 3x d'y dx² +9y=2e³x +18x+18

A: We need to solve D.E.

Q: Determine the Cartesian equation of a plane that passes through a point (2,1,-5) and perpendicular…

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Q: 3x+2 2+9x+1 dx

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Q: 1. Given a. b. C. [(5x + + + + 1) dx Evaluate the indefinite integral above Evaluate the integral…

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Q: 5a) Suppose y = f(g(x)). State the chain rule. That is, what is y' = dy/dx? Now, suppose f(x) =…

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Q: Give the domain and range of the graph shown to the right. Then, use the graph to answer parts (a)…

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Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: Evaluate the integral Select the correct answer. ( x + 6 In ( e* - 1 ) + C ○ 4x-31n (e*-1) + C 6x…

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Q: 1. In x x² dx

A: The given integral is: I=∫16lnxx2dx   So, we can also write as; ∫16lnxx2dx=∫16lnx·1x2dx=∫16lnx·x-2dx…

Q: TC d) x² sinx dx e) ₁x² Inx dx f) so xe dx

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Q: 1 x-3 x2-3x-4 dx

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Q: d²y dx² +6 dy dx +9y = 0

A: The given differential equation is;  d2y/dx2 + 6dy/dx +9y=0

Q: 3) lim(x - 1)-¹ Inx x-1

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Q: A region bounded by f(y) = y, y = 1, y = 8, and x = 0 is shown below. Find the volume of the solid…

A: The region bounded by f(y)=y3, y=1, y=8 and x=0, trhe region revolved about y-axis.

Q: dx √x(x+1)

A: We have to integrate given term.

Q: Solve: 9 d2y/dx²-24 dy/dx +16y=0; y(0)=3, y'(0)=3 Write the letter corresponding to your answer. The…

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Q: Suppose that f(x, y) = y√³+1 on the domain D = {(x, y) | 0 ≤ y ≤ x ≤ 1}. D Then the double integral…

A: We have to find D.

Q: Determine the critical points of f(x) = 8x3+81x2−42x−8.

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Q: 06: b: dw (1) Find if dt w= w = tanx and x = 4t³ + t.

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